Jamming of directed traffic on a square lattice

TL;DR

This paper investigates the phase transition from free-flow to jammed states in a square lattice traffic network, analyzing how data posting rate and neighbor selection influence congestion.

Contribution

It introduces a parameter controlling neighbor selection based on queued traffic and maps the critical conditions for jamming in the network.

Findings

Critical data posting rate determines jamming transition

Average load diverges logarithmically near critical point

Queue length distribution varies between exponential and algebraic forms

Abstract

Phase transition from a free-flow phase to a jammed phase is an important feature of traffic networks. We study this transition in the case of a simple square lattice network for different values of data posting rate $(\rho)$ by introducing a parameter $p$ which selects a neighbour for onward data transfer depending on queued traffic. For every $\rho$ there is a critical value of $p$ above which the system become jammed. The $\rho-p$ phase diagram shows some interesting features. We also show that the average load diverges logarithmically as $p$ approaches $p_c$ and the queue length distribution exhibits exponential and algebraic nature in different regions of the phase diagram.