From Travel Times to Hourly Traffic Flows: An Explainable Machine Learning Framework

From Travel Times to Hourly Traffic Flows: An Explainable Machine Learning Framework | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article From Travel Times to Hourly Traffic Flows: An Explainable Machine Learning Framework Charis Chalkiadakis, Eleni Vlahogianni This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7317470/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 03 Oct, 2025 Read the published version in Data Science for Transportation → Version 1 posted 10 You are reading this latest preprint version Abstract Predicting lane‑based hourly traffic flow urban networks with limited data coverage remains a critical challenge for network and traffic management. This paper develops a data‑driven methodology that leverages publicly available travel time feeds from Google Maps API spatially matched to detector locations, and contextual features including the number of lanes, the capacity per lane, the signalization status, the functional class, the period of day (peak/ off‑peak), and day of week, as well as the emergence of a disturbance and/or extreme weather conditions to predict lane-based hourly traffic flow at locations within the urban transport network of the Athens wider metropolitan area. A variety of supervised learning techniques are trained and models’ interpretability is revealed with a novel approach combining the SHAP summary plot and the permutation importance vs Mean Partial Dependence plot. Results show that Gradient Boosting Decision Tree yields the best performance, demonstrating that even aggregated and crowd-sourced travel times inputs can reliably approximate true flow without dense sensor infrastructures. Feature importance insights identified signalization and longer travel times as features that lead to increased predictions, and additional lanes, counterintuitively, as a feature that leads to lower hourly traffic flow. Out‑of‑sample validation on ten previously unseen locations from the pNEUMA dataset demonstrates the model’s robustness to unseen traffic patterns without retraining. Future work will investigate transfer learning across different cities, as well as the integration of real‑time incident and weather feeds in the model for improved accuracy. Traffic flow prediction Travel times Machine learning Gradient Boosting Decision Trees Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 INTRODUCTION Urban congestion poses persistent and complex challenges for modern transport systems, especially in rapidly growing cities. Accurate and scalable traffic flow prediction plays a pivotal role in modern traffic management systems, influencing signal control optimization, dynamic routing, and congestion mitigation strategies. As urban populations continue to grow and transport systems become more complex, low-cost, real-time, and reliable flow prediction tools are increasingly important (Papageorgiou et al. 2003 ; Vlahogianni et al. 2014 ). Traditional flow prediction relies on fixed‑location sensors (inductive loops, radar, cameras or microwave detectors) that directly count vehicles or infer occupancy. While highly accurate in well-instrumented corridors, these systems are expensive to install and maintain and leave large swaths of urban networks unobserved. The proliferation of GPS‐enabled devices, connected vehicles, and mapping platforms has therefore spurred a rich literature on using travel‐time measurements as a proxy for flow. Probe‐based data are ubiquitous, low‑cost and offer network‐wide coverage, but pose two key challenges: 1) translating a travel‐time sample into an aggregate flow estimate, and 2) doing so without knowing penetration rates or relying on dense calibration sensors. Early efforts focused on network-level research. Geroliminis & Daganzo (Geroliminis and Daganzo 2008 ) aggregated link travel time and detector counts across entire urban regions to empirically derive city‑scale fundamental diagrams, demonstrating that average trip times alone can reveal global flow–density regimes. Building on these macroscopic insights, Herrera and Bayen (Herrera and Bayen 2010 ) pioneered the integration of Lagrangian (probe‑vehicle) travel time measurements with Eulerian (loop detector) data in a recursive filtering framework. They formulated a first‑order macroscopic traffic model in Eulerian coordinates and assimilated sparse GPS-based travel times via an Extended Kalman Filter. Additionally, Neumann et al. (Neumann et al. 2013 ) introduced a Bayesian‑network representation of the fundamental diagram, treating probe‑vehicle travel times (augmented by time‑of‑day and day‑of‑week indicators) as observations to infer link‐level flows with around 90% accuracy. Ren et al. (Ren et al. 2014 ) generalized the Social Sciences radiation model, which considers the population of the origin and destination locations, as well as the population within a circle defined by the distance between them to predict the number of commuters between different locations, with a focus on short-distance moves, by replacing geographic distance with travel time costs, predicting origin–destination commuter flows purely from time‐based betweenness. Saberi et al. (Saberi et al. 2014 ) extended Edie’s definitions (Edie 1961 , 1963 ) to network‐wide 3D trajectories, “inverting” travel‐time patterns to recover both densities and flows. As machine learning techniques matured, regression and data fusion approaches started being further utilized. Meng et al. (Meng et al. 2017 ) combined taxi-based travel times with loop detector counts in a constrained optimization framework, outperforming single‐source methods. Young et al. (Young et al. 2018 ) developed a feed‑forward neural network to learn the residual between this profile and actual volumes, using inputs that include GPS probe counts and trajectories, traffic counts, GPS‐derived speeds, road geometry attributes and weather indicators. Sekuła et al. (Sekuła et al. 2018 ) applied a feed-forward neural network augmented by a traditional volume‐profiling method. The profiling provides a baseline estimate, while the neural network learns residual corrections based on real probe observations. Gu et al. (Gu et al. 2017 ) employed a link‑queue dynamic model that ingests real‑time travel‑time feeds and signal‑timing plans to estimate link flow, density and speed across signalized networks. Pun et al. (Pun et al. 2019 ) demonstrated a multiple‑linear‑regression approach using Google Maps and floating car travel time inputs, achieving high R-squared values on urban corridors. The past five years have seen a surge of hybrid and data‑driven frameworks. Jiang et al. (Jiang et al. 2020 ) embedded observed link travel times into a hybrid LWR–Road‑Sharing model to jointly recover flows and times under dynamic OD demands. Genser et al. (Genser et al. 2021 ) fused thermal camera, video and Google travel time sources in a multiple regression setting to estimate link‑level flow with remarkable accuracy using time inputs alone. Li et al. (Li et al. 2021 ) leveraged Gaussian Process Regression on floating car data, reconstructing flows up to 85% accurate compared to loop detectors. Othman et al. (Othman et al. 2022 ) augmented travel time inputs with static topographic features (slope, curvature, lane count) in a physics‑informed regression, yielding significant gains over detector-only baselines. More recent innovations embrace transfer learning, deep learning and physics‑informed architectures. Mahajan et al. (Mahajan et al. 2023 ) trained neural‑network models to map probe-based speeds (the inverse of travel times) to flows across multiple cities, showing robustness to sparse sensor density. Pan et al. (Pan et al. 2024 ) made use of a Markovian fundamental diagram core with an LSTM to capture temporal dynamics, delivering accurate real‑time flow estimates in complex urban grids. Konstantinidis et al. (Konstantinidis et al. 2024 ) proposed a hybrid approach for arterial traffic volume estimation on the Athens network. They first computed a baseline travel time using the Bureau of Public Roads formula, then trained a single decision tree and a Gradient Boosting Decision Tree (GBDT) model to capture the difference between this baseline estimate and the actual observed volumes. Both models achieved a MAPE of 14.55%, improving on the baseline Bureau of Public Roads formula. Their results highlight that augmenting classical parametric curves with Machine Learning (ML) residuals yield accurate, low‑cost volume estimates on signalized arterials. Finally, Guarda & Qian (Guarda and Qian 2025 ) a data‑driven macroscopic estimator that uses observed travel times and flow-conservation laws to infer both flow and time on unobserved links. Table 1 abstracts these developments, illustrating the evolution from foundational network analyses to sophisticated hybrid models, that leverage the richness of probe‑derived data. Table 1 Relevant literature for traffic flow estimation Ref. Approach Input Output Results (Geroliminis and Daganzo 2008 ) Aggregate link speeds and flows into network bins, fit a polynomial Macroscopic Fundamental Diagram relating density to throughput, analyze flow–density regimes Average trip travel times; aggregated loop‑detector counts Network flow / density Clear flow–density regimes at network level (Herrera and Bayen 2010 ) Formulate Lighthill–Whitham–Richards partial differential equation in state‑space, apply Extended Kalman Filter to fuse sparse GPS‑derived travel times and loop counts GPS travel times; loop‑detector counts; time‑of‑day Link flow / density Estimation error < 15% under low probe penetration (Neumann et al. 2013 ) Construct a Bayesian network over fundamental‑diagram variables, learn conditional probability tables via expectation‑maximization, infer link flows by belief propagation Probe‑vehicle travel times; time‑of‑day; day‑of‑week Link flow ≈ 90% accuracy in link‑level flow estimation (Ren et al. 2014 ) Replace Euclidean distance with travel‑time cost in the radiation model, derive origin–destination flux via closed‑form radiation equations Travel‑time–based costs; O/D population & employment; network topology metrics Origin–destination commuter flows Pearson r ≈ 0.75 between predicted and observed flows (Saberi et al. 2014 ) Extract 3D space‑time vehicle trajectories, compute link flows and densities via Edie’s definitions, fit fundamental‑diagram parameters by nonlinear least squares 3D vehicle trajectory travel times; link distances Link flow / density Successful recovery of fundamental diagram parameters (Meng et al. 2017 ) Formulate a quadratic programming problem minimizing deviation from taxi travel times and loop counts, enforce spatial smoothness via Laplacian regularization Taxi travel times; loop‑detector counts; time‑of‑day Link volume Outperformed single‑source methods in volume recovery (Young et al. 2018 ) Build baseline hourly volumes from automatic traffic recorder profiles, train a multilayer perceptron on residual errors (two hidden layers, ReLU activation, dropout), optimize with Adam GPS probe counts & trajectories; ATR counts; speed from GPS; road geometry; weather Hourly traffic volume R²: 0.61–0.94 (median 0.82); MAPE median 27%; w/o GPS traces → R² 0.73, MAPE 37%; capacity error ≈ 9.5% (Sekuła et al. 2018 ) Generate diurnal volume profiles, use a three‑layer multilayer perceptron to correct profiles based on probe data, apply early stopping to avoid overfitting Vehicle probe data; automatic traffic recorder counts; volume profiles Historical hourly traffic volume 24% more accurate than standard profiling (MAPE ≈ 21% where probe rate is 30–47 veh/hr) (Gu et al. 2017 ) Discretize the link‑queue model of the Lighthill–Whitham–Richards equation using a Godunov scheme, treat real‑time travel‑time measurements as boundary conditions, invert for flow and density Real‑time link travel times; signal timing plans Link flow / density / speed High accuracy across signalized network segments (Pun et al. 2019 ) Perform stepwise multiple linear regression with variance inflation factor checking for multicollinearity, use heteroskedasticity‑robust standard errors, validate by cross‑validation Google Maps travel times; floating‑car travel times; link length Link flow High R² (≈ 0.9) on urban corridor datasets (Jiang et al. 2020 ) Integrate the Lighthill–Whitham–Richards partial differential equation with origin–destination source terms, iteratively fit road‑sharing coefficients to match observed travel times Observed link travel times; dynamic OD demand profiles Link flow Accurate time‑varying flow & travel‑time recovery under disturbances (Genser et al. 2021 ) Stack travel‑time features from multiple sensor types, apply ridge‑penalized multiple linear regression, impute missing data via k‑nearest neighbors, bootstrap confidence intervals Google travel times; thermal‑camera times; video‑derived travel times Link flow High accuracy using travel‑time inputs alone (Li et al. 2021 ) Train Gaussian process regression with automatic relevance determination kernel, optimize hyperparameters by maximizing marginal likelihood, quantify uncertainty from posterior variance Floating‑Car Data travel times; day‑type classification Link flow Up to 85% accuracy vs. loop‑detector counts (Othman et al. 2022 ) Embed physics constraints in a neural network by adding topography‑based residual penalties, train with conservation penalty terms via stochastic gradient descent Floating‑car data travel times; slope; curvature; lane count Link flow Significant error reduction vs. detector‑only baselines (Mahajan et al. 2023 ) Pretrain a neural network on a data‑rich source city, fine‑tune its last layers on target‑city data, apply correlation alignment loss for domain adaptation Probe‑vehicle & public speeds; network metadata Link flow Robust multi‑city estimation under sparse sensors (Pan et al. 2024 ) Couple Macroscopic Fundamental Diagram equations with a long short‑term memory residual module in a sequence‑to‑sequence framework, train with mean squared error plus physics penalty Link travel‑time measurements; historical flow data Link flow MAPE < 10% in complex urban networks (Konstantinidis et al. 2024 ) Compute base travel time using the Bureau of Public Roads formula, learn residual flow errors via GBDT, merge predictions and explain via SHAP values Historical volume; travel time; time‑of‑day; day‑of‑week Arterial volume; travel time For traffic volume prediction, both Decision Trees and GBDT have MAPE of 14.55% (Guarda and Qian 2025 ) Fit link‑level flows under flow‑conservation constraints, solve a constrained least‑squares problem for unobserved links Observed travel‑time measurements; network connectivity Link flow; travel time High correlation (> 0.8) and low error on unobserved links Evidently, a rich variety of methods, spanning from fundamental diagram reconstruction to deep learning and trajectory clustering exists in literature aiming at leveraging travel time as a proxy for flow. However, most of these approaches share common limitations: many depend on high probe penetration, rely on sensor-based calibration, or operate as black-box models with limited interpretability. There remains a clear research gap for models that are theoretically grounded, practically deployable, and require only publicly available travel time data, particularly suited for mid-sized cities with limited traffic sensing infrastructure. The goal of the present research is to produce a novel supervised ML model that accurately predicts lane-based hourly traffic flow, by making use of publicly available data like loop detectors’ data, Google Maps API travel times, and other (static) data related to the infrastructure and the data collection period. We, therefore, propose a simple, transferable methodology supported by real-world deployment and validation. To this end, the present research aims at addressing the following research questions: Can publicly available travel time feeds (e.g., Google Maps) reliably serve as proxies for predicting lane‑based traffic flow in urban areas with sparse sensor coverage? Which combination of contextual network attributes (lane count, signalization, functional class), temporal indicators (peak/ off‑peak, weekend/weekday, disturbances) and travel time inputs yields the most accurate flow predictions? For investigating the above, various supervised ML techniques are trained and their outcome, in terms of statistical significance, is evaluated using as input a multi-variable synthetic dataset spanning from lane-based traffic flow and travel times to topological features of the section like number of lanes and capacity per lane. The remainder of the paper is organized as follows: In Section 2, the methodological approach followed is presented. In Section 3, the results of the supervised ML are presented and further analyzed. Finally, in Section 4, the main findings of this research are presented and discussed, as well as some future research initiatives are established. METHODOLOGICAL APPROACH The present approach relies on the development of generic supervised learning models that predict vehicle flow at any given location on the urban road network using travel time at the same location as a key explanatory variable, along with and other contextual information. The ultimate objective is to construct a robust and interpretable model capable of capturing the underlying patterns in traffic dynamics, thereby enabling accurate prediction of section based hourly traffic flow under varying conditions. Data Sources and Collection Data were collected from selected urban transport network road segments within the urban transport network of the wider Athens metropolitan area for 2023. Two main sources were used: 1) Travel times, and 2) Hourly traffic counts. Concerning travel times, the data have been retrieved from the Google Maps API, using its publicly available traffic service. Travel times data were recorded over multiple weekdays in March, with measurements collected during different time intervals to capture both peak and non-peak traffic patterns, as well as during different conditions in the network (e.g., working days or weekends, disturbance or not disturbance). Travel times were collected in a 15-minute basis and then were aggregated in hourly travel times, matching that way the resolution of the provided traffic counts. To ensure spatial consistency with physical detector data, each travel time query was constructed by setting the origin and destination within a 50-meter radius of the actual detector location. This approach aimed to convert travel time data, which is typically aggregated over segments, into a point-based representation, thereby mimicking the spatial granularity of detectors. Concerning the hourly traffic counts, they are collected from the Greek Government open data repository. The Greek Government open data repository contains, among others, data from the detectors’ network of the urban transport network of the metropolitan area of Athens, Greece. The hourly traffic counts are collected for the same dates, time periods, and locations as the travel times data collection process seen in Figure 1 . In addition to the above, Figure 2 illustrates the hourly traffic counts (up) and travel times (down) timeseries for all selected data collection locations. Except for the above, other data concerning 1) the characteristics of the sections where the detectors’ are placed (number of lanes, capacity per lane, functional class), 2) the type of the node exceeding said section (signalized or not signalized), and 3) other characteristics related to the data collection period (date with a known disturbance or not except for Extreme Weather Events, date with Extreme Weather Events, whether the data collection refers to working day or weekend, whether the data collection period is during peak hour period or not) are included in the final dataset. This combined dataset allowed for direct supervised learning between travel time–derived features and actual vehicle flow at localized detector positions. Lane-based Hourly Traffic Flow Prediction In the present research, predicting lane-based hourly traffic flow is done using the following supervised ML techniques: 1) Linear Regression, 2) Ridge Regression, 3) Lasso Regression, 4) Elastic Net, 5) Random Forest, 6) GBDT, 7) Support Vector Regression – SVR, and 8) XGBoost. These categories of models are very popular in traffic flow analysis and prediction tasks due to their accuracy and ability to handle complex multidimensional datasets (Karlaftis and Vlahogianni 2011). The dataset is split with a 80:20 ratio for train and test set respectively, with stratification ensured. Stratification means that sampling involves dividing a population into homogeneous subgroups (strata) and then sampling from each stratum. Additionally, for each of the techniques, an initial set of hyperparameters is used. To enhance predictive accuracy, two hyperparameter tuning methods were employed: Randomized Search and Grid Search. These methods iteratively tested combinations of key model parameters for each algorithm. Finally, the best model is selected after examining the evaluation metrics associated with it. The evaluation metrics used in the present research are 1) the goodness-of-fit (R-squared value) which measures how well the predictions match the observed data, and 2) the Minimum Absolute Percentage Error (MAPE) which quantifies the relative error. Once the best-performing model is identified, the SHapley Additive exPlanations (SHAP) analysis (Shapley 1953) is used to interpret how each input feature contributed to the final selected supervised ML model predictions. The SHAP diagrams offer an interpretable, model-agnostic method for explaining how much each input variable pushes the predicted value up or down, allowing for visualization of the variable importance in context. In addition to the SHAP analysis, and to have the ability to interpret the interaction among the features of the final selected supervised ML model the unified permutation importance vs Mean Partial Dependence plot is utilized, which quantifies each feature’s unique contribution to predictive accuracy, as well as the average directional effect that varying a feature has on the predictions. By combining SHAP analysis and permutation importance vs Mean Partial Dependence plot we can have a clear perspective on feature relevance and feature importance on the final supervised ML model. RESULTS Lane-based Hourly Traffic Flow Prediction Model Development In the present subsection, the effort of developing a supervised ML model towards predicting lane-based hourly traffic flow is presented. The model predicts the lane-based hourly traffic flow (veh/h/lane) for each of the selected locations in the urban transport network of the wider metropolitan area of Athens, Greece (multiple points prediction) taking as inputs the travel time for crossing the selected locations, the characteristics of the sections where the detectors’ are placed (number of lanes, capacity per lane, functional class), the type of the node exceeding said section (signalized or not signalized), and other characteristics related to the data collection period (date with a known disturbance or not except for Extreme Weather Events, date with Extreme Weather Events, whether the data collection refers to working day or weekend, whether the data collection period is during peak hour period or not). This information is presented in Table 2 . TABLE 2 Variables used as input in the training of the supervised ML models Variable name Description Type of variable Dependent variable traffic_flow Lane-based hourly traffic flow (veh/h/lane) - associated in the developed model with locations of detectors in the network Numeric Independent variables nb_lanes The number of lanes of the section in which hourly traffic flow is predicted Numeric signalized Whether the exceeding node for the selected location is signalized or not (0 if the node is unsignalized; 1 if it is signalized) Categorical travel_time The time needed to cross the selected location (a boundary box of 100 meters is used for this purpose, as previously mentioned) Numeric capacity_per_lane The capacity per lane of the section in which hourly traffic flow is predicted Numeric normal_date Whether any disturbance (not including Extreme Weather Events) took place during the data collection date (0 if it is a normal day; 1 if any disturbance except for Extreme Weather Events took place) Categorical peak Whether the data collection point refers to peak or off-peak hour (0 if the data collection point is out of the peak hours; 1 if it is during peak hour) Categorical bad_weather Whether any Extreme Weather Events (e.g., floods) took place during the data collection date (0 if no Extreme Weather Events took place; 1 if they took) Categorical func_class The functional class of the section in which hourly traffic flow is predicted Categorical is_weekend Whether the data collection date refers to working day or weekend (0 if the data collection took place during working day; 1 if it took place during the weekend) Categorical Due to the multiplex and complementary nature of the independent variables, we performed a preliminary check for multicollinearity. While multicollinearity is often discussed in the context of traditional regression models, it is equally relevant in ML. Many ML algorithms, such as linear regression, logistic regression, and support vector machines, can be adversely affected by multicollinearity. However, some algorithms like Tree-Based Models, Lasso Regression, and Ridge Regression are more robust to multicollinearity. Since multiple models are to be developed and evaluated, multicollinearity is investigated through the correlation matrix and a Variance Inflation Factor (VIF) analysis. The correlation matrix for the independent variables is illustrated in Figure 3 . The correlation matrix revealed no strong linear relationships (i.e., |r| > 0.85) between any feature pairs. The most notable moderate associations include normal_date and bad_weather and capacity_per_lane with func_class. Additionally, VIF provides a measure of multicollinearity among the independent variables in a multiple regression model. The VIF values common threshold is 5; a VIF value greater than 5 is often considered indicative of multicollinearity. In our dataset the highest VIF values is just over 1.8. This confirms the absence of significant multicollinearity, suggesting that each feature contributes unique and non-redundant information to the model. Therefore, all features were retained in the final model to preserve interpretability and predictive capacity. The VIF values are presented in Table 3 . It should be noted that a constant is presented in the VIF values; such a constant is not included in the training of the supervised ML models, but this is the standard practice in regression diagnostics. TABLE 3 VIF values for all independent variables used as input in the training of the supervised ML models Feature Initial set of values const 54.03 travel_time 1.32 peak 1.04 normal_date 1.38 bad_weather 1.47 nb_lanes 1.30 capacity_per_lane 1.87 func_class 1.74 signalized 1.18 is_weekend 1.24 After ensuring that multicollinearity is absent for the independent variables of the dataset, we proceeded with developing a supervised ML model for lane-based hourly traffic flow prediction. As mentioned above, various techniques are used and hyperparameter tuning is achieved in the initial set of parameters. In Table 4 the hyperparameters used per technique are presented. TABLE 4 Hyperparameters used per supervised ML technique Model Hyperparameter Initial set of values Description Linear Regression N/A Ridge Regression alpha Five values logarithmically spaced between 0.01 and 100 Regularization strength; larger values specify stronger regularization max_iter 15 000 Maximum number of iterations Lasso Regression alpha Five values logarithmically spaced between 0.01 and 100 Regularization strength; larger values specify stronger regularization max_iter 15 000 Maximum number of iterations Elastic Net alpha Five values logarithmically spaced between 0.01 and 100 Regularization strength; larger values specify stronger regularization l1_ratio Values from 0.1 to 0.9 The L1 and L2 penalties mixing parameter Random Forest n_estimators Values from 1 to 10 The number of trees in the forest max_depth Depth from 1 through 10, plus 20 The maximum depth of the tree min_samples_split Values from 10 to 20 The minimum number of samples required to split an internal node min_samples_leaf Values from 4 to 10 The minimum number of samples required to be at a leaf node max_features Square root of features, log₂ of features, or all features (None value) The number of features to consider when looking for the best split GBDT n_estimators Values from 1 to 20 The number of boosting stages to be run learning_rate Values from 0.1 to 0.2 with a 0.01 step Shrinks the contribution of each tree by learning rate to prevent overfitting max_depth Depth from 1 through 10, plus 20 The maximum depth of the individual regression estimators min_samples_split Values from 2 to 10 The minimum number of samples required to split an internal node min_samples_leaf Values from 1 to 4 The minimum number of samples required to be at a leaf node subsample Values from 0.6 to 1 The fraction of samples used for fitting the individual base learners SVR C Values from 1 to 10 with a 0.1 step Regularization parameter; the strength of the regularization is inversely proportional to C kernel Linear, radial‑basis function, or polynomial Specifies the kernel type to be used in the algorithm (linear, rbf, poly) gamma Scale or auto Kernel coefficient XGBoost n_estimators Values from 1 to 20 Sets the number of boosting rounds (i.e., the total trees in the ensemble) learning_rate Values from 0.01 to 0.1 Shrinks the contribution of each tree by learning rate to prevent overfitting After examining each of the developed models and evaluating their goodness-of-fit, with the application of Grid and Randomized Search, the finally selected model is a GBDT model with Grid Search for hyperparameter tuning. The tuned hyperparameters and the evaluation metrics (R-squared value and MAPE) for all developed best-performing supervised ML models are presented in Table 5 . TABLE 5 R-squared and MAPE values for both Grid and Randomized Search for all developed supervised ML models Model Hyperparameter Tuned value R-squared MAPE Linear Regression N/A 0.61 31.31% Ridge Regression alpha 10 0.61 31.51% max_iter 15000 Lasso Regression alpha 1 0.61 31.47% max_iter 15000 Elastic Net alpha 0.1 0.61 31.47% l1_ratio 0.9 Random Forest n_estimators 10 0.84 15.40% max_depth 20 min_samples_split 10 min_samples_leaf 4 max_features None GBDT n_estimators 20 0.85 15.41% learning_rate 0.2 max_depth 5 min_samples_split 10 min_samples_leaf 4 subsample 1.0 SVR C 10 0.60 32.32% kernel linear gamma scale XGBoost n_estimators 20 0.83 18.60% learning_rate 0.1 The finally selected supervised ML model is the GBDT with Randomized Search. Concerning the goodness-of-fit of the selected GBDT model, the R-squared value is equal to 0.85 and MAPE is equal to 15.41%. Those values are considered good. Firstly, the R-squared value indicates a good fitness on the outcome of the dependent variable (lane-based hourly traffic flow (veh/h/lane)); an R-squared value of 0.85 indicates that approximately 85% of the variance in observed traffic volumes is explained by the model, which reflects good explanatory power, especially given the inherent noise and variability in travel time data. Then, a MAPE value of 15.41% reveals that the GBDT model has a good accuracy. Such a MAPE value is in line with the results of previous research like (Young et al. 2018; Sekuła et al. 2018; Konstantinidis et al. 2024; Pan et al. 2024). Our proposed model outperforms simpler profile‑based and pure regression baselines (21–27% MAPE). It is slightly less accurate than (Konstantinidis et al. 2024), which however was trained and evaluated on just one arterial corridor with only two detector locations, which constrains its scalability and limits its applicability across more extensive urban networks. Finally, our GBDT model trails the most sophisticated hybrid deep‑learning frameworks (Pan et al. 2024) (MAPE below 10%); however developing and deploying such a model requires extensive sequence‑to‑sequence training on large historical datasets and careful tuning of both physics‑based and neural components. That way implementation complexity is increased, more computational power is needed, and it leads to reduced model transparency compared to our more straightforward, tree‑based solution. Concerning feature importance, at first the SHAP values were leveraged. SHAP values are a way to explain the output of any ML model. SHAP values use a game theoretic approach that measures the influence of each feature (predictor) to the final outcome (Shapley 1953). Figure 4 below depicts the SHAP values of the features. The color gradient from blue (low value of feature) to red (high value of feature) reveals how the feature’s actual value contributes to each prediction. For the input variables, the SHAP summary plot of Figure 4 displays each feature’s distribution of impacts on the model’s predicted traffic flow in magnitude (horizontal axis) and direction (positive vs. negative). The SHAP summary plot makes it clear that number of lanes and travel time are the most impactful features, as they exhibit the widest spread of SHAP values. The number of lanes exerts a strong, but mixed influence. Fewer lanes (blue points in the “nb_lanes” row) often lead to higher predicted hourly traffic flows, perhaps because traffic stays more uniform. On the other hand, higher number of lanes (red points) yield negative SHAP contributions, suggesting the existence of bottlenecks or spillback. Additionally, shorter travel times (blue points in the “travel_time” row) mostly lead to reduced predicted hourly traffic flow, reflecting conditions of low congestion. In contrast, longer travel times (red points) mostly lead to increased hourly traffic flow predictions, since that mean that congestion is increased and, therefore, more vehicles are on the road. Then, three categorical features are of importance (is_weekend, normal_date, and peak), however they do not have such high influence in the predicted hourly traffic flow. For is_weekend and normal_date, the illustrated results are obvious and expected. Concerning peak, it appears that the results are mixed since peak and off- peak hours do not clearly lead to increased or decreased hourly traffic flow predictions. This can be sourced in the high congestion levels that might appear during peak hours. Afterwards, capacity per lane shows a clear monotonic effect; high‑capacity links (red) lead to higher estimated hourly traffic flows, while lower capacities (blue) mean less hourly traffic flow. Func_class comes after with results mostly in line with those for nb_lanes, higher functional classes lead to slightly reduced hourly traffic flow predictions, medium functional classes lead to higher hourly traffic flow predictions, and lower functional classes lead to lower prediction values. Finally, two binary categorical features appear: signalized and bad_weather. Sites that are signalized (red points in the “signalized” row) lead to lower hourly traffic flow predictions, opposed to the unsignalized locations (blue points) which have no significant impact on the predictions. This is in line with the func_class results; mostly higher functional class sections have upstream signalized intersections. For bad_weather, only the existence of an Extreme Weather event even so slightly leads to mostly higher predicted hourly traffic flow. The SHAP point of view presented before is useful to interpret the feature importance of the final GDBT model developed in the present research. However, it does not offer any interpretation concerning the interaction among the features of the GBDT model. Thus, to get a better insight into the factors that influence the estimation of the lane-based hourly traffic flow, we investigate the permutation importance vs Mean Partial Dependence plot. Said plot was first introduced in (Vlahogianni et al. 2012) and later used in various research like (Fafoutellis et al. 2022). The Permutation Importance versus Mean Partial Dependence plot combines two complementary measures of feature relevance. On the horizontal axis, permutation importance quantifies how much model performance deteriorates when each feature’s values are randomly shuffled, thus indicating its unique contribution to predictive accuracy. On the vertical axis, Mean Partial Dependence captures the average directional effect that varying a feature across its range has on the predicted traffic flow, offering a direct interpretation of its marginal influence. The Permutation Importance versus Mean Partial Dependence plot is illustrated in Figure 5 . From Figure 5 , a clear three‑way separation emerges. At the bottom left, number of lanes stands alone: each additional lane reduces the predicted hourly traffic flow by roughly 200 veh/h, and shuffling this feature modestly degrades overall accuracy. Number of lanes, therefore, are a predictor of importance for our model. Above it, near the center, sit travel_time, capacity_per_lane, and normal_date. Travel time drives the largest average increase in flow (around +70 veh/h/lane) yet carries almost zero permutation importance. That means that the model can infer congestion effects through other correlated inputs if travel time values are randomized. Likewise, capacity_per_lane and normal_date each add roughly +25 veh/h/lane and +15 veh/h/lane to predictions on average, yet their low permutation importance shows that randomizing these values has little effect on accuracy, implying the model relies on other correlated features to capture the same information. On the right side, the peak period and weekend indicators each change the predicted flow by only a few vehicles per hour (peak near zero and is_weekend about –10 veh/h/lane), but shuffling them still slightly reduces accuracy, showing they provide some unique information. Finally, signalization status, adverse weather, and functional class have almost zero average effect and zero permutation importance, meaning that randomizing these features neither shifts predictions nor harms accuracy, so they only tweak the model under very specific conditions. A comparison between the SHAP summary plot ( Figure 4 ) and the permutation importance vs Mean Partial Dependence plot ( Figure 5 ) provides an opportunity to examine feature importance under two different perspectives, which lead to a consistent overall picture. SHAP summary plot reveal how individual predictions respond to feature values, showing that travel time and lane count have major impact in individual predictions, while signalization values cluster near zero, indicating almost no local effect. The permutation importance vs Mean Partial Dependence plot confirms that lane count is the feature the model relies on most, and that travel time consistently increases hourly traffic flow predictions even though it can be permuted without a large drop in accuracy. Signalization, peak period, weekend, weather, and functional class all have low importance and small mean effects, showing they only tweak the results in specific cases. Out-of-Sample Validation For out‑of‑sample validation, we applied the finalized GBDT model to the pNEUMA dataset (Barmpounakis and Geroliminis 2020). The pNEUMA dataset is a large-scale open dataset of urban vehicle trajectories collected using a drone swarm in Athens, Greece during 2018. All drones’ data for a selected date (11/01/2018) and for morning peak hour (08:00-09:00) have been downloaded and further analyzed. Additionally, ten (10) locations in central arterials of the Athens city center have been selected for evaluating the developed GBDT model ( Figure 6 ). Said locations were not included in the dataset used during the development of the GBDT model. Concerning data, the ground truth lane-based hourly traffic flow (veh/h/lane) is the total number of trajectories crossing the selected locations derived by the number of lanes. Since some of the locations are close to intersections, it is worth noting that a heading control is also applied. For travel time, and for the trajectories used in the previous step, we extracted the time difference for trajectories’ data points upstream and downstream of the selected locations. All other data needed were manually imported in the dataset. Applying the finalized GBDT model to the pNEUMA dataset yielded a MAPE of 15.97%, performance similar to the validation performed during the development of the model. To assess whether our prediction errors satisfy the key assumptions of classical regression, we further statistically analyzed the goodness-of-fit of the out-of-sample GBDT model validation by applying the following statistical tests: paired t-test, Shapiro-Wilk test, Breusch-Pagan test, Durbin-Watson test, and Bonferroni outlier test. First we applied a paired t‑test, which evaluates whether the mean difference between observed and predicted flows is zero, thus ensuring the absence of systematic bias. Paired t-test is applied since we dealing with matched pairs of data. With p = 0.83 we fail to reject the null hypothesis, indicating unbiased predictions. Next, the Shapiro-Wilk test (p = 0.64) and Breusch-Pagan test (p = 0.17) verify that the residuals are approximately normally distributed and no heteroscedasticity exists, respectively. A Bonferroni-adjusted outlier analysis on externally studentized residuals found no significant extreme values, demonstrating that no single observation unduly influences the model. The only statistical test for which the desired results were not achieved is the Durbin-Watson test. With a value of the test statistic (d) equal to 1.14 (d<2), the test indicates positive autocorrelation in the residuals. That means that the errors from one observation are related to the errors from other observations. This finding of positive autocorrelation is a direct consequence of the spatiotemporal dynamics inherent to traffic flow conditions. As traffic flow conditions like queue formation or shockwaves propagate through the network, the error in the predicted hourly traffic flow at one location is likely to be correlated with the error at a downstream location and in subsequent time periods. This indicates that the observed autocorrelation is not a deficiency of the GBDT model, but rather a characteristic of the data. Such out‑of‑sample performance suggests that the trained model can be used as an “off the shelf” solution for estimating lane CONCLUSIONS The present research addresses two (2) main research questions : 1) whether publicly available travel time feeds (such as Google Maps) can serve as reliable proxies for lane‑based traffic flow in sensor‑sparse urban corridors, and 2) which mix of network attributes (lane count, signalization, functional class), temporal indicators (peak/off‑peak, weekend/weekday, disturbance flags) and travel time inputs produces the most accurate estimates. To investigate these, we assembled and spatially matched hourly loop detector traffic counts in the urban transport network of the wider metropolitan area of Athens, Greece with Google Maps travel time data and enriched them with contextual features, then trained, tuned and compared eight (8) supervised ML models. By doing that, we concluded to a GBDT model as the top performer. Interpretability analyses via the SHAP summary plot and the permutation importance vs Mean Partial Dependence plot converged on consistent insights. Number of lanes and travel times emerge as the most influential features. Sections with lower number of lanes lead to higher hourly traffic flow predictions. This counterintuitive and it is likely due to downstream spillback. Additionally, higher travel times correspond to higher predictions for hourly traffic flow. Other categorical features (peak period, weekend, disturbance days) exert smaller yet meaningful effects. The modest but meaningful effects of said features further reveal the model’s sensitivity to both routine and disruptive conditions, equipping planners with the ability to anticipate performance under varied scenarios. To further investigate our model’s prediction capabilities, we performed an out‑of‑sample validation on ten (10) locations making use of the pNEUMA dataset. The results prove the predictive of our model, even in data from different year and in locations for which no training took place during the development of the GBDT model. As future work, transfer learning approaches should be explored, to adapt the GBDT model across cities for further testing and evaluation. Such an application requires only publicly available data (travel times) and data related to the infrastructure (e.g., number of lanes, signalization, etc.), making this approach a cost‑effective complement to fixed sensors. Additionally, we could explore the extension of the capabilities of the models by incorporating real‑time incident and weather feeds. Such extensions will further reduce error margins, enhance spatial generalization and enable self‑optimizing Traffic Management solutions, even in areas or cities where detectors’ networks are either sparce or absent. Finally, we think that our model can be used as an integral tool for Traffic Management Centers, both allowing for a better understanding of the operational performance of the network and giving the opportunity to properly select the necessary Traffic Management Strategies to mitigate the impacts of any incident. Declarations ACKNOWLEDGMENTS No AI or LLMs were used in drafting the present research paper. AUTHOR CONTRIBUTIONS The authors confirm contribution to the paper as follows: study conception, design, implementation, analysis, interpretation of results, and draft manuscript preparation: C. Chalkiadakis, E.I. Vlahogianni. All authors reviewed the results and approved the final version of the manuscript. DECLARATION OF CONFLICTING INTERESTS The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. FUNDING This work is part of the project ACUMEN which has received funding from the European Union’s Horizon Europe RIA programme under GA No 101103808. References Barmpounakis E, Geroliminis N (2020) On the new era of urban traffic monitoring with massive drone data: The pNEUMA large-scale field experiment. Transportation Research Part C: Emerging Technologies 111:50–71. https://doi.org/10.1016/j.trc.2019.11.023 Edie LC (1963) Discussion of Traffic Stream Measurements and Definitions. Port of New York Authority Edie LC (1961) Car-Following and Steady-State Theory for Noncongested Traffic. Operations Research 9:66–76. https://doi.org/10.1287/opre.9.1.66 Fafoutellis P, Mantouka EG, Vlahogianni EI (2022) Acceptance of a Pay-How-You-Drive pricing scheme for city traffic: The case of Athens. Transportation Research Part A: Policy and Practice 156:270–284. https://doi.org/10.1016/j.tra.2022.01.009 Genser A, Hautle N, Makridis M, Kouvelas A (2021) An Experimental Urban Case Study with Various Data Sources and a Model for Traffic Estimation. Sensors 22:144. https://doi.org/10.3390/s22010144 Geroliminis N, Daganzo CF (2008) Existence of urban-scale macroscopic fundamental diagrams: Some experimental findings. Transportation Research Part B: Methodological 42:759–770. https://doi.org/10.1016/j.trb.2008.02.002 Gu Y, Qian Z (Sean), Zhang G (2017) Traffic State Estimation for Urban Road Networks Using a Link Queue Model. 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Transportation Research Part C: Emerging Technologies 19:387–399. https://doi.org/10.1016/j.trc.2010.10.004 Konstantinidis C, Chalkiadakis C, Fafoutellis P, Vlahogianni EI (2024) Urban Arterial Traffic Volume and Travel Time Estimation with Use of Data Driven Models. IFAC-PapersOnLine 58:102–107. https://doi.org/10.1016/j.ifacol.2024.07.325 Li J, Boonaert J, Doniec A, Lozenguez G (2021) Multi-models machine learning methods for traffic flow estimation from Floating Car Data. Transportation Research Part C: Emerging Technologies 132:103389. https://doi.org/10.1016/j.trc.2021.103389 Mahajan V, Cantelmo G, Rothfeld R, Antoniou C (2023) Predicting network flows from speeds using open data and transfer learning. IET Intelligent Trans Sys 17:804–824. https://doi.org/10.1049/itr2.12305 Meng C, Yi X, Su L, et al (2017) City-wide Traffic Volume Inference with Loop Detector Data and Taxi Trajectories. In: Proceedings of the 25th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems. ACM, Redondo Beach CA USA, pp 1–10 Neumann T, Bohnke PL, Touko Tcheumadjeu LC (2013) Dynamic representation of the fundamental diagram via Bayesian networks for estimating traffic flows from probe vehicle data. In: 16th International IEEE Conference on Intelligent Transportation Systems (ITSC 2013). IEEE, The Hague, Netherlands, pp 1870–1875 Othman B, De Nunzio G, Laraki M, Sabiron G (2022) A Novel Approach To Traffic Flow Estimation based on Floating Car Data and Road Topography: Experimental Validation in Lyon, France. In: 2022 IEEE 25th International Conference on Intelligent Transportation Systems (ITSC). IEEE, Macau, China, pp 2571–2576 Pan YA, Guo J, Chen Y, et al (2024) A fundamental diagram based hybrid framework for traffic flow estimation and prediction by combining a Markovian model with deep learning. Expert Systems with Applications 238:122219. https://doi.org/10.1016/j.eswa.2023.122219 Papageorgiou M, Kiakaki C, Dinopoulou V, et al (2003) Review of road traffic control strategies. Proc IEEE 91:2043–2067. https://doi.org/10.1109/jproc.2003.819610 Pun L, Zhao P, Liu X (2019) A Multiple Regression Approach for Traffic Flow Estimation. IEEE Access 7:35998–36009. https://doi.org/10.1109/access.2019.2904645 Ren Y, Ercsey-Ravasz M, Wang P, et al (2014) Predicting commuter flows in spatial networks using a radiation model based on temporal ranges. Nat Commun 5:. https://doi.org/10.1038/ncomms6347 Saberi M, Mahmassani HS, Hou T, Zockaie A (2014) Estimating Network Fundamental Diagram Using Three-Dimensional Vehicle Trajectories: Extending Edie’s Definitions of Traffic Flow Variables to Networks. Transportation Research Record: Journal of the Transportation Research Board 2422:12–20. https://doi.org/10.3141/2422-02 Sekuła P, Marković N, Vander Laan Z, Sadabadi KF (2018) Estimating historical hourly traffic volumes via machine learning and vehicle probe data: A Maryland case study. Transportation Research Part C: Emerging Technologies 97:147–158. https://doi.org/10.1016/j.trc.2018.10.012 Shapley LS (1953) A Value for n-Person Games. In: Kuhn HW, Tucker AW (eds) Contributions to the Theory of Games, Volume II. Princeton University Press, Princeton, pp 307–318 Vlahogianni EI, Karlaftis MG, Golias JC (2014) Short-term traffic forecasting: Where we are and where we’re going. Transportation Research Part C: Emerging Technologies 43:3–19. https://doi.org/10.1016/j.trc.2014.01.005 Vlahogianni EI, Karlaftis MG, Orfanou FP (2012) Modeling the Effects of Weather and Traffic on the Risk of Secondary Incidents. Journal of Intelligent Transportation Systems 16:109–117. https://doi.org/10.1080/15472450.2012.688384 Young SE, Hou Y, Sadabadi K, et al (2018) Estimating Highway Volumes Using Vehicle Probe Data - Proof of Concept: Preprint. National Renewable Energy Laboratory Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7317470","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":499619784,"identity":"ecd96eb5-ce3b-4009-8fcf-d6ed1d8ef225","order_by":0,"name":"Charis Chalkiadakis","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA90lEQVRIiWNgGAWjYJCCA0AsI8HewMCQUECCFh4JHiCVYABkEWsTj4REApAiRovB8bMPD/5ss+ORnPk68cMDA4Y8e4nkB4xf9+DWItmTbnCY50wyj7R07mYJoMOKeSTSDJhlnuHWws+QxnCYoYKZR046dwNIS2IPkGSWOIBbCxv/M4aDPwzqeeQkz27+AdGS/gGvFn6JNIYDPBWHeaQleLdBbckxYPyAR4vkjGcMQL8c55Hsyd1mkWAgkdhz5k3BYQY8WgzOpzF//NlWLSdx/Ozmmz8qbBLb29M3PvyBRws6kACTh4mOTzhg/EGyllEwCkbBKBjGAADQJE0J+yzcBAAAAABJRU5ErkJggg==","orcid":"","institution":"National Technical University of Athens","correspondingAuthor":true,"prefix":"","firstName":"Charis","middleName":"","lastName":"Chalkiadakis","suffix":""},{"id":499619786,"identity":"8d5e7b44-b29f-44fa-9589-90e9aa9c9a7f","order_by":1,"name":"Eleni Vlahogianni","email":"","orcid":"","institution":"National Technical University of Athens","correspondingAuthor":false,"prefix":"","firstName":"Eleni","middleName":"","lastName":"Vlahogianni","suffix":""}],"badges":[],"createdAt":"2025-08-07 10:08:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7317470/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7317470/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s42421-025-00133-5","type":"published","date":"2025-10-03T15:56:55+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":89073879,"identity":"3adb8746-ebdf-460c-88f2-1f9f76c849df","added_by":"auto","created_at":"2025-08-14 11:43:31","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1412271,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDetectors network (in green) and travel times data collection locations (in red) on the urban transport network of the wider metropolitan area of Athens, Greece\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7317470/v1/cebb06ebf6fe33f6303ac33b.jpeg"},{"id":89073881,"identity":"25ee3ac1-ab1a-44c6-8570-e96e14cd6bc9","added_by":"auto","created_at":"2025-08-14 11:43:31","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1656331,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eHourly traffic counts (up) and travel times (down) timeseries for all selected data collection locations\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7317470/v1/0a5a0b4e6f37a8f6ef7c4cc7.jpeg"},{"id":89073880,"identity":"fc5c4578-1770-4618-beb1-7a117f4706a2","added_by":"auto","created_at":"2025-08-14 11:43:31","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":424746,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCorrelation matrix of all independent variables used as input in the training of the supervised ML models\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7317470/v1/24b1b4c769654e03d0fa053b.jpeg"},{"id":89073887,"identity":"c0d6217c-29ca-4e3e-93a4-efd640992f82","added_by":"auto","created_at":"2025-08-14 11:43:31","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":239302,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSHAP summary plot for all independent variables included in the final GBDT model\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7317470/v1/5fa138b8834cbd276efa625d.jpeg"},{"id":89075047,"identity":"6bf051eb-06c4-4cd9-b485-90f1b99bc52b","added_by":"auto","created_at":"2025-08-14 11:59:31","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":167978,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePermutation Importance vs. Mean Partial Dependence Plot\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7317470/v1/0157cffab3ab2dfde9bfa8be.jpeg"},{"id":89075048,"identity":"bea8b61d-9e0d-4281-8e96-e134777e7dad","added_by":"auto","created_at":"2025-08-14 11:59:31","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":1312587,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSelected locations, from the pNEUMA dataset, to evaluate the developed GBDT model\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7317470/v1/700ff4a505b6f78898efc1e8.jpeg"},{"id":92883611,"identity":"cfc68799-fc74-4e16-841b-8e75211720d2","added_by":"auto","created_at":"2025-10-06 16:05:14","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6422190,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7317470/v1/34aa8fd4-f3b9-4303-aad2-8708b8b34219.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"From Travel Times to Hourly Traffic Flows: An Explainable Machine Learning Framework","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eUrban congestion poses persistent and complex challenges for modern transport systems, especially in rapidly growing cities. Accurate and scalable traffic flow prediction plays a pivotal role in modern traffic management systems, influencing signal control optimization, dynamic routing, and congestion mitigation strategies. As urban populations continue to grow and transport systems become more complex, low-cost, real-time, and reliable flow prediction tools are increasingly important (Papageorgiou et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2003\u003c/span\u003e; Vlahogianni et al. \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eTraditional flow prediction relies on fixed‑location sensors (inductive loops, radar, cameras or microwave detectors) that directly count vehicles or infer occupancy. While highly accurate in well-instrumented corridors, these systems are expensive to install and maintain and leave large swaths of urban networks unobserved. The proliferation of GPS‐enabled devices, connected vehicles, and mapping platforms has therefore spurred a rich literature on using travel‐time measurements as a proxy for flow. Probe‐based data are ubiquitous, low‑cost and offer network‐wide coverage, but pose two key challenges: 1) translating a travel‐time sample into an aggregate flow estimate, and 2) doing so without knowing penetration rates or relying on dense calibration sensors.\u003c/p\u003e\u003cp\u003eEarly efforts focused on network-level research. Geroliminis \u0026amp; Daganzo (Geroliminis and Daganzo \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) aggregated link travel time and detector counts across entire urban regions to empirically derive city‑scale fundamental diagrams, demonstrating that average trip times alone can reveal global flow\u0026ndash;density regimes.\u003c/p\u003e\u003cp\u003eBuilding on these macroscopic insights, Herrera and Bayen (Herrera and Bayen \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) pioneered the integration of Lagrangian (probe‑vehicle) travel time measurements with Eulerian (loop detector) data in a recursive filtering framework. They formulated a first‑order macroscopic traffic model in Eulerian coordinates and assimilated sparse GPS-based travel times via an Extended Kalman Filter. Additionally, Neumann et al. (Neumann et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) introduced a Bayesian‑network representation of the fundamental diagram, treating probe‑vehicle travel times (augmented by time‑of‑day and day‑of‑week indicators) as observations to infer link‐level flows with around 90% accuracy. Ren et al. (Ren et al. \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) generalized the Social Sciences radiation model, which considers the population of the origin and destination locations, as well as the population within a circle defined by the distance between them to predict the number of commuters between different locations, with a focus on short-distance moves, by replacing geographic distance with travel time costs, predicting origin\u0026ndash;destination commuter flows purely from time‐based betweenness. Saberi et al. (Saberi et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) extended Edie\u0026rsquo;s definitions (Edie \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e1961\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1963\u003c/span\u003e) to network‐wide 3D trajectories, \u0026ldquo;inverting\u0026rdquo; travel‐time patterns to recover both densities and flows.\u003c/p\u003e\u003cp\u003eAs machine learning techniques matured, regression and data fusion approaches started being further utilized. Meng et al. (Meng et al. \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) combined taxi-based travel times with loop detector counts in a constrained optimization framework, outperforming single‐source methods. Young et al. (Young et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) developed a feed‑forward neural network to learn the residual between this profile and actual volumes, using inputs that include GPS probe counts and trajectories, traffic counts, GPS‐derived speeds, road geometry attributes and weather indicators.\u003c/p\u003e\u003cp\u003eSekuła et al. (Sekuła et al. \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) applied a feed-forward neural network augmented by a traditional volume‐profiling method. The profiling provides a baseline estimate, while the neural network learns residual corrections based on real probe observations. Gu et al. (Gu et al. \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) employed a link‑queue dynamic model that ingests real‑time travel‑time feeds and signal‑timing plans to estimate link flow, density and speed across signalized networks. Pun et al. (Pun et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) demonstrated a multiple‑linear‑regression approach using Google Maps and floating car travel time inputs, achieving high R-squared values on urban corridors.\u003c/p\u003e\u003cp\u003eThe past five years have seen a surge of hybrid and data‑driven frameworks. Jiang et al. (Jiang et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) embedded observed link travel times into a hybrid LWR\u0026ndash;Road‑Sharing model to jointly recover flows and times under dynamic OD demands. Genser et al. (Genser et al. \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) fused thermal camera, video and Google travel time sources in a multiple regression setting to estimate link‑level flow with remarkable accuracy using time inputs alone. Li et al. (Li et al. \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) leveraged Gaussian Process Regression on floating car data, reconstructing flows up to 85% accurate compared to loop detectors. Othman et al. (Othman et al. \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) augmented travel time inputs with static topographic features (slope, curvature, lane count) in a physics‑informed regression, yielding significant gains over detector-only baselines.\u003c/p\u003e\u003cp\u003eMore recent innovations embrace transfer learning, deep learning and physics‑informed architectures. Mahajan et al. (Mahajan et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) trained neural‑network models to map probe-based speeds (the inverse of travel times) to flows across multiple cities, showing robustness to sparse sensor density. Pan et al. (Pan et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) made use of a Markovian fundamental diagram core with an LSTM to capture temporal dynamics, delivering accurate real‑time flow estimates in complex urban grids.\u003c/p\u003e\u003cp\u003eKonstantinidis et al. (Konstantinidis et al. \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) proposed a hybrid approach for arterial traffic volume estimation on the Athens network. They first computed a baseline travel time using the Bureau of Public Roads formula, then trained a single decision tree and a Gradient Boosting Decision Tree (GBDT) model to capture the difference between this baseline estimate and the actual observed volumes. Both models achieved a MAPE of 14.55%, improving on the baseline Bureau of Public Roads formula. Their results highlight that augmenting classical parametric curves with Machine Learning (ML) residuals yield accurate, low‑cost volume estimates on signalized arterials. Finally, Guarda \u0026amp; Qian (Guarda and Qian \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) a data‑driven macroscopic estimator that uses observed travel times and flow-conservation laws to infer both flow and time on unobserved links.\u003c/p\u003e\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e abstracts these developments, illustrating the evolution from foundational network analyses to sophisticated hybrid models, that leverage the richness of probe‑derived data.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eRelevant literature for traffic flow estimation\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRef.\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eApproach\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eInput\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eOutput\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eResults\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e(Geroliminis and Daganzo \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2008\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eAggregate link speeds and flows into network bins, fit a polynomial Macroscopic Fundamental Diagram relating density to throughput, analyze flow\u0026ndash;density regimes\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eAverage trip travel times; aggregated loop‑detector counts\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eNetwork flow / density\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eClear flow\u0026ndash;density regimes at network level\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e(Herrera and Bayen \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2010\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eFormulate Lighthill\u0026ndash;Whitham\u0026ndash;Richards partial differential equation in state‑space, apply Extended Kalman Filter to fuse sparse GPS‑derived travel times and loop counts\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eGPS travel times; loop‑detector counts; time‑of‑day\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLink flow / density\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eEstimation error\u0026thinsp;\u0026lt;\u0026thinsp;15% under low probe penetration\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e(Neumann et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2013\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eConstruct a Bayesian network over fundamental‑diagram variables, learn conditional probability tables via expectation‑maximization, infer link flows by belief propagation\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eProbe‑vehicle travel times; time‑of‑day; day‑of‑week\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLink flow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u0026asymp;\u0026thinsp;90% accuracy in link‑level flow estimation\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e(Ren et al. \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2014\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eReplace Euclidean distance with travel‑time cost in the radiation model, derive origin\u0026ndash;destination flux via closed‑form radiation equations\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eTravel‑time\u0026ndash;based costs; O/D population \u0026amp; employment; network topology metrics\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eOrigin\u0026ndash;destination commuter flows\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003ePearson r\u0026thinsp;\u0026asymp;\u0026thinsp;0.75 between predicted and observed flows\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e(Saberi et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2014\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eExtract 3D space‑time vehicle trajectories, compute link flows and densities via Edie\u0026rsquo;s definitions, fit fundamental‑diagram parameters by nonlinear least squares\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3D vehicle trajectory travel times; link distances\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLink flow / density\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eSuccessful recovery of fundamental diagram parameters\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e(Meng et al. \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2017\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eFormulate a quadratic programming problem minimizing deviation from taxi travel times and loop counts, enforce spatial smoothness via Laplacian regularization\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eTaxi travel times; loop‑detector counts; time‑of‑day\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLink volume\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eOutperformed single‑source methods in volume recovery\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e(Young et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2018\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eBuild baseline hourly volumes from automatic traffic recorder profiles, train a multilayer perceptron on residual errors (two hidden layers, ReLU activation, dropout), optimize with Adam\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eGPS probe counts \u0026amp; trajectories; ATR counts; speed from GPS; road geometry; weather\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHourly traffic volume\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eR\u0026sup2;: 0.61\u0026ndash;0.94 (median\u0026nbsp;0.82); MAPE median\u0026nbsp;27%; w/o GPS traces \u0026rarr; R\u0026sup2;\u0026nbsp;0.73, MAPE\u0026nbsp;37%; capacity error\u0026thinsp;\u0026asymp;\u0026thinsp;9.5%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e(Sekuła et al. \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2018\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eGenerate diurnal volume profiles, use a three‑layer multilayer perceptron to correct profiles based on probe data, apply early stopping to avoid overfitting\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eVehicle probe data; automatic traffic recorder counts; volume profiles\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHistorical hourly traffic volume\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e24% more accurate than standard profiling (MAPE\u0026thinsp;\u0026asymp;\u0026thinsp;21% where probe rate is 30\u0026ndash;47 veh/hr)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e(Gu et al. \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2017\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDiscretize the link‑queue model of the Lighthill\u0026ndash;Whitham\u0026ndash;Richards equation using a Godunov scheme, treat real‑time travel‑time measurements as boundary conditions, invert for flow and density\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eReal‑time link travel times; signal timing plans\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLink flow / density / speed\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eHigh accuracy across signalized network segments\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e(Pun et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2019\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePerform stepwise multiple linear regression with variance inflation factor checking for multicollinearity, use heteroskedasticity‑robust standard errors, validate by cross‑validation\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eGoogle Maps travel times; floating‑car travel times; link length\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLink flow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eHigh R\u0026sup2; (\u0026asymp;\u0026thinsp;0.9) on urban corridor datasets\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e(Jiang et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2020\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIntegrate the Lighthill\u0026ndash;Whitham\u0026ndash;Richards partial differential equation with origin\u0026ndash;destination source terms, iteratively fit road‑sharing coefficients to match observed travel times\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eObserved link travel times; dynamic OD demand profiles\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLink flow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eAccurate time‑varying flow \u0026amp; travel‑time recovery under disturbances\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e(Genser et al. \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2021\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eStack travel‑time features from multiple sensor types, apply ridge‑penalized multiple linear regression, impute missing data via k‑nearest neighbors, bootstrap confidence intervals\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eGoogle travel times; thermal‑camera times; video‑derived travel times\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLink flow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eHigh accuracy using travel‑time inputs alone\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e(Li et al. \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2021\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTrain Gaussian process regression with automatic relevance determination kernel, optimize hyperparameters by maximizing marginal likelihood, quantify uncertainty from posterior variance\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eFloating‑Car Data travel times; day‑type classification\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLink flow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eUp to 85% accuracy vs. loop‑detector counts\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e(Othman et al. \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2022\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eEmbed physics constraints in a neural network by adding topography‑based residual penalties, train with conservation penalty terms via stochastic gradient descent\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eFloating‑car data travel times; slope; curvature; lane count\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLink flow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eSignificant error reduction vs. detector‑only baselines\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e(Mahajan et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2023\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePretrain a neural network on a data‑rich source city, fine‑tune its last layers on target‑city data, apply correlation alignment loss for domain adaptation\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eProbe‑vehicle \u0026amp; public speeds; network metadata\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLink flow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eRobust multi‑city estimation under sparse sensors\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e(Pan et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2024\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCouple Macroscopic Fundamental Diagram equations with a long short‑term memory residual module in a sequence‑to‑sequence framework, train with mean squared error plus physics penalty\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eLink travel‑time measurements; historical flow data\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLink flow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMAPE\u0026thinsp;\u0026lt;\u0026thinsp;10% in complex urban networks\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e(Konstantinidis et al. \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2024\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCompute base travel time using the Bureau of Public Roads formula, learn residual flow errors via GBDT, merge predictions and explain via SHAP values\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eHistorical volume; travel time; time‑of‑day; day‑of‑week\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eArterial volume; travel time\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eFor traffic volume prediction, both Decision Trees and GBDT have MAPE of 14.55%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e(Guarda and Qian \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2025\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eFit link‑level flows under flow‑conservation constraints, solve a constrained least‑squares problem for unobserved links\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eObserved travel‑time measurements; network connectivity\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLink flow; travel time\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eHigh correlation (\u0026gt;\u0026thinsp;0.8) and low error on unobserved links\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eEvidently, a rich variety of methods, spanning from fundamental diagram reconstruction to deep learning and trajectory clustering exists in literature aiming at leveraging travel time as a proxy for flow. However, most of these approaches share common limitations: many depend on high probe penetration, rely on sensor-based calibration, or operate as black-box models with limited interpretability. There remains a clear research gap for models that are theoretically grounded, practically deployable, and require only publicly available travel time data, particularly suited for mid-sized cities with limited traffic sensing infrastructure.\u003c/p\u003e\u003cp\u003eThe goal of the present research is to produce a novel supervised ML model that accurately predicts lane-based hourly traffic flow, by making use of publicly available data like loop detectors\u0026rsquo; data, Google Maps API travel times, and other (static) data related to the infrastructure and the data collection period. We, therefore, propose a simple, transferable methodology supported by real-world deployment and validation. To this end, the present research aims at addressing the following research questions:\u003c/p\u003e\u003cp\u003e\u003col\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eCan publicly available travel time feeds (e.g., Google Maps) reliably serve as proxies for predicting lane‑based traffic flow in urban areas with sparse sensor coverage?\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eWhich combination of contextual network attributes (lane count, signalization, functional class), temporal indicators (peak/ off‑peak, weekend/weekday, disturbances) and travel time inputs yields the most accurate flow predictions?\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e\u003cp\u003eFor investigating the above, various supervised ML techniques are trained and their outcome, in terms of statistical significance, is evaluated using as input a multi-variable synthetic dataset spanning from lane-based traffic flow and travel times to topological features of the section like number of lanes and capacity per lane. The remainder of the paper is organized as follows: In Section 2, the methodological approach followed is presented. In Section 3, the results of the supervised ML are presented and further analyzed. Finally, in Section 4, the main findings of this research are presented and discussed, as well as some future research initiatives are established.\u003c/p\u003e"},{"header":"METHODOLOGICAL APPROACH","content":"\u003cp\u003eThe present approach relies on the development of generic supervised learning models that predict vehicle flow at any given location on the urban road network using travel time at the same location as a key explanatory variable, along with and other contextual information. The ultimate objective is to construct a robust and interpretable model capable of capturing the underlying patterns in traffic dynamics, thereby enabling accurate prediction of section based hourly traffic flow under varying conditions. \u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e\u003cstrong\u003eData Sources and Collection\u003c/strong\u003e\u003c/h2\u003e\n\u003cp\u003eData were collected from selected urban transport network road segments within the urban transport network of the wider Athens metropolitan area for 2023. Two main sources were used: 1) Travel times, and 2) Hourly traffic counts. Concerning travel times, the data have been retrieved from the Google Maps API, using its publicly available traffic service. Travel times data were recorded over multiple weekdays in March, with measurements collected during different time intervals to capture both peak and non-peak traffic patterns, as well as during different conditions in the network (e.g., working days or weekends, disturbance or not disturbance). Travel times were collected in a 15-minute basis and then were aggregated in hourly travel times, matching that way the resolution of the provided traffic counts. To ensure spatial consistency with physical detector data, each travel time query was constructed by setting the origin and destination within a 50-meter radius of the actual detector location. This approach aimed to convert travel time data, which is typically aggregated over segments, into a point-based representation, thereby mimicking the spatial granularity of detectors.\u003c/p\u003e\n\u003cp\u003eConcerning the hourly traffic counts, they are collected from the Greek Government open data repository. The Greek Government open data repository contains, among others, data from the detectors\u0026rsquo; network of the urban transport network of the metropolitan area of Athens, Greece. The hourly traffic counts are collected for the same dates, time periods, and locations as the travel times data collection process seen in \u003cstrong\u003eFigure 1\u003c/strong\u003e.\u003c/p\u003e\n\u003cp\u003eIn addition to the above, \u003cstrong\u003eFigure 2\u0026nbsp;\u003c/strong\u003eillustrates the hourly traffic counts (up) and travel times (down) timeseries for all selected data collection locations.\u003c/p\u003e\n\u003cp\u003eExcept for the above, other data concerning 1) the characteristics of the sections where the detectors\u0026rsquo; are placed (number of lanes, capacity per lane, functional class), 2) the type of the node exceeding said section (signalized or not signalized), and 3) other characteristics related to the data collection period (date with a known disturbance or not except for Extreme Weather Events, date with Extreme Weather Events, whether the data collection refers to working day or weekend, whether the data collection period is during peak hour period or not) are included in the final dataset. This combined dataset allowed for direct supervised learning between travel time\u0026ndash;derived features and actual vehicle flow at localized detector positions.\u003c/p\u003e\n\u003ch2\u003eLane-based Hourly Traffic Flow Prediction\u003c/h2\u003e\n\u003cp\u003eIn the present research, predicting lane-based hourly traffic flow is done using the following supervised ML techniques: 1) Linear Regression, 2) Ridge Regression, 3) Lasso Regression, 4) Elastic Net, 5) Random Forest, 6) GBDT, 7) Support Vector Regression \u0026ndash; SVR, and 8) XGBoost. These categories of models are very popular in traffic flow analysis and prediction tasks due to their accuracy and ability to handle complex multidimensional datasets (Karlaftis and Vlahogianni 2011).\u003c/p\u003e\n\u003cp\u003eThe dataset is split with a 80:20 ratio for train and test set respectively, with stratification ensured. Stratification means that sampling involves dividing a population into homogeneous subgroups (strata) and then sampling from each stratum. Additionally, for each of the techniques, an initial set of hyperparameters is used. To enhance predictive accuracy, two hyperparameter tuning methods were employed: Randomized Search and Grid Search. These methods iteratively tested combinations of key model parameters for each algorithm. \u0026nbsp;Finally, the best model is selected after examining the evaluation metrics associated with it. The evaluation metrics used in the present research are 1) the goodness-of-fit (R-squared value) which measures how well the predictions match the observed data, and 2) the Minimum Absolute Percentage Error (MAPE) which quantifies the relative error.\u003c/p\u003e\n\u003cp\u003eOnce the best-performing model is identified, the SHapley Additive exPlanations (SHAP) analysis (Shapley 1953) is used to interpret how each input feature contributed to the final selected supervised ML model predictions. The SHAP diagrams offer an interpretable, model-agnostic method for explaining how much each input variable pushes the predicted value up or down, allowing for visualization of the variable importance in context. In addition to the SHAP analysis, and to have the ability to interpret the interaction among the features of the final selected supervised ML model the unified permutation importance vs Mean Partial Dependence plot is utilized, which quantifies each feature\u0026rsquo;s unique contribution to predictive accuracy, as well as the average directional effect that varying a feature has on the predictions. By combining SHAP analysis and permutation importance vs Mean Partial Dependence plot we can have a clear perspective on feature relevance and feature importance on the final supervised ML model.\u003c/p\u003e"},{"header":"RESULTS","content":"\u003ch2\u003eLane-based Hourly Traffic Flow Prediction Model Development\u003c/h2\u003e\n\u003cp\u003eIn the present subsection, the effort of developing a supervised ML model towards predicting lane-based hourly traffic flow is presented. The model predicts the lane-based hourly traffic flow (veh/h/lane) for each of the selected locations in the urban transport network of the wider metropolitan area of Athens, Greece (multiple points prediction) taking as inputs the travel time for crossing the selected locations, the characteristics of the sections where the detectors\u0026rsquo; are placed (number of lanes, capacity per lane, functional class), the type of the node exceeding said section (signalized or not signalized), and other characteristics related to the data collection period (date with a known disturbance or not except for Extreme Weather Events, date with Extreme Weather Events, whether the data collection refers to working day or weekend, whether the data collection period is during peak hour period or not). This information is presented in \u003cstrong\u003eTable 2\u003c/strong\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTABLE 2 Variables used as input in the training of the supervised ML models\u003c/strong\u003e\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"100%\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eVariable name\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 61px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eDescription\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eType of variable\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"3\" style=\"width: 100px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eDependent variable\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003etraffic_flow\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 61px;\"\u003e\n \u003cp\u003eLane-based hourly traffic flow (veh/h/lane) - associated in the developed model with locations of detectors in the network\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eNumeric\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"3\" style=\"width: 100px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eIndependent variables\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003enb_lanes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 61px;\"\u003e\n \u003cp\u003eThe number of lanes of the section in which hourly traffic flow is predicted\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eNumeric\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003esignalized\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 61px;\"\u003e\n \u003cp\u003eWhether the exceeding node for the selected location is signalized or not (0 if the node is unsignalized; 1 if it is signalized)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eCategorical\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003etravel_time\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 61px;\"\u003e\n \u003cp\u003eThe time needed to cross the selected location (a boundary box of 100 meters is used for this purpose, as previously mentioned)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eNumeric\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003ecapacity_per_lane\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 61px;\"\u003e\n \u003cp\u003eThe capacity per lane of the section in which hourly traffic flow is predicted\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eNumeric\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003enormal_date\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 61px;\"\u003e\n \u003cp\u003eWhether any disturbance (not including Extreme Weather Events) took place during the data collection date (0 if it is a normal day; 1 if any disturbance except for Extreme Weather Events took place)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eCategorical\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003epeak\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 61px;\"\u003e\n \u003cp\u003eWhether the data collection point refers to peak or off-peak hour (0 if the data collection point is out of the peak hours; 1 if it is during peak hour)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eCategorical\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003ebad_weather\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 61px;\"\u003e\n \u003cp\u003eWhether any Extreme Weather Events (e.g., floods) took place during the data collection date (0 if no Extreme Weather Events took place; 1 if they took)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eCategorical\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003efunc_class\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 61px;\"\u003e\n \u003cp\u003eThe functional class of the section in which hourly traffic flow is predicted\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eCategorical\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eis_weekend\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 61px;\"\u003e\n \u003cp\u003eWhether the data collection date refers to working day or weekend (0 if the data collection took place during working day; 1 if it took place during the weekend)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eCategorical\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eDue to the multiplex and complementary nature of the independent variables, we performed a preliminary check for multicollinearity. While multicollinearity is often discussed in the context of traditional regression models, it is equally relevant in ML. Many ML algorithms, such as linear regression, logistic regression, and support vector machines, can be adversely affected by multicollinearity. However, some algorithms like Tree-Based Models, Lasso Regression, and Ridge Regression are more robust to multicollinearity. Since multiple models are to be developed and evaluated, multicollinearity is investigated through the correlation matrix and a Variance Inflation Factor (VIF) analysis.\u003c/p\u003e\n\u003cp\u003eThe correlation matrix for the independent variables is illustrated in \u003cstrong\u003eFigure 3\u003c/strong\u003e. The correlation matrix revealed no strong linear relationships (i.e., |r| \u0026gt; 0.85) between any feature pairs. The most notable moderate associations include normal_date and bad_weather and capacity_per_lane with func_class.\u003c/p\u003e\n\u003cp\u003eAdditionally, VIF provides a measure of multicollinearity among the independent variables in a multiple regression model. The VIF values common threshold is 5; a VIF value greater than 5 is often considered indicative of multicollinearity. In our dataset the highest VIF values is just over 1.8. This confirms the absence of significant multicollinearity, suggesting that each feature contributes unique and non-redundant information to the model. Therefore, all features were retained in the final model to preserve interpretability and predictive capacity. The VIF values are presented in \u003cstrong\u003eTable 3\u003c/strong\u003e. It should be noted that a constant is presented in the VIF values; such a constant is not included in the training of the supervised ML models, but this is the standard practice in regression diagnostics.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTABLE 3 VIF values for all independent variables used as input in the training of the supervised ML models\u003c/strong\u003e\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"43%\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eFeature\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eInitial set of values\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003econst\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e54.03\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003etravel_time\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e1.32\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003epeak\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e1.04\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003enormal_date\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e1.38\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003ebad_weather\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e1.47\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003enb_lanes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e1.30\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003ecapacity_per_lane\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e1.87\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003efunc_class\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e1.74\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003esignalized\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e1.18\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003eis_weekend\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e1.24\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eAfter ensuring that multicollinearity is absent for the independent variables of the dataset, we proceeded with developing a supervised ML model for lane-based hourly traffic flow prediction. As mentioned above, various techniques are used and hyperparameter tuning is achieved in the initial set of parameters. In \u003cstrong\u003eTable 4\u003c/strong\u003e the hyperparameters used per technique are presented.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTABLE 4 Hyperparameters used per supervised ML technique\u003c/strong\u003e\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"102%\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 14px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eModel\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eHyperparameter\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eInitial set of values\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eDescription\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 14px;\"\u003e\n \u003cp\u003eLinear Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"3\" style=\"width: 85px;\"\u003e\n \u003cp\u003eN/A\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" style=\"width: 14px;\"\u003e\n \u003cp\u003eRidge Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003ealpha\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eFive values logarithmically spaced between 0.01 and 100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eRegularization strength; larger values specify stronger regularization\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003emax_iter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003e15 000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eMaximum number of iterations\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" style=\"width: 14px;\"\u003e\n \u003cp\u003eLasso Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003ealpha\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eFive values logarithmically spaced between 0.01 and 100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eRegularization strength; larger values specify stronger regularization\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003emax_iter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003e15 000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eMaximum number of iterations\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" style=\"width: 14px;\"\u003e\n \u003cp\u003eElastic Net\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003ealpha\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eFive values logarithmically spaced between 0.01 and 100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eRegularization strength; larger values specify stronger regularization\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003el1_ratio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eValues from 0.1 to 0.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eThe L1 and L2 penalties mixing parameter\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"5\" style=\"width: 14px;\"\u003e\n \u003cp\u003eRandom Forest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003en_estimators\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eValues from 1 to 10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eThe number of trees in the forest\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003emax_depth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eDepth from 1 through 10, plus 20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eThe maximum depth of the tree\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003emin_samples_split\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eValues from 10 to 20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eThe minimum number of samples required to split an internal node\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003emin_samples_leaf\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eValues from 4 to 10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eThe minimum number of samples required to be at a leaf node\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003emax_features\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eSquare root of features, log₂ of features, or all features (None value)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eThe number of features to consider when looking for the best split\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"6\" style=\"width: 14px;\"\u003e\n \u003cp\u003eGBDT\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003en_estimators\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eValues from 1 to 20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eThe number of boosting stages to be run\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003elearning_rate\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eValues from 0.1 to 0.2 with a 0.01 step\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eShrinks the contribution of each tree by learning rate to prevent overfitting\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003emax_depth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eDepth from 1 through 10, plus 20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eThe maximum depth of the individual regression estimators\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003emin_samples_split\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eValues from 2 to 10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eThe minimum number of samples required to split an internal node\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003emin_samples_leaf\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eValues from 1 to 4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eThe minimum number of samples required to be at a leaf node\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003esubsample\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eValues from 0.6 to 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eThe fraction of samples used for fitting the individual base learners\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"3\" style=\"width: 14px;\"\u003e\n \u003cp\u003eSVR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eValues from 1 to 10 with a 0.1 step\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eRegularization parameter; the strength of the regularization is inversely proportional to C\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003ekernel\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eLinear, radial‑basis function, or polynomial\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eSpecifies the kernel type to be used in the algorithm (linear, rbf, poly)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003egamma\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eScale or auto\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eKernel coefficient\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" style=\"width: 14px;\"\u003e\n \u003cp\u003eXGBoost\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003en_estimators\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eValues from 1 to 20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eSets the number of boosting rounds (i.e., the total trees in the ensemble)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003elearning_rate\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 19px;\"\u003e\n \u003cp\u003eValues from 0.01 to 0.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eShrinks the contribution of each tree by learning rate to prevent overfitting\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eAfter examining each of the developed models and evaluating their goodness-of-fit, with the application of Grid and Randomized Search, the finally selected model is a GBDT model with Grid Search for hyperparameter tuning. The tuned hyperparameters and the evaluation metrics (R-squared value and MAPE) for all developed best-performing supervised ML models are presented in \u003cstrong\u003eTable 5\u003c/strong\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTABLE 5 R-squared and MAPE values for both Grid and Randomized Search for all developed supervised ML models\u003c/strong\u003e\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"100%\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 23px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eModel\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eHyperparameter\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eTuned value\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 17px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eR-squared\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eMAPE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 23px;\"\u003e\n \u003cp\u003eLinear Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" style=\"width: 45px;\"\u003e\n \u003cp\u003eN/A\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 17px;\"\u003e\n \u003cp\u003e0.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e31.31%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" style=\"width: 23px;\"\u003e\n \u003cp\u003eRidge Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003ealpha\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" style=\"width: 17px;\"\u003e\n \u003cp\u003e0.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" style=\"width: 13px;\"\u003e\n \u003cp\u003e31.51%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003emax_iter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e15000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" style=\"width: 23px;\"\u003e\n \u003cp\u003eLasso Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003ealpha\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" style=\"width: 17px;\"\u003e\n \u003cp\u003e0.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" style=\"width: 13px;\"\u003e\n \u003cp\u003e31.47%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003emax_iter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e15000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" style=\"width: 23px;\"\u003e\n \u003cp\u003eElastic Net\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003ealpha\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e0.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" style=\"width: 17px;\"\u003e\n \u003cp\u003e0.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" style=\"width: 13px;\"\u003e\n \u003cp\u003e31.47%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003el1_ratio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e0.9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"5\" style=\"width: 23px;\"\u003e\n \u003cp\u003eRandom Forest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003en_estimators\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"5\" style=\"width: 17px;\"\u003e\n \u003cp\u003e0.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"5\" style=\"width: 13px;\"\u003e\n \u003cp\u003e15.40%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003emax_depth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003emin_samples_split\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003emin_samples_leaf\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003emax_features\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003eNone\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"6\" style=\"width: 23px;\"\u003e\n \u003cp\u003eGBDT\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003en_estimators\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"6\" style=\"width: 17px;\"\u003e\n \u003cp\u003e0.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"6\" style=\"width: 13px;\"\u003e\n \u003cp\u003e15.41%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003elearning_rate\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e0.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003emax_depth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003emin_samples_split\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003emin_samples_leaf\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003esubsample\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e1.0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"3\" style=\"width: 23px;\"\u003e\n \u003cp\u003eSVR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003eC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"3\" style=\"width: 17px;\"\u003e\n \u003cp\u003e0.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"3\" style=\"width: 13px;\"\u003e\n \u003cp\u003e32.32%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003ekernel\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003elinear\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003egamma\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003escale\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" style=\"width: 23px;\"\u003e\n \u003cp\u003eXGBoost\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003en_estimators\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" style=\"width: 17px;\"\u003e\n \u003cp\u003e0.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" style=\"width: 13px;\"\u003e\n \u003cp\u003e18.60%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 25px;\"\u003e\n \u003cp\u003elearning_rate\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e0.1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n\u003c/table\u003e\n\u003cp\u003eThe finally selected supervised ML model is the GBDT with Randomized Search. Concerning the goodness-of-fit of the selected GBDT model, the R-squared value is equal to 0.85 and\u0026nbsp;MAPE is equal to 15.41%. Those values are considered good. Firstly, the R-squared value indicates a good fitness on the outcome of the dependent variable (lane-based\u0026nbsp;hourly traffic flow (veh/h/lane)); an R-squared value of 0.85 indicates that approximately 85% of the variance in observed traffic volumes is explained by the model, which reflects good explanatory power, especially given the inherent noise and variability in travel time data. Then, a MAPE value of 15.41% reveals that the\u0026nbsp;GBDT\u0026nbsp;model has a good accuracy. Such a MAPE value is in line with the results of previous research like\u0026nbsp;(Young et al. 2018; Sekuła et al. 2018; Konstantinidis et al. 2024; Pan et al. 2024). Our proposed model outperforms simpler profile‑based and pure regression baselines (21\u0026ndash;27% MAPE). It is slightly less accurate than\u0026nbsp;(Konstantinidis et al. 2024), which however was trained and evaluated on just one arterial corridor with only two detector locations, which constrains its scalability and limits its applicability across more extensive urban networks. Finally, our\u0026nbsp;GBDT\u0026nbsp;model trails the most sophisticated hybrid deep‑learning frameworks\u0026nbsp;(Pan et al. 2024)\u0026nbsp;(MAPE below 10%); however developing and deploying such a model requires extensive sequence‑to‑sequence training on large historical datasets and careful tuning of both physics‑based and neural components. That way implementation complexity is increased, more computational power is needed, and it leads to reduced model transparency compared to our more straightforward, tree‑based solution.\u003c/p\u003e\n\u003cp\u003eConcerning feature importance, at first the SHAP values were leveraged. SHAP values are a way to explain the output of any ML model. SHAP values use a game theoretic approach that measures the influence of each feature (predictor) to the final outcome (Shapley 1953). \u003cstrong\u003eFigure 4\u003c/strong\u003e below depicts the SHAP values of the features. The color gradient from blue (low value of feature) to red (high value of feature) reveals how the feature\u0026rsquo;s actual value contributes to each prediction.\u003c/p\u003e\n\u003cp\u003eFor the input variables, the SHAP summary plot of \u003cstrong\u003eFigure 4\u0026nbsp;\u003c/strong\u003edisplays each feature\u0026rsquo;s distribution of impacts on the model\u0026rsquo;s predicted traffic flow in magnitude (horizontal axis) and direction (positive vs. negative). The SHAP summary plot makes it clear that number of lanes and travel time are the most impactful features, as they exhibit the widest spread of SHAP values. The number of lanes exerts a strong, but mixed influence. Fewer lanes (blue points in the \u0026ldquo;nb_lanes\u0026rdquo; row) often lead to higher predicted hourly traffic flows, perhaps because traffic stays more uniform. On the other hand, higher number of lanes (red points) yield negative SHAP contributions, suggesting the existence of bottlenecks or spillback. Additionally, shorter travel times (blue points in the \u0026ldquo;travel_time\u0026rdquo; row) mostly lead to reduced predicted hourly traffic flow, reflecting conditions of low congestion. In contrast, longer travel times (red points) mostly lead to increased hourly traffic flow predictions, since that mean that congestion is increased and, therefore, more vehicles are on the road.\u003c/p\u003e\n\u003cp\u003eThen, three categorical features are of importance (is_weekend, normal_date, and peak), however they do not have such high influence in the predicted hourly traffic flow. For is_weekend and normal_date, the illustrated results are obvious and expected. Concerning peak, it appears that the results are mixed since peak and off- peak hours do not clearly lead to increased or decreased hourly traffic flow predictions. This can be sourced in the high congestion levels that might appear during peak hours.\u003c/p\u003e\n\u003cp\u003eAfterwards, capacity per lane shows a clear monotonic effect; high‑capacity links (red) lead to higher estimated hourly traffic flows, while lower capacities (blue) mean less hourly traffic flow. Func_class comes after with results mostly in line with those for nb_lanes, higher functional classes lead to slightly reduced hourly traffic flow predictions, medium functional classes lead to higher hourly traffic flow predictions, and lower functional classes lead to lower prediction values.\u003c/p\u003e\n\u003cp\u003eFinally, two binary categorical features appear: signalized and bad_weather. Sites that are signalized (red points in the \u0026ldquo;signalized\u0026rdquo; row) lead to lower hourly traffic flow predictions, opposed to the unsignalized locations (blue points) which have no significant impact on the predictions. This is in line with the func_class results; mostly higher functional class sections have upstream signalized intersections. For bad_weather, only the existence of an Extreme Weather event even so slightly leads to mostly higher predicted hourly traffic flow.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe SHAP point of view presented before is useful to interpret the feature importance of the final GDBT model developed in the present research. However, it does not offer any interpretation concerning the interaction among the features of the GBDT model. Thus, to get a better insight into the factors that influence the estimation of the lane-based hourly traffic flow, we investigate the permutation importance vs Mean Partial Dependence plot. Said plot was first introduced\u0026nbsp;in\u0026nbsp;(Vlahogianni et al. 2012) and later used in various research like (Fafoutellis et al. 2022).\u003c/p\u003e\n\u003cp\u003eThe Permutation Importance versus Mean Partial Dependence plot combines two complementary measures of feature relevance. On the horizontal axis, permutation importance quantifies how much model performance deteriorates when each feature\u0026rsquo;s values are randomly shuffled, thus indicating its unique contribution to predictive accuracy. On the vertical axis, Mean Partial Dependence captures the average directional effect that varying a feature across its range has on the predicted traffic flow, offering a direct interpretation of its marginal influence. The Permutation Importance versus Mean Partial Dependence plot is illustrated in \u003cstrong\u003eFigure 5\u003c/strong\u003e.\u003c/p\u003e\n\u003cp\u003eFrom \u003cstrong\u003eFigure 5\u003c/strong\u003e, a clear three‑way separation emerges. At the bottom left, number of lanes stands alone: each additional lane reduces the predicted hourly traffic flow by roughly 200 veh/h, and shuffling this feature modestly degrades overall accuracy. Number of lanes, therefore, are a predictor of importance for our model.\u003c/p\u003e\n\u003cp\u003eAbove it, near the center, sit travel_time, capacity_per_lane, and normal_date. Travel time drives the largest average increase in flow (around +70 veh/h/lane) yet carries almost zero permutation importance. That means that the model can infer congestion effects through other correlated inputs if travel time values are randomized. Likewise, capacity_per_lane and normal_date each add roughly +25 veh/h/lane and +15 veh/h/lane to predictions on average, yet their low permutation importance shows that randomizing these values has little effect on accuracy, implying the model relies on other correlated features to capture the same information.\u003c/p\u003e\n\u003cp\u003eOn the right side, the peak period and weekend indicators each change the predicted flow by only a few vehicles per hour (peak near zero and is_weekend about \u0026ndash;10 veh/h/lane), but shuffling them still slightly reduces accuracy, showing they provide some unique information. Finally, signalization status, adverse weather, and functional class have almost zero average effect and zero permutation importance, meaning that randomizing these features neither shifts predictions nor harms accuracy, so they only tweak the model under very specific conditions.\u003c/p\u003e\n\u003cp\u003eA comparison between the SHAP summary plot (\u003cstrong\u003eFigure 4\u003c/strong\u003e) and the permutation importance vs Mean Partial Dependence plot (\u003cstrong\u003eFigure 5\u003c/strong\u003e) provides an opportunity to examine feature importance under two different perspectives, which lead to a consistent overall picture. SHAP summary plot reveal how individual predictions respond to feature values, showing that travel time and lane count have major impact in individual predictions, while signalization values cluster near zero, indicating almost no local effect. The permutation importance vs Mean Partial Dependence plot confirms that lane count is the feature the model relies on most, and that travel time consistently increases hourly traffic flow predictions even though it can be permuted without a large drop in accuracy. Signalization, peak period, weekend, weather, and functional class all have low importance and small mean effects, showing they only tweak the results in specific cases.\u003c/p\u003e\n\u003ch2\u003eOut-of-Sample Validation\u003c/h2\u003e\n\u003cp\u003eFor out‑of‑sample validation, we applied the finalized GBDT model to the pNEUMA dataset\u0026nbsp;(Barmpounakis and Geroliminis 2020). The pNEUMA dataset is a large-scale open dataset of urban vehicle trajectories collected using a drone swarm in Athens, Greece during 2018. All drones\u0026rsquo; data for a selected date (11/01/2018) and for morning peak hour (08:00-09:00) have been downloaded and further analyzed. Additionally, ten (10) locations in central arterials of the Athens city center have been selected for evaluating the developed GBDT model (\u003cstrong\u003eFigure 6\u003c/strong\u003e). Said locations were not included in the dataset used during the development of the GBDT model.\u003c/p\u003e\n\u003cp\u003eConcerning data, the ground truth lane-based hourly traffic flow (veh/h/lane) is the total number of trajectories crossing the selected locations derived by the number of lanes. Since some of the locations are close to intersections, it is worth noting that a heading control is also applied. For travel time, and for the trajectories used in the previous step, we extracted the time difference for trajectories\u0026rsquo; data points upstream and downstream of the selected locations. All other data needed were manually imported in the dataset.\u003c/p\u003e\n\u003cp\u003eApplying the finalized GBDT model to the pNEUMA dataset yielded a MAPE of 15.97%, performance similar to the validation performed during the development of the model. To assess whether our prediction errors satisfy the key assumptions of classical regression, we further statistically analyzed the goodness-of-fit of the out-of-sample GBDT model validation by applying the following statistical tests: paired t-test, Shapiro-Wilk test, Breusch-Pagan test, Durbin-Watson test, and Bonferroni outlier test.\u003c/p\u003e\n\u003cp\u003eFirst we applied a paired t‑test, which evaluates whether the mean difference between observed and predicted flows is zero, thus ensuring the absence of systematic bias. Paired t-test is applied since we dealing with matched pairs of data. With p = 0.83 we fail to reject the null hypothesis, indicating unbiased predictions. Next, the Shapiro-Wilk test (p = 0.64) and Breusch-Pagan test (p = 0.17) verify that the residuals are approximately normally distributed and no heteroscedasticity exists, respectively. A Bonferroni-adjusted outlier analysis on externally studentized residuals found no significant extreme values, demonstrating that no single observation unduly influences the model. The only statistical test for which the desired results were not achieved is the Durbin-Watson test. With a value of the test statistic (d) equal to 1.14 (d\u0026lt;2), the test indicates positive autocorrelation in the residuals. That means that the errors from one observation are related to the errors from other observations. This finding of positive autocorrelation is a direct consequence of the spatiotemporal dynamics inherent to traffic flow conditions. As traffic flow conditions like queue formation or shockwaves propagate through the network, the error in the predicted hourly traffic flow at one location is likely to be correlated with the error at a downstream location and in subsequent time periods. This indicates that the observed autocorrelation is not a deficiency of the GBDT model, but rather a characteristic of the data.\u003c/p\u003e\n\u003cp\u003eSuch out‑of‑sample performance suggests that the trained model can be used as an \u0026ldquo;off the shelf\u0026rdquo; solution for estimating lane\u003c/p\u003e"},{"header":"CONCLUSIONS","content":"\u003cp\u003eThe present research addresses two (2) main research questions : 1) whether publicly available travel time feeds (such as Google Maps) can serve as reliable proxies for lane‑based traffic flow in sensor‑sparse urban corridors, and 2) which mix of network attributes (lane count, signalization, functional class), temporal indicators (peak/off‑peak, weekend/weekday, disturbance flags) and travel time inputs produces the most accurate estimates. To investigate these, we assembled and spatially matched hourly loop detector traffic counts in the urban transport network of the wider metropolitan area of Athens, Greece with Google Maps travel time data and enriched them with contextual features, then trained, tuned and compared eight (8) supervised ML models. By doing that, we concluded to a GBDT model as the top performer.\u003c/p\u003e\u003cp\u003eInterpretability analyses via the SHAP summary plot and the permutation importance vs Mean Partial Dependence plot converged on consistent insights. Number of lanes and travel times emerge as the most influential features. Sections with lower number of lanes lead to higher hourly traffic flow predictions. This counterintuitive and it is likely due to downstream spillback. Additionally, higher travel times correspond to higher predictions for hourly traffic flow. Other categorical features (peak period, weekend, disturbance days) exert smaller yet meaningful effects. The modest but meaningful effects of said features further reveal the model\u0026rsquo;s sensitivity to both routine and disruptive conditions, equipping planners with the ability to anticipate performance under varied scenarios.\u003c/p\u003e\u003cp\u003eTo further investigate our model\u0026rsquo;s prediction capabilities, we performed an out‑of‑sample validation on ten (10) locations making use of the pNEUMA dataset. The results prove the predictive of our model, even in data from different year and in locations for which no training took place during the development of the GBDT model.\u003c/p\u003e\u003cp\u003eAs future work, transfer learning approaches should be explored, to adapt the GBDT model across cities for further testing and evaluation. Such an application requires only publicly available data (travel times) and data related to the infrastructure (e.g., number of lanes, signalization, etc.), making this approach a cost‑effective complement to fixed sensors. Additionally, we could explore the extension of the capabilities of the models by incorporating real‑time incident and weather feeds. Such extensions will further reduce error margins, enhance spatial generalization and enable self‑optimizing Traffic Management solutions, even in areas or cities where detectors\u0026rsquo; networks are either sparce or absent. Finally, we think that our model can be used as an integral tool for Traffic Management Centers, both allowing for a better understanding of the operational performance of the network and giving the opportunity to properly select the necessary Traffic Management Strategies to mitigate the impacts of any incident.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eACKNOWLEDGMENTS\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNo AI or LLMs were used in drafting the present research paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAUTHOR CONTRIBUTIONS\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors confirm contribution to the paper as follows: study conception, design, implementation, analysis, interpretation of results, and draft manuscript preparation: C. Chalkiadakis, E.I. Vlahogianni. All authors reviewed the results and approved the final version of the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDECLARATION OF CONFLICTING INTERESTS\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFUNDING\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work is part of the project ACUMEN which has received funding from the European Union\u0026rsquo;s Horizon Europe RIA programme under GA No 101103808.\u003cbr\u003e\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eBarmpounakis E, Geroliminis N (2020) On the new era of urban traffic monitoring with massive drone data: The pNEUMA large-scale field experiment. 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National Renewable Energy Laboratory\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"data-science-for-transportation","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Data Science for Transportation](https://www.springer.com/journal/42421)","snPcode":"42421","submissionUrl":"https://submission.nature.com/new-submission/42421/3","title":"Data Science for Transportation","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"snapp","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Traffic flow prediction, Travel times, Machine learning, Gradient Boosting Decision Trees","lastPublishedDoi":"10.21203/rs.3.rs-7317470/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7317470/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePredicting lane‑based hourly traffic flow urban networks with limited data coverage remains a critical challenge for network and traffic management. This paper develops a data‑driven methodology that leverages publicly available travel time feeds from Google Maps API spatially matched to detector locations, and contextual features including the number of lanes, the capacity per lane, the signalization status, the functional class, the period of day (peak/ off‑peak), and day of week, as well as the emergence of a disturbance and/or extreme weather conditions to predict lane-based hourly traffic flow at locations within the urban transport network of the Athens wider metropolitan area. A variety of supervised learning techniques are trained and models\u0026rsquo; interpretability is revealed with a novel approach combining the SHAP summary plot and the permutation importance vs Mean Partial Dependence plot. Results show that Gradient Boosting Decision Tree yields the best performance, demonstrating that even aggregated and crowd-sourced travel times inputs can reliably approximate true flow without dense sensor infrastructures. Feature importance insights identified signalization and longer travel times as features that lead to increased predictions, and additional lanes, counterintuitively, as a feature that leads to lower hourly traffic flow. Out‑of‑sample validation on ten previously unseen locations from the pNEUMA dataset demonstrates the model\u0026rsquo;s robustness to unseen traffic patterns without retraining. Future work will investigate transfer learning across different cities, as well as the integration of real‑time incident and weather feeds in the model for improved accuracy.\u003c/p\u003e","manuscriptTitle":"From Travel Times to Hourly Traffic Flows: An Explainable Machine Learning Framework","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-14 11:43:26","doi":"10.21203/rs.3.rs-7317470/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-08-24T21:05:09+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-08-24T09:08:46+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-08-14T16:07:57+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"48816318120078489698250778401718521165","date":"2025-08-14T15:04:49+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"22674603398651127431693376139140743594","date":"2025-08-12T22:47:22+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"245946660218216340485302918000055423725","date":"2025-08-08T18:18:13+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-08-08T17:02:32+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-08-08T05:08:55+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-08-08T05:08:16+00:00","index":"","fulltext":""},{"type":"submitted","content":"Data Science for Transportation","date":"2025-08-07T09:59:45+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"data-science-for-transportation","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Data Science for Transportation](https://www.springer.com/journal/42421)","snPcode":"42421","submissionUrl":"https://submission.nature.com/new-submission/42421/3","title":"Data Science for Transportation","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"snapp","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"279cc451-97d3-41e6-8473-b5913947f456","owner":[],"postedDate":"August 14th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-10-06T15:58:52+00:00","versionOfRecord":{"articleIdentity":"rs-7317470","link":"https://doi.org/10.1007/s42421-025-00133-5","journal":{"identity":"data-science-for-transportation","isVorOnly":false,"title":"Data Science for Transportation"},"publishedOn":"2025-10-03 15:56:55","publishedOnDateReadable":"October 3rd, 2025"},"versionCreatedAt":"2025-08-14 11:43:26","video":"","vorDoi":"10.1007/s42421-025-00133-5","vorDoiUrl":"https://doi.org/10.1007/s42421-025-00133-5","workflowStages":[]},"version":"v1","identity":"rs-7317470","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7317470","identity":"rs-7317470","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}