A Product Form Approximation for Arbitrary Discrete Time Networks of Shared Buffer Queues

Abstract

A product form approximation, based on the principle of maximum entropy (ME), is characterised for arbitrary open discrete time queueing network models (QNMs) of shared buffer ATM switches under the departures first (DF) buffer management policy. Traffic entering and flowing in the network is assumed to be bursty and is modelled by a Compound Bernoulli Process (CBP) with geometrically distributed bulk sizes. Entropy maximisation implies decomposition of the network into individual shared buffer switches which are analysed to obtain cell loss probabilities and mean delays. The ME queue length distribution of a single shared buffer queue under DF policy, together with closed form expressions for the first two moments of the effective flow, play the role of building blocks in the solution process. Typical numerical results are included to demonstrate the utility and computational efficiency of the ME procedure. Comments on current work, involving discrete time finite capacity queues with space priority and correlated traffic, are included.