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 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 it 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 startup 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. 'This research was partially supported by the Applied Mathematical Sciences Program, U.S. Department of Energy and by the US. National Science Foundation. 1 DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or sewice by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement. reammendrtion. or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. . . . DISCLAIMER Portions of this document may 'be illegible in electronic image products. Images are produced from the best available original document.