The Renewal-Based Asymptotics and Accelerated Estimation of a System with Random Volume Customers

Abstract

We consider a single-server system in which each customer is described by its service time and a random volume. The total volume of customers accepted by the system is upper bounded by a finite constant (system capacity) M. We give renewal-based approximations for a number of important stationary parameters of the system, in particular, the mean lost volume. For a large M, the loss is typically a rare event, and Crude Monte-Carlo method is time-consuming to obtain accurate estimate of the loss probability in an acceptable simulation time. We apply splitting method to speed-up estimation of the parameters by simulation. In particular, we focus on heavy load. We perform simulations for different values of capacity, different volume size distributions, including heavy- and light-tailed distributions, and also for different values of traffic intensity.