M/g/c/c state dependent queueing model for road traffic simulation

TL;DR

This paper introduces a stochastic queueing model for road traffic that accurately captures congestion dynamics and stationary flow-density relationships, extending existing models with new formulations and performance metrics.

Contribution

The paper reformulates the $M/g/c/c$ model to use density-flow diagrams, extends it to include upstream demand and downstream supply, and derives new performance measures for traffic simulation.

Findings

The proposed model accurately predicts traffic flow and congestion states.

It provides reliable estimates of travel time and throughput.

The model outperforms previous approaches in representing traffic dynamics.

Abstract

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 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 dynamics of traffic and gives good performances measures. The results illustrate the good accuracy of the proposed model.