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

Nacira Guerouahane (1) , Djamil Aissani (1) , Nadir Farhi (2) , Louiza Bouallouche-Medjkoune (1)

1 Unité de recherche LaMOS = Research unit LaMOS - Unité de recherche Laboratoire de Modélisation et Optimisation des Systèmes [Université de Béjaïa]
2 IFSTTAR/COSYS/GRETTIA - Génie des Réseaux de Transport Terrestres et Informatique Avancée

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.

Mots clés: TRAFFIC FLOW; FINITE QUEUING SYSTEM; M/G/C/C STATE DEPENDENT

Mots clés: MODELISATION

Domaines: Recherche opérationnelle [math.OC]; Modélisation et simulation

Nacira Guerouahane, Djamil Aissani, Nadir Farhi, Louiza Bouallouche-Medjkoune. M/G/c/c state dependent queuing model for a road traffic system of two sections in tandem. Computers and Operations Research, 2017, 87, pp.98-106. ⟨10.1016/j.cor.2017.05.017⟩. ⟨hal-01611598⟩