A Rigorous Treatment of a Follow-the-Leader Traffic Model with Traffic Lights Present

Traffic flow on a unidirectional roadway in the presence of traffic lights is modeled. Individual car responses to green, yellow, and red lights are postulated and these result in rules governing the acceleration and deceleration of individual cars. The essence of the model is that only specific car...

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Bibliographic Details
Published inSIAM journal on applied mathematics Vol. 63; no. 1; pp. 149 - 168
Main Authors Argall, Brenna, Cheleshkin, Eugene, Greenberg, J. M., Hinde, Colin, Lin, Pei-Jen
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.08.2002
Subjects
Acceleration
Applied mathematics
Automobiles
Mathematical functions
Pith
Road intersections
Speed
Traffic flow
Traffic lights
Traffic models
Velocity
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Summary:Traffic flow on a unidirectional roadway in the presence of traffic lights is modeled. Individual car responses to green, yellow, and red lights are postulated and these result in rules governing the acceleration and deceleration of individual cars. The essence of the model is that only specific cars are directly affected by the lights. The other cars behave according to simple follow-the-leader rules which limit their speed by the spacing between them and the car directly ahead. The model has a number of desirable properties; namely, cars do not run red lights, cars do not smash into one another, and cars exhibit no velocity reversals. In a situation with multiple lights operating in-phase, we get, after an initial start-up period, a constant number of cars through each light during any green-yellow period. Moreover, this flux is less by one or two cars per period than the flux obtained in discretized versions of the idealized Lighthill-Whitham-Richards model which allows for infinite accelerations.
ISSN:0036-1399
1095-712X
DOI:10.1137/S0036139901391215