Approximate analytic performance study of an ATM switching element with train arrivals

A N×N switching element with output queueing, as used in a large asynchronous transfer mode (ATM) switching network, is considered. All the inlets of the switching elements are synchronized on minislots, where a minislot is the fixed-length time unit for transmission of one minicell. When entering the network, an ATM cell is converted into a minicell train, consisting of a fixed number of minicells. Using a two-state model, it is assumed that on each inlet, the number of minicell trains in an active period and the length of a silence period are both geometrically distributed, and the arriving minicell trains are uniformly distributed among all the outlets. The performance of the switching element can thus be obtained by analyzing one single output queue, which can be modeled as a discrete-time single-server queue with train arrivals. An upper bound and an approximate expression for the mean queue length are derived. An analytical method to obtain an upper bound and an approximation for the tail distribution of the queue length are presented. A comparison with simulation results shows that this upper bound is very tight