Point-Process modeling of Secondary Crashes

Point-Process modeling of Secondary Crashes | 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 Point-Process modeling of Secondary Crashes Samarth Motagi, Sirish Namilae, Audrey Gbaguidi, Scott Parr, Dahai Liu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-388055/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Secondary crashes or crashes that occur in the wake of a preceding or primary crash are among the most critical incidents occurring on highways, due to the exceptional danger they present to the first responders and victims of the primary crash. In this work, we developed a self-exciting temporal point process to analyze crash events data and classify it into primary and secondary crashes. Our model uses a self-exciting function to describe secondary crashes while primary crashes are modeled using a background rate function. We fit the model to crash incidents data from the Florida Department of Transportation, on Interstate-4 (I-4) highway for the years 2015-2017, to determine the model parameters. These are used to estimate the probability that a given crash is secondary crash and to find queue times. To represent the periodically varying traffic levels and crash incidents, we model the background rate, as a stationary function, a sinusoidal non-stationary function, and a piecewise non-stationary function. We show that the sinusoidal non-stationary background rate fits the traffic data better and replicates the daily and weekly peaks in crash events due to traffic rush hours. Secondary crashes are found to account for up to 15.09% of the traffic incident, depending on the city on the I4 Highway. Civil Engineering Computational Mathematics Self-exciting Temporal Point Process Background Rate Function Queue Times Non-Stationary Functions Figures Figure 1 Figure 2 Figure 3 Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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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-388055","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":22596721,"identity":"ba2f2c4e-26f6-459c-a9dd-ad3f17b060fd","order_by":0,"name":"Samarth Motagi","email":"","orcid":"","institution":"Embry-Riddle Aeronautical University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Samarth","middleName":"","lastName":"Motagi","suffix":""},{"id":22596722,"identity":"2855eaf2-ca53-4bd0-a2b9-6b1f5a17aab8","order_by":1,"name":"Sirish Namilae","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwElEQVRIiWNgGAWjYJCCAw+ABD+Uw9hAlJYEICHZQIoWBpAWgwPEajFnP514IKHGxt74eO/DzzwMNrIbDhDQYtmTu+FAwrG0xG1njhtL8zCkGRPUYnAApIXtcILZjTQGoJbDiYS1nH8L1PLvv73x/GfMv3kY/hOh5QbQlsS2A4wbJNjYgLYcIEYL0JbEvuTEGWfS2CznGCQbzyTssNzNHz58s7Pnbz/GfONNhZ1sHyEt6CaQpnwUjIJRMApGAQ4AAPf3SRIcZtPjAAAAAElFTkSuQmCC","orcid":"","institution":"Embry-Riddle Aeronautical University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Sirish","middleName":"","lastName":"Namilae","suffix":""},{"id":22596723,"identity":"4a44ba25-fc4a-4ce1-8410-26ee017ad106","order_by":2,"name":"Audrey Gbaguidi","email":"","orcid":"","institution":"Embry-Riddle Aeronautical University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Audrey","middleName":"","lastName":"Gbaguidi","suffix":""},{"id":22596724,"identity":"1f4c46cd-8ee2-416e-a28c-547a4385f651","order_by":3,"name":"Scott Parr","email":"","orcid":"","institution":"Embry-Riddle Aeronautical University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Scott","middleName":"","lastName":"Parr","suffix":""},{"id":22596725,"identity":"71a3dbf8-733f-47c2-b4d2-a1ddf502a96e","order_by":4,"name":"Dahai Liu","email":"","orcid":"","institution":"Embry-Riddle Aeronautical University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Dahai","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2021-04-02 20:43:59","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-388055/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-388055/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":8352105,"identity":"7627b9e6-dd2f-40b7-b0c7-543259556719","added_by":"auto","created_at":"2021-04-23 01:13:09","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":50674,"visible":true,"origin":"","legend":"Histograms showing the distribution of crashes according to (a) time and (b) day of the week.","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-388055/v1/9a3e7336d4df441467b45a34.png"},{"id":8352068,"identity":"ed079252-413e-43af-8e1d-cbe81e4be837","added_by":"auto","created_at":"2021-04-23 01:10:09","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":211544,"visible":true,"origin":"","legend":"Primary and secondary crashes classified form the model for Tampa, Orlando and Daytona Beach along the I-4 highway. 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In this work, we developed a self-exciting temporal point process to analyze crash events data and classify it into primary and secondary crashes. Our model uses a self-exciting function to describe secondary crashes while primary crashes are modeled using a background rate function. We fit the model to crash incidents data from the Florida Department of Transportation, on Interstate-4 (I-4) highway for the years 2015-2017, to determine the model parameters. These are used to estimate the probability that a given crash is secondary crash and to find queue times. To represent the periodically varying traffic levels and crash incidents, we model the background rate, as a stationary function, a sinusoidal non-stationary function, and a piecewise non-stationary function. We show that the sinusoidal non-stationary background rate fits the traffic data better and replicates the daily and weekly peaks in crash events due to traffic rush hours. 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