A Universal Maximum Entropy Algorithm for General Multiple Class Open Networks with Mixed Service Disciplines

Abstract

The principle of maximum entropy (ME) is used to characterise a new product-form approximation for the analysis of arbitrary open networks of queues at equilibrium with infinite capacities, single servers, multiple job classes, distinct general exogeneous interarrival-time and service-time distributions per class, non-priority (first-come-first-served, processorsharing, last-come-first-served with or without pre or priority (preemptive-resume, non-preemptive head-of-line) service disciplines and random routing under class switching. The ME approximation suggests a decomposition of the open network into individual multiple class G/G/l queues at equilibrium with a revised arrival process for each class of jobs. A universal implementation of the ME solution is achieved by making use of the Generalised Exponential (GE) distribution to model the service and flow processes of each G/G/l queue per class. As a consequence, the ME analysis of open queueing networks can be interpreted in terms of bulkarrival and bulk-service queues with geometrically distributed bulk sizes. The credibility of the ME approximation is demonstrated by some illustrative examples and favourable comparisons with simulation and other approximate methods are made. Comments on the extension of the work to multiple server queues and general closed networks are included.