Jamming of directed traffic on a square lattice

Abstract

The phase transition from a free-flow phase to a jammed phase is animportant feature of traffic networks. We study this transition in the caseof a simple square lattice network for different values of data posting rate(ρ) by introducinga parameter p which selects a neighbour for onward data transfer depending on queued traffic. For everyρ there is acritical value of p above which the system becomes jammed. Theρ–p phasediagram shows some interesting features. We also show that the average load diverges logarithmicallyas p approaches pc and the queue length distribution exhibits exponential and algebraic nature in differentregions of the phase diagram.