On the asymptotic behavior of heterogeneous statistical multiplexer with applications

The author combines a heterogeneous statistical multiplexer in heavy traffic with different characteristics in discrete time which is representative of the asynchronous transfer mode (ATM) environment at the cell level. An exact formulation of the queuing model for the multiplexer is presented. Using spectral decomposition method and asymptotic analysis, it is shown that for fixed source average utilization and peak rate, as the burst size of the individual sources increase the tail behavior of the distribution of the number of cells queued in the multiplexer has a simple characterization. This characterization provides a simple approximation of the queuing behavior of the multiplexer, where the impact of each source is quite evident. The accuracy of this approximation is examined. Some applications are considered where both buffer sizing and admission control are discussed