Realization probability in multi-class closed queueing networks (Q1111919)

Perturbation analysis is a technique for estimating the sample derivatives of the throughput with respect to mean service times based on one sample path of a queueing network. It has been proved that the sample derivative converges with probability one to the derivative of the steady-state throughput in a closed single-class Jackson network. In this paper, perturbation analysis of multi-class queueing networks is considered. The realization probability and its properties are discussed. The limiting value of the sample derivative of the system throughput with respect to mean service time can be calculated by using realization probabilities. An example is given to illustrate the idea. Unlike the single-class case, the sample derivative obtained by perturbation analysis in the multi-class case does not generally converge to the derivative of the steady-state throughput. A necessary condition for the perturbation analysis to be an asymptotically unbiased estimate of the derivative of the steady-state throughput is given.