Queue-length distributions for two-stage CBR multiplexing

This paper is concerned with the queue length distribution at the output of an ATM multiplexer. More specifically, we derive an upper bound on the complementary queue-length distribution for a multiplex of several pre-aggregated cell streams arising from a multiplex of constant bit rate (CBR) cell streams. An upper bound on the second-stage complementary queuelength distribution is useful when sizing queues and determining cell delay bounds for any system using more than one level of CBR multiplexing. The upper bound is shown to be very tight throughout the domain and hence a very good approximation of the actual distribution. We compare our second-stage upper bound to that obtained by assuming all sources arrive at a single multiplexer (i.e., no pre-aggregation).