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

## TL;DR

This paper introduces a novel M/G/c/c state-dependent queuing model for tandem road sections that incorporates upstream demand and downstream supply, providing accurate traffic flow predictions and performance metrics.

## Contribution

It extends existing linear models to include flow variables and mutual dependence between road sections, enhancing traffic flow modeling accuracy.

## Key findings

- Model accurately captures traffic dynamics.
- Provides reliable throughput and travel time estimates.
- Outperforms previous models in simulation comparisons.

## 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.