A Maximum Entropy Analysis of the G/G/1 Queue at Equilibrium

The principle of maximum entropy is used to analyse a G/G/1 queue at equilibrium when the constraints involve only the first two moments of the interarrival-time and service-time distributions. Robust recursive relations for the queue-length distribution are determined, and a probability density function analogue is characterized. Furthermore, connections with classical queueing theory and operational analysis are established, and an overall approximation, based on the concept of ‘global’ maximum entropy, is introduced. Numerical examples provide useful information on how critically system behaviour is affected by the distributional form of the interarrival and service times, and favourable comparisons are made with diffusion and other approximations. Comments on the implication of the work to the analysis of more general queueing systems are included.

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