Title: M/G/c/c state dependent queuing model for a road traffic system of two sections in tandem,
Abstract: We propose in this article a M/G/c/c state dependent queuing model for road
traffic flow. The model is based on finite capacity queuing theory which
captures the stationary density-flow relationships. It is also inspired from
the deterministic Godunov scheme for the road traffic simulation. We first
present a reformulation of the existing linear case of M/G/c/c state dependent
model, in order to use flow rather than speed variables. We then extend this
model in order to consider upstream traffic demand and downstream traffic
supply. After that, we propose the model for two road sections in tandem where
both sections influence each other. In order to deal with this mutual
dependence, we solve an implicit system given by an algebraic equation.
Finally, we derive some performance measures (throughput and expected travel
time). A comparison with results predicted by the M/G/c/c state dependent
queuing networks shows that the model we propose here captures really the
dynamics of the road traffic.