Advancing density waves and phase transitions in a velocity dependent randomization traffic cellular automaton

TL;DR

This paper investigates a specific stochastic cellular automaton model of traffic flow, revealing four distinct phases, complex phase transitions, and non-concave flow-density relations with forward propagating density waves.

Contribution

It introduces a detailed classification of phases and transitions in the velocity dependent randomization traffic cellular automaton model, highlighting complex dynamics and wave phenomena.

Findings

Four distinct traffic phases identified

Non-concave flow-density relation with density waves

Vehicles cannot increase speed at equilibrium

Abstract

Within the class of stochastic cellular automata models of traffic flows, we look at the velocity dependent randomization variant (VDR-TCA) whose parameters take on a specific set of extreme values. These initial conditions lead us to the discovery of the emergence of four distinct phases. Studying the transitions between these phases, allows us to establish a rigorous classification based on their tempo-spatial behavioral characteristics. As a result from the system's complex dynamics, its flow-density relation exhibits a non-concave region in which forward propagating density waves are encountered. All four phases furthermore share the common property that moving vehicles can never increase their speed once the system has settled into an equilibrium.