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We propose in this article a M/G/c/c state dependent queuing model for roadtraffic flow. The model is based on finite capacity queuing theory whichcaptures the stationary density-flow relationships. It is also inspired fromthe deterministic Godunov scheme for the road traffic simulation. We firstpresent a reformulation of the existing linear case of M/G/c/c state dependentmodel, in order to use flow rather than speed variables. We then extend thismodel in order to consider upstream traffic demand and downstream trafficsupply. After that, we propose the model for two road sections in tandem whereboth sections influence each other. In order to deal with this mutualdependence, we solve an implicit system given by an algebraic equation.Finally, we derive some performance measures (throughput and expected traveltime). A comparison with results predicted by the M/G/c/c state dependentqueuing networks shows that the model we propose here captures really thedynamics of the road traffic.

M/G/c/c state dependent queuing model for a road traffic system of two sections in tandem