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M/g/c/c State Dependent Queueing Model for Road Traffic Simulation |
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PP: 59-68 |
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doi:10.18576/amis/110108
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Author(s) |
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Nacira Guerrouahane,
Djamil Aissani,
Louiza Bouallouche-Medjkoune,
Nadir Farhi,
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Abstract |
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| In this paper, we present a stochastic queuing model for the road traffic, which captures the stationary density-flow
relationships in both uncongested and congestion conditions. The proposed model is based on the M/g/c/c state dependent queuing
model of Jain and Smith, and is inspired from the deterministic Godunov scheme for the road traffic simulation. We first propose a
reformulation of the M/g/c/c state dependent model that works with density-flow fundamental diagrams rather than density-speed
relationships. We then extend this model in order to consider upstream traffic demand as well as downstream traffic supply. Finally
we calculate the speed and travel time distributions for the M/g/c/c state dependent queuing model and for the proposed model and
we derive stationary performance measures (expected number of cars, blocking probability, expected travel time and throughput). A
comparison with results predicted by the M/g/c/c state dependent queuing model shows that the proposed model correctly represents
the dynamic of traffic and gives a good performances measures. The results illustrate the good accuracy of the proposed model. |
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