Performance evaluation of MMPP/D/1/K queues for aggregate ATM traffic models

The performance of an asynchronous transfer mode (ATM) multiplexer is evaluated, with the aggregate arrivals modeled as a Markov-modulated Poisson process (MMPP). The analysis is based on two simplifying assumptions: the probability that the MMPP goes through multiple state transitions between two successive departures is negligible, and state transitions occur at departure points. The transition probability matrix that describes the number of cells in the buffer after a departure can then be partitioned into submatrices, each of which is analogous to that of an M/D/1/K queue. These assumptions are reasonable for ATM traffic models in which the arrival rates are large and cell size is small. The accuracy of the analysis is evaluated, using a four-state MMPP model to represent the aggregate arrival process. The departure point and arrival point queue-length distributions, cell loss probabilities and average queuing delays are obtained analytically and compared to simulation results