Rare event simulation of delay in packet switching networks using DPR-based splitting

Rare event simulation using splitting has been shown to provide significant speed-up for large classes of problems, especially when queue length distribution is of primary interest. However, choice of the control parameters is much less straightforward in cases where splitting is applied to systems in which the target event is delay, rather than packet loss. We propose a control strategy for splitting that allows computationally efficient analysis of very low delay threshold probabilities which typically occur in communication networks. A different technique is required for delay because unlike the cell or packet loss case, the target event (delay) and the prerequisite condition that leads to a rare delay event (a full buffer) do not coincide temporally. We demonstrate the technique by using it to measure delay probabilities in three examples: a simple ATM multiplexer, a queueing system with multiple traffic classes, and a tandem queueing network with tagged and background traffic.