Queueing Systems

, Volume 26, Issue 1, pp 169–186

New bounds for expected delay in FIFO M/G/c queues

  • Alan Scheller-Wolf
  • Karl Sigman

DOI: 10.1023/A:1019177023405

Cite this article as:
Scheller-Wolf, A. & Sigman, K. Queueing Systems (1997) 26: 169. doi:10.1023/A:1019177023405


Most bounds for expected delay, E[D], in GI/GI/c queues are modifications of bounds for the GI/GI/1 case. In this paper we exploit a new delay recursion for the GI/GI/c queue to produce bounds of a different sort when the traffic intensity p = λ/μ = E[S]/E[T] is less than the integer portion of the number of servers divided by two. (S AND T denote generic service and interarrival times, respectively.) We derive two different families of new bounds for expected delay, both in terms of moments of S AND T. Our first bound is applicable when E[S2] < ∞. Our second bound for the first time does not require finite variance of S; it only involves terms of the form E[Sβ], where 1 < β < 2. We conclude by comparing our bounds to the best known bound of this type, as well as values obtained from simulation.

delay finite moments GI/GI/c queue bounds 

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Alan Scheller-Wolf
    • 1
  • Karl Sigman
    • 2
  1. 1.Graduate School of Industrial AdministrationCarnegie Mellon UniversityPittsburghUSA
  2. 2.Department of Industrial Engineering and Operations ResearchColumbia UniversityNew YorkUSA

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