Performance of a non-blocking space-division packet switch in a time variant non-uniform traffic environment

The authors study the performance of a non-blocking space-division packet switch, which experiences nonuniform traffic intensities that also change as a function of time. A finite-state Markov chain is used as an underlying process to govern the time variation of traffic for the entire switch. The packet arrivals at each input form an independent Bernoulli process modulated by the underlying Markov chain. Also, the output address of each packet is independently and randomly assigned with probability distributions, which are gain modulated by the Markov chain. Provided that the traffic at each output is not dominated by individual inputs, it is shown that the service time of each input queue for sufficiently large switches can be characterized by an independent Markov-modulated phase-type process. A matrix geometric solution for the resultant quasi-birth-death-type queuing process is presented. The maximum throughput is obtained at the system saturation. The performance of the switch is numerically examined under various traffic conditions. A contention priority scheme is also proposed to improve the switch performance