On regenerative envelopes for cluster model simulation

Abstract

We continue to develop a novel approach for confidence estimation of the stationary measures in the model describing high performance multiserver queueing systems, such as high performance clusters (HPC). We call this model cluster model. This model is described by a stochastic process, and in the framework of the approach, we construct two envelopes, minorant and majorant regenerative processes for the queue size process in the original system. These envelopes have classical regenerations while the original process may not be regenerative or its regenerations happen too rare to be useful for statistical estimation. It allows to construct confidence intervals for the steady-state queue size of the cluster model. We use simulation to illustrate the applicability of the approach and give recommendations how to select the predefined parameters of the envelopes to increase the efficiency of estimation. As simulation shows, the constructed envelopes allow to estimate the mean stationary queue size in the original system with a given accuracy in an acceptable time.