Non-concave fundamental diagrams and phase transitions in a stochastic traffic cellular automaton

TL;DR

This paper investigates a stochastic cellular automaton traffic model with extreme parameters, revealing four distinct phases, non-concave flow-density relations, and unique phase transition behaviors.

Contribution

It introduces a novel classification of phases in the VDR-TCA model based on their spatiotemporal dynamics and identifies non-concave flow-density regions.

Findings

Four distinct phases identified in the VDR-TCA model.

Non-concave flow-density relation with forward density waves.

Vehicles cannot increase speed once equilibrium is reached.

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.