Queueing Systems

, Volume 40, Issue 1, pp 5–31

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

Authors

  • O.J. Boxma
    • Department of Mathematics and Computer ScienceEindhoven University of Technology
    • CWI
  • Q. Deng
    • Department of Mathematics and Computer ScienceEindhoven University of Technology
  • A.P. Zwart
    • Department of Mathematics and Computer ScienceEindhoven University of Technology
Article

DOI: 10.1023/A:1017913826973

Cite this article as:
Boxma, O., Deng, Q. & Zwart, A. Queueing Systems (2002) 40: 5. doi:10.1023/A:1017913826973

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 queueheterogeneous serversqueue lengthwaiting timetail behaviourslowly varying functionregularly varying distributionsemi-exponential distribution

Copyright information

© Kluwer Academic Publishers 2002