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Asymptotic Analysis of Traffic Lights Performance Under Heavy Traffic Assumption

Author

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  • Larisa Afanasyeva

    (Moscow State University)

  • Ekaterina Bulinskaya

    (Moscow State University)

Abstract

The main drawback of Markov models for traffic lights performance considered in our previous investigations is exponential distribution of intervals between lights switchings. To analyze the impact of this assumption we introduce a model with arbitrary distribution of interswitching intervals. An algorithm is proposed to calculate imbedded Markov chain stationary probabilities and mean length of a queue at crossroads. Although the difference between two models (exponentially distributed and constant intervals) is slight for traffic intensity ρ ≈ 0.5, it is significant for ρ close to 1. We investigate the queue length behaviour as ρ → 1. Weak convergence of normalized characteristics (waiting time, queue length etc.) to exponential ones can be established under heavy traffic assumption. To prove one uses the asymptotic equivalence of these characteristics to supremum of a random walk with zero reflecting boundary.

Suggested Citation

  • Larisa Afanasyeva & Ekaterina Bulinskaya, 2013. "Asymptotic Analysis of Traffic Lights Performance Under Heavy Traffic Assumption," Methodology and Computing in Applied Probability, Springer, vol. 15(4), pages 935-950, December.
    • Handle: RePEc:spr:metcap:v:15:y:2013:i:4:d:10.1007_s11009-012-9291-x
    DOI: 10.1007/s11009-012-9291-x
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    References listed on IDEAS

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    1. Baykal-Gürsoy, M. & Xiao, W. & Ozbay, K., 2009. "Modeling traffic flow interrupted by incidents," European Journal of Operational Research, Elsevier, vol. 195(1), pages 127-138, May.
    2. Schadschneider, Andreas, 2000. "Statistical physics of traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 285(1), pages 101-120.
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    Cited by:

    1. L. G. Afanasyeva, 2020. "Asymptotic Analysis of Queueing Models Based on Synchronization Method," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1417-1438, December.

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