Maximum Entropy Analysis of Queueing Network Models

The principle of Maximum Entropy (ME) provides a consistent method of inference for estimating the form of an unknown discrete-state probability distribution, based on information expressed in terms of tree expected values. In this tutorial paper entropy maximisation is used to characterise product-form approximations and resolution algorithms for arbitrary continuoustime and discrete-time Queueing Network Models (QNMs) at equilibrium under RepetitiveService (RS) blocking and Arrivals First (AF) or Departures First (DF) buffer management policies. An ME application to the performance modelling of a shared-buffer Asynchronous Transfer Mode (ATM) switch architecture is also presented. The ME solutions are implemented subject to Generalised Exponential (GE) and Generalised Geometric (GGeo) queueing theoretic mean value constraints, as appropriate. In this context, single server GE and GGeo type queues in conjunction with associated effective flow streams (departure, splitting, merging) are used as building blocks in the solution process. Physical interpretations of the results are given and extensions to the quantitative analysis of more complex queueing networks are discussed.