Asymptotic Analysis of Traffic Lights Performance Under Heavy Traffic Assumption

Larisa Afanasyeva and Ekaterina Bulinskaya ()
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Larisa Afanasyeva: Moscow State University
Ekaterina Bulinskaya: Moscow State University

Methodology and Computing in Applied Probability, 2013, vol. 15, issue 4, 935-950

Abstract: 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.

Keywords: Asymptotic analysis; Traffic lights; Heavy traffic conditions; Primary 90B20; Secondary 90B22, 60F05 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s11009-012-9291-x

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