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Note on a series for M/G/1 queues

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  • Percy H. Brill

Abstract

This paper provides a geometrical (physical) interpretation for a series representing the steady-state probability density function (pdf) of wait in a standard M/G/1 queue. This series was called 'intriguing' by a prominent queueing theorist in 1975. The series converges geometrically fast, making it potentially useful for approximating the pdf. We provide an intuitive explanation in terms of sample-path upcrossings of a level of the virtual wait. We also consider a similar series for an M/G/1 variant with zero-wait customers receiving special service. This leads to a generalised explanation of both series in terms of sample-path upcrossings.

Suggested Citation

  • Percy H. Brill, 2009. "Note on a series for M/G/1 queues," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 5(3), pages 363-373.
    • Handle: RePEc:ids:ijores:v:5:y:2009:i:3:p:363-373
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