On resource management and QoS guarantees for long range dependent traffic

The effect of long-memory processes on queue length statistics of a single queue system is studied through a controlled fractionally differenced ARIMA (1,d,0) input process. This process has two parameters φ₁ and d representing an auto-regressive component and a long-range dependent component, respectively. Results show that the queue length statistics studied (mean, variance and the 0.999 quantile) are proportional to e(c^cφ1) e(c₂d), where (c ₁, c₂) are positive constants, and c₂>c₁. The effect of the auto-correlation structure on queue length statistics is also dependent on the tail of the distribution of the input process. Therefore, multiplexing gains can be achieved for long-range dependent processes because the resulting process has a tighter tail distribution. Given these observations, and the need to provide guaranteed maximum-delay, delay-jitter bounds, and low cell-loss probabilities, the solution appears to be (a) allocating higher rates if the distribution tails are large, (b) using multiplexing to narrow these tails, (c) applying a per circuit frame-clock in conjunction with an active cell-discard strategy to deal with long-range dependence