Multi-queue system with finite shared buffer under batch Poisson and/or interrupted batch Poisson arrivals: a computational analysis

Abstract

This paper studies a model of a multi-queue system with a finite common buffer shared by queues with batch arrivals. The study is performed for a few buffer-sharing policies. For batch Poisson arrivals with an arbitrary batch size distribution, the analysis benefits from the fact that the stationary state distribution has a product form. For the special case of geometrically distributed batches, closed form solutions for normalisation constant are obtained. They lead to efficient computational procedures. For bursty interrupted batch Poisson arrivals, it is shown that an exact numerical analytic analysis is only possible for very small models. For real-life sized systems, an approximation method has been developed.