Limits and approximations for the M/G/1 LIFO waiting-time distribution

Authors:
Joseph Abate;Ward Whitt
Affiliations:
900 Hammond Road, Ridgewood, NJ 07450-2908, USA;AT&T Labs Research, Room 2C-178, Murray Hill, NJ 07974-0636, USA
Venue:
Operations Research Letters
Year:
1997

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Abstract

We provide additional descriptions of the steady-state waiting-time distribution in the M/G/1 queue with the last-in firstout (LIFO) service discipline. We establish heavy-traffic limits for both the cumulative distribution function (cdf) and the moments. We develop an approximation for the cdf that is asymptotically correct both as the traffic intensity @r - 1 for each time t and as t - ~ for each @r. We show that in heavy traffic the LIFO moments are related to the FIFO moments by the Catalan numbers. We also develop a new recursive algorithm for computing the moments.