A rigorous treatment of a follow-the-leader traffic model with traffic lights present

Brenna Argall, Eugene Cheleshkin, J. M. Greenberg*, Colin Hinde, Pei Jen Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)149-168
Number of pages20
JournalSIAM Journal on Applied Mathematics
Issue number1
StatePublished - Aug 2002


  • Conservation laws
  • Follow-the-leader
  • Relaxation models
  • Traffic flow

ASJC Scopus subject areas

  • Applied Mathematics

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