Discrete-time queueing models with feedback for input-buffered ATM switches

We present the analysis of some discrete-time single-server queueing models with feedback that capture the behavior of the head-of-line request queues in large input-buffered ATM switches when correlation in the destinations of the cell streams at the input links is present. Three different switch selection policies are considered: message based first-in-first-out, cell based first-in-first-out or round-robin and cell based random-order-of-service. Although some close analogy exists with continuous-time feedback queueing models, the discrete-time nature of the models considered here brings about some complications not found in the former. The joint analysis, based on generating functions, of the system contents and the waiting time of a tagged message leads to a number of (functional) equations. Without explicitly solving these equations, mean values and higher-order moments for the (conditional) waiting time are obtained. Numerical results illustrate the effect of correlation in the cell destinations and of burstiness in the input traffic on switch performance.