Effect of stochastic transition in the fundamental diagram of traffic flow

TL;DR

This paper introduces a stochastic mesoscopic model for traffic flow that captures both the fundamental diagram and its variance, providing insights into flow-concentration relations and transition dynamics with minimal parameters.

Contribution

The work presents a novel stochastic model based on vehicle speed transitions that accounts for uncertainty in traffic flow and includes vehicle size effects through a maximum congestion density parameter.

Findings

Model accurately reproduces the fundamental diagram and its variance.

Analytic solutions derived for simplified speed states.

Model captures capacity drop at maximum flow.

Abstract

In this work, we propose an alternative stochastic model for the fundamental diagram of traffic flow with minimal number of parameters. Our approach is based on a mesoscopic viewpoint of the traffic system in terms of the dynamics of vehicle speed transitions. A key feature of the present approach lies in its stochastic nature which makes it possible to study not only the flow-concentration relation, namely, the fundamental diagram, but also its uncertainty, namely, the variance of the fundamental diagram \textemdash an important characteristic in the observed traffic flow data. It is shown that in the simplified versions of the model consisting of only a few speed states, analytic solutions for both quantities can be obtained, which facilitate the discussion of the corresponding physical content. We also show that the effect of vehicle size can be included into the model by introducing the maximal congestion density $k_{max}$. By making use of this parameter, the free flow region and congested flow region are naturally divided, and the transition is characterized by the capacity drop at the maximum of the flow-concentration relation. The model parameters are then adjusted to the observed traffic flow on the I-80 Freeway Dataset in the San Francisco area from the NGSIM program, where both the fundamental diagram and its variance are reasonably reproduced. Despite its simplicity, we argue that the current model provides an alternative description for the fundamental diagram and its uncertainty in the study of traffic flow.