Article

Queueing Systems

, Volume 40, Issue 1, pp 5-31

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

  • O.J. BoxmaAffiliated withDepartment of Mathematics and Computer Science, Eindhoven University of TechnologyCWI
  • , Q. DengAffiliated withDepartment of Mathematics and Computer Science, Eindhoven University of Technology
  • , A.P. ZwartAffiliated withDepartment of Mathematics and Computer Science, Eindhoven University of Technology

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

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