The Renewal-Based Asymptotics and Accelerated Estimation of a System with Random Volume Customers
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.
KeywordsQueueing system Random volume customer Finite capacity Accelerated simulation Splitting Heavy-tailed volume
Research is supported by Russian Foundation for Basic Research, projects 15-07-02341, 15-07-02354, 15-07-02360.
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