Dynamical Phase Transition in One Dimensional Traffic Flow Model with Blockage

TL;DR

This paper investigates how a blockage affects traffic flow in a cellular automaton model, revealing phase transitions and finite-size effects, with exact analytical expressions for key quantities.

Contribution

It introduces a modified cellular automaton model with a blockage, identifying phase boundaries and deriving exact formulas for flow characteristics.

Findings

Identification of free, jam, and mixed phases in traffic flow.

Exact expressions for flow and density at phase boundaries.

Finite-size effects significantly influence phase transition behavior.

Abstract

Effects of a bottleneck in a linear trafficway is investigated using a simple cellular automaton model. Introducing a blockage site which transmit cars at some transmission probability into the rule-184 cellular automaton, we observe three different phases with increasing car concentration: Besides the free phase and the jam phase, which exist already in the pure rule-184 model, the mixed phase of these two appears at intermediate concentration with well-defined phase boundaries. This mixed phase, where cars pile up behind the blockage to form a jam region, is characterized by a constant flow. In the thermodynamic limit, we obtain the exact expressions for several characteristic quantities in terms of the car density and the transmission rate. These quantities depend strongly on the system size at the phase boundaries; We analyse these finite size effects based on the finite-size scaling.