Bound analysis for WRR scheduling in a statistical multiplexer with bursty sources

Among various cell scheduling schemes for ATM networks, weighted round-robin (WRR) seems a promising algorithm for explicit bandwidth allocation [15]. In this paper, we present a method for analyzing a discrete-time queueing model of a statistical multiplexer with contiguous slot assignments, deterministic vacations, and bursty input sources, which serves as a bound analysis for WRR scheduling in ATM networks. Similar models have been studied as well in the context of TDMA (time division multiple access) schemes with multiple contiguous slots assigned per frame [3,16]. For the model under study, after establishing an expression for the probability generating function (pgf) of the system contents, we derive closed-form expressions for performance measures such as the expected value, and an asymptotic approximation for the tail probabilities of the system contents distribution. Also, after examining the cell delay, we formulate the pgf of the cell delay in a closed form in terms of the system contents pgf. The numerical results obtained for the system contents and cell delay distributions illustrate that they match with simulation results extremely well, especially in the low probability area. We also discuss the impact of the slot assignment cycle of WRR on the system performance.