A Hyperbolic Transport Model for Passenger Flow on Tram Networks

A Hyperbolic Transport Model for Passenger Flow on Tram Networks | 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Article A Hyperbolic Transport Model for Passenger Flow on Tram Networks Thomas Schillinger This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8985432/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 6 You are reading this latest preprint version Abstract We introduce a modeling framework for an urban tram network based on a hyperbolicpartial differential equation describing the transport of passengers along the network,coupled with a family of stochastic processes representing passenger boarding. Solutionsare considered in a measure-valued sense. The system is further extended and subjectedto uncertainties such as delays and service interruptions through a numerical study. Itsrobustness is assessed using appropriate risk measures. AMS Classification. 90B20, 65M06, 60K30 Hyperbolic transport equation on networks passenger flow modeling measure-valued solutions Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 29 Apr, 2026 Reviewers agreed at journal 15 Apr, 2026 Reviewers invited by journal 09 Mar, 2026 Editor assigned by journal 04 Mar, 2026 Submission checks completed at journal 03 Mar, 2026 First submitted to journal 27 Feb, 2026 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-8985432","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":602990121,"identity":"c0c3988c-ea69-4091-92da-79b6cc717db5","order_by":0,"name":"Thomas Schillinger","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABFElEQVRIiWNgGAWjYFACHoYDDwokQCzGBwwMYAYDM4SRgFtLggFYJbMB0VoYEgzALDYJmBgzhMKuRb797EGgLRZ58u69z6p5d1gw6LafPfa4oMIimoE9+QA2LQZn8hJADis2PHPc7DbvGQkGszN56cYzzkjkNvA8w2qNgQSPAUhL4sYZaWy3edsk6rcdyDGTBjJyGyRyDLA6bAZMy/xnbMVAlQxm598AtfwDacn/gNUzN6Ba5kuwsTGDtdwA2dIAtgWrDoMzORAtG3jSmCXngrUAbeE5JpHbxvMMu8Pazxh/+FBRlzi//Rjjh7dtdUCHAW3hqanL7WdPfoDVGrh1B9BF2PCqB1nXQEjFKBgFo2AUjFgAANaoW380RzhLAAAAAElFTkSuQmCC","orcid":"","institution":"University of Mannheim","correspondingAuthor":true,"prefix":"","firstName":"Thomas","middleName":"","lastName":"Schillinger","suffix":""}],"badges":[],"createdAt":"2026-02-27 08:38:25","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8985432/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8985432/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104783440,"identity":"7eea3c60-a61e-4f3c-ae71-1686ce1bee96","added_by":"auto","created_at":"2026-03-17 07:58:59","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":559104,"visible":true,"origin":"","legend":"","description":"","filename":"TramModelingSubmission02.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8985432/v1_covered_60453876-dbcb-41de-81f8-203bbb87a4f7.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Hyperbolic Transport Model for Passenger Flow on Tram Networks","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"computational-science-and-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Computational Science and Engineering](https://link.springer.com/journal/44207)","snPcode":"44207","submissionUrl":"https://submission.springernature.com/new-submission/44207/3","title":"Computational Science and Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Open","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Hyperbolic transport equation on networks, passenger flow modeling, measure-valued solutions","lastPublishedDoi":"10.21203/rs.3.rs-8985432/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8985432/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe introduce a modeling framework for an urban tram network based on a hyperbolicpartial differential equation describing the transport of passengers along the network,coupled with a family of stochastic processes representing passenger boarding. Solutionsare considered in a measure-valued sense. The system is further extended and subjectedto uncertainties such as delays and service interruptions through a numerical study. Itsrobustness is assessed using appropriate risk measures.\u003c/p\u003e\n\u003cp\u003eAMS Classification. 90B20, 65M06, 60K30\u003c/p\u003e","manuscriptTitle":"A Hyperbolic Transport Model for Passenger Flow on Tram Networks","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-16 13:30:53","doi":"10.21203/rs.3.rs-8985432/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2026-04-29T13:58:44+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"83565505913000275704594717922902369824","date":"2026-04-15T09:06:52+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-03-09T08:53:19+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-03-04T14:23:34+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-03-03T14:12:34+00:00","index":"","fulltext":""},{"type":"submitted","content":"Computational Science and Engineering","date":"2026-02-27T08:25:33+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"computational-science-and-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Computational Science and Engineering](https://link.springer.com/journal/44207)","snPcode":"44207","submissionUrl":"https://submission.springernature.com/new-submission/44207/3","title":"Computational Science and Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Open","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"1d0dc20a-ad16-4b2b-9df6-4dabc5d14a43","owner":[],"postedDate":"March 16th, 2026","published":true,"recentEditorialEvents":[{"type":"editorInvitedReview","content":"","date":"2026-04-29T13:58:44+00:00","index":27,"fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-03-16T13:30:53+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-16 13:30:53","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8985432","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8985432","identity":"rs-8985432","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}