Queueing Systems

, Volume 40, Issue 1, pp 5–31

Waiting-Time Asymptotics for the M/G/2 Queue with Heterogeneous Servers

  • O.J. Boxma
  • Q. Deng
  • A.P. Zwart
Article

Abstract

This paper considers a heterogeneous M/G/2 queue. The service times at server 1 are exponentially distributed, and at server 2 they have a general distribution B(⋅). We present an exact analysis of the queue length and waiting time distribution in case B(⋅) has a rational Laplace–Stieltjes transform. When B(⋅) is regularly varying at infinity of index −ν, we determine the tail behaviour of the waiting time distribution. This tail is shown to be semi-exponential if the arrival rate is lower than the service rate of the exponential server, and regularly varying at infinity of index 1−ν if the arrival rate is higher than that service rate.

M/G/2 queue heterogeneous servers queue length waiting time tail behaviour slowly varying function regularly varying distribution semi-exponential distribution 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • O.J. Boxma
    • 1
    • 2
  • Q. Deng
    • 1
  • A.P. Zwart
    • 1
  1. 1.Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.CWIAmsterdamThe Netherlands

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