Multiple-server polling systems

A multiple-server polling system is a multiple-queue system attended to by a number of servers. Like the single-server versions, multiple-server polling systems find many applications in computer systems, communication networks and manufacturing environments. We consider multiple-server polling systems in which each server visits the queues according to a general service order table. Such systems are generally very hard to analyze by means of mathematical techniques. We show how the model can be analyzed by means of the so-called power-series algorithm (PSA), a promising tool for the numerical evaluation and optimization of a broad class of multi-queue models. The PSA can be applied to determine the joint probability distributions of the queue lengths and the positions of the servers in the system. From the latter joint distribution other relevant performance measures like the mean waiting times and utilization factors of the individual servers may be obtained. Numerical experiments with the PSA are performed to investigate the tendency for the servers to cluster, to address the option of partitioning the system, and to make some comparisons with single-server systems carrying a comparable load.