Queueing Systems

, Volume 40, Issue 1, pp 93–115

The Dependence of Optimal Returns from Multi-class Queueing Systems on Their Customer Base

  • M.J. Dacre
  • K.D. Glazebrook

DOI: 10.1023/A:1017948530608

Cite this article as:
Dacre, M. & Glazebrook, K. Queueing Systems (2002) 40: 93. doi:10.1023/A:1017948530608


We identify structured collections of multi-class queueing systems whose optimal return (a minimised cost) is a supermodular function of the set of customer classes allowed external access to the system. Our results extend considerably the range of systems for which such a claim can be made. The returns from such systems also exhibit a form of directional convexity when viewed as functions of a vector of arrival rates. Applications to load balancing problems are indicated.

achievable region generalised conservation laws Gittins index load balancing multi-class queueing systems supermodular set function stochastic scheduling 

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • M.J. Dacre
    • 1
  • K.D. Glazebrook
    • 1
  1. 1.Department of StatisticsNewcastle UniversityNewcastle upon TyneUK

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