On the asymptotic analysis of statistical multiplexers with hyper-bursty arrivals

Abstract

We consider multiplexers in discrete time fed by the superposition of “Ternary Markov Sources”. Such sources are the natural extension of the Binary Markov Sources (BMS) recently used to model bursty arrivals in a high speed environment. Unlike BMS, we allow sources to have arbitrary (large) variance in the duration of their OFF (silence) or ON (burst) periods. This paper focuses mainly on the impact of large variability either in the ON or OFF period on the performance. Following some asymptotic analysis, simple results on the tail behavior of the number of cells queued in the multiplexer are given. Our results indicate that ignoring the variability in the ON period may grossly underestimate the cell buildup in the multiplexer queue for all levels of the utilization. Furthermore, the impact of large variability of the OFF period depends very much on the utilization of the system. For a lightly-loaded multiplexer (utilization below a given threshold), the impact of large variability of the OFF period is minimal. However, for a heavy-loaded multiplexer (utilization above the threshold) the impact of the large variability in the OFF period is similar to that of the ON period.