Traffic flow on directed square lattice

The generic phase transition from a phase of freely flowing traffic of electronic data packets to a congested phase is studied in a very simple model. Here the network is an oriented square lattice. Packets are randomly introduced at the nodes located at one boundary with a certain posting rate, they execute a directed diffusive motion transverse to the boundary and are delivered at nodes positioned at the opposite boundary. There exists the possibility of accumulation of packets forming queues at all nodes and at every time-step data packets up to a maximum number m are allowed to move out of every queue on a first-in-first-out (FIFO) basis. A phase transition between a free-flow to a congested phase is observed at a critical value of the posting rate of packets where the mean load of the system diverges. The characteristic time or latency distribution shows log-normal behavior.