Detecting the Critical Thresholds of an Urban Traffic System Using Percolation Theory

Detecting the Critical Thresholds of an Urban Traffic System Using Percolation Theory | 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 Article Detecting the Critical Thresholds of an Urban Traffic System Using Percolation Theory Reza Marzban, Meisam Akbarzadeh, Anastasios Kouvelas This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6688617/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 We employ high-resolution speed data to develop a percolation theory-based network analysis framework by integrating two identified critical thresholds. This framework effectively captures the dynamic behaviors of traffic networks before, during, and after the critical phase transition point. Our study reveals characteristic congestion thresholds around this critical phase transition for each studied network. C ritical thresholds mark tipping points where small disruptions may trigger widespread congestion in traffic systems. Near these thresholds, traffic behavior akin to a first-order phase transition occurs during rush periods, while a second-order phase transition is observed during non-rush periods. These insights facilitate the establishment of critical thresholds for urban areas. Additionally, our framework identifies essential links, termed bottlenecks, which are crucial for maintaining the functional connectivity of urban transport networks and ensuring the required level of service in cities. Our findings indicate that these traffic bottlenecks consistently appear at the same times on different days. Notably, links with high betweenness centralities often act as persistent seeds of congestion at the onset and throughout rush periods. Finally, the results indicate that disturbances in links with low congestion index and low betweenness centrality are unlikely to cause catastrophic fragmentation or the decomposition of the giant component. Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics/Complex networks Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics/Nonlinear phenomena Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics/Phase transitions and critical phenomena 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-6688617","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":466278560,"identity":"61ce41ed-722b-4f7e-a451-8e307572eed4","order_by":0,"name":"Reza Marzban","email":"","orcid":"","institution":"Isfahan University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Reza","middleName":"","lastName":"Marzban","suffix":""},{"id":466278561,"identity":"f8178070-3702-4c12-9243-ae1154ed2c66","order_by":1,"name":"Meisam Akbarzadeh","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIiWNgGAWjYFACNjYIfYCH8UECVOwAsVqYDRIYDEjTwibBANWCF+i2H0t78HNPnTzf8d5jFQ/b/jDwtx9gPFyBR4vZmbTjhj3P2AxnnjmXdiOxzYBB4kwCw8Ez+LQcSG+T4AF6fcONHDOwFoYbDAwHG/BpOf+8TfLPAQn7DfffmBWAtMgT1HIj7Zg0zwGDxA03eMwYQFoMCGt5lm4scyAheeaZHGOJhHPGPIZnEhsIOCzN7OGbA3W2fcfPGH78USYnJ3f88OGP+LRgAB4GBkaSNIyCUTAKRsEowAIA2aFUaIarZVYAAAAASUVORK5CYII=","orcid":"","institution":"Isfahan University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Meisam","middleName":"","lastName":"Akbarzadeh","suffix":""},{"id":466278562,"identity":"cd7a0eea-6ce4-4ce4-93aa-3f8e9bdffbe2","order_by":2,"name":"Anastasios Kouvelas","email":"","orcid":"","institution":"ETH Zurich","correspondingAuthor":false,"prefix":"","firstName":"Anastasios","middleName":"","lastName":"Kouvelas","suffix":""}],"badges":[],"createdAt":"2025-05-17 18:53:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6688617/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6688617/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":84877184,"identity":"fe9a9469-3c68-4687-b5e7-4d06f5a9e196","added_by":"auto","created_at":"2025-06-18 10:08:15","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1742387,"visible":true,"origin":"","legend":"","description":"","filename":"DetectingtheCriticalThresholdsofanUrbanTrafficSystemUsingPercolationTheory.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6688617/v1_covered_c43cc4f4-de88-4bda-aafc-18b47428a05f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Detecting the Critical Thresholds of an Urban Traffic System Using Percolation Theory","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-6688617/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6688617/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e \u003cb\u003eWe employ high-resolution speed data to develop a percolation theory-based network analysis framework by integrating two identified critical thresholds. 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