Bound analysis for WRR scheduling in a statistical multiplexer with burstysources

Among various cell scheduling schemes for ATM networks, weighted round-robi n (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, determ inistic vacations, and bursty input sources, which serves as a bound analys is for WRR scheduling in ATM networks. Similar models have been studied as well in the context of TDMA (time division multiple access) schemes with mu ltiple contiguous slots assigned per frame [3,16]. For the model under stud y, after establishing an expression for the probability generating function (pgf) of the system contents, we derive closed-form expressions for perfor mance 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 clos ed 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 probabi lity area. We also discuss the impact of the slot assignment cycle of WRR o n the system performance.