A note on the equilibrium M/G/1 queue length

A note on the equilibrium M/G/1 queue length

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Article ID: iaor1988780
Country: Israel
Volume: 25
Issue: 1
Start Page Number: 228
End Page Number: 231
Publication Date: Mar 1988
Journal: Journal of Applied Probability
Authors:
Abstract:

This note concerns the distribution of the equilibrium M/G/1 queue length. A representation for the probability generating function is given which allows for an explicit finite sum representation of the associated probabilities. The radius of convergence of the probability generating function and an asymptotic formula for the right tail of the distribution also follow from this representation, as well as infinite divisibility of the queue-length distribution when the service distribution is infinitely divisible. Extension of these results to the bulk arrival case is straightforward.

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