On estimation of the large deviation asymptotic of a single server regenerative stationary queue

A. V. Borodina, E. V. Morozov

Institute of Applied Mathematical Research, Karelian Research Centre, RAS

Abstract: The (small) probabilities estimation of such undesirable events like loss/collapse of data, buffer overflow, collision of packets in the modern telecommunication systems by classical methods requires unacceptable large time and computational efforts. However, exact analytical results are known only for a narrow class of queues and queueing networks. It calls a necessity to develop both asymptotic methods of analysis and speed up simulation to estimate the probabilities of this type. In this paper, a speed-up simulation method based on the splitting of the trajectories of a regenerative process developed by the authors is applied to estimation of the overflow probability for a stationary workload/queue-size process. It allows to simplify and accelerate considerably the estimation of the exponent in the asymptotic representation of the large deviation probability provided that service time has a finite moment generating function (the so-called light tail). Numerical simulation results are presented.

Keywords: large deviation asymptotic; single-server system; stationary waiting time; splitting method; accelerated simulation.