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The Maximum Queue Length for Heavy-Tailed Service Times in the M/G/1 FB Queue

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Abstract

This paper treats the maximum queue length M, in terms of the number of customers present, in a busy cycle in the M/G/1 queue. The distribution of M depends both on the service time distribution and on the service discipline. Assume that the service times have a logconvex density and the discipline is Foreground Background (FB). The FB service discipline gives service to the customer(s) that have received the least amount of service so far. It is shown that under these assumptions the tail of M is bounded by an exponential tail. This bound is used to calculate the time to overflow of a buffer, both in stable and unstable queues.

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  1. University of Amsterdam, Plantage Muidergracht 24, 1018 TV, Amsterdam, The Netherlands

    M.F.M. Nuyens

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  1. M.F.M. Nuyens
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Nuyens, M. The Maximum Queue Length for Heavy-Tailed Service Times in the M/G/1 FB Queue. Queueing Systems 47, 107–116 (2004). https://doi.org/10.1023/B:QUES.0000032803.93977.bd

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  • DOI: https://doi.org/10.1023/B:QUES.0000032803.93977.bd

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