Analytical study on the criticality of the Stochastic Optimal Velocity model

TL;DR

This paper analytically investigates a stochastic extension of the Optimal Velocity traffic model, deriving the fundamental diagram and critical points for traffic jams, and comparing these with the classical model.

Contribution

It provides an explicit analytical estimation of the fundamental diagram and critical points in a stochastic optimal velocity model with a step function.

Findings

Fundamental diagram forms an inverted-λ shape.

Critical point formula for traffic jam onset derived.

Comparison highlights key differences from classical models.

Abstract

In recent works, we have proposed a stochastic cellular automaton model of traffic flow connecting two exactly solvable stochastic processes, i.e., the Asymmetric Simple Exclusion Process and the Zero Range Process, with an additional parameter. It is also regarded as an extended version of the Optimal Velocity model, and moreover it shows particularly notable properties. In this paper, we report that when taking Optimal Velocity function to be a step function, all of the flux-density graph (i.e. the fundamental diagram) can be estimated. We first find that the fundamental diagram consists of two line segments resembling an {\it inversed-$\lambda$} form, and next identify their end-points from a microscopic behaviour of vehicles. It is otable that by using a microscopic parameter which indicates a driver's sensitivity to the traffic situation, we give an explicit formula for the critical point at which a traffic jam phase arises. We also compare these analytical results with those of the Optimal Velocity model, and point out the crucial differences between them.