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Performance-analysis of a switching system using priority-based dynamic capacity allocation is presented. The system provides connectivity between a number of point-to-multipoint communication access clusters. The scheduling of traffic transmission at each access cluster is based on a priority scheme with priority given to real-time (rt) traffic over nonreal-time (nrt) traffic. An analytical model is developed to evaluate the covariance functions of both rt and nrt traffic arriving at the output ports. Aggregate traffic arrival streams are approximated to 2-state Markov-modulated Poisson processes (MMPPs) by matching their statistical characteristics. Analytical and simulation results on performance of an example 4 × 4 switch for different traffic loads are discussed.