On uniformly distributed on/off arrivals in virtual output queued switches with geometric service times

Virtual queueing is commonly deployed as a buffering technique in high-performance input-queued switch architectures. This paper presents the analysis for discrete-time virtual output queued switches with incoming traffic governed by a uniformly distributed Markov modulated on/off process, and geometrically distributed service times. We utilize the k-step first-passage time probability matrix to derive the probability generating function of the inter-arrival times distribution. Based on the latter, closed-form expressions for the queue size distribution and mean delay are obtained. The validity of the analysis is established through computer simulations.