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Some Problems in Traffic Delay

Author

Listed:
  • George H. Weiss

    (Institute for Fluid Dynamics and Applied Mathematics, College Park, Maryland)

  • Alexei A. Maradudin

    (Institute for Fluid Dynamics and Applied Mathematics, College Park, Maryland)

Abstract

The problems that are considered here concern the delay to a single car waiting at a stop sign for a sufficiently large gap in the oncoming traffic to present itself so that the driver considers it safe to cross the highway. The systematic application of renewal theory techniques offers a method of solving these problems, which is much simpler than the combinatorial solutions published by Tanner and Mayne in the treatment of somewhat simpler versions. It is assumed that successive gaps in the main highway traffic are uncorrelated random variables with known probability density. We treat the case that the probability of crossing the highway is a known function, a ( t ) rather than a step function. It is shown that the distribution of delay times satisfies a convolution integral equation, and that the moments are easily found using Laplace transforms Integral equations are also found for the delay distribution when the gap distribution is non-stationary, e.g., when traffic light effects are important. Finally the case of semi-Markov correlated gaps are considered, and a formal expression for the delay distribution is given.

Suggested Citation

  • George H. Weiss & Alexei A. Maradudin, 1962. "Some Problems in Traffic Delay," Operations Research, INFORMS, vol. 10(1), pages 74-104, February.
  • Handle: RePEc:inm:oropre:v:10:y:1962:i:1:p:74-104
    DOI: 10.1287/opre.10.1.74
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    Cited by:

    1. Xiaoping Guo & Michael C. Dunne & John A. Black, 2004. "Modeling of Pedestrian Delays with Pulsed Vehicular Traffic Flow," Transportation Science, INFORMS, vol. 38(1), pages 86-96, February.
    2. Abhishek & Marko A. A. Boon & Michel Mandjes, 2019. "Generalized gap acceptance models for unsignalized intersections," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(3), pages 385-409, June.
    3. Abhishek, & Boon, Marko A.A. & Mandjes, Michel & Núñez-Queija, Rudesindo, 2019. "Congestion analysis of unsignalized intersections: The impact of impatience and Markov platooning," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1026-1035.
    4. Dekker, H., 1991. "Multisite spin hopping analysis of multilevel dissipative quantum tunneling and coherence at finite temperatures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 178(2), pages 289-331.
    5. Zheng, Yinan & Elefteriadou, Lily, 2017. "A model of pedestrian delay at unsignalized intersections in urban networks," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 138-155.

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