Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-27T20:00:19.634Z Has data issue: false hasContentIssue false
  • English
  • Français

A new heavy traffic limit for the asymmetric shortest queue problem

Published online by Cambridge University Press:  01 October 1999

CHARLES KNESSL
CHARLES KNESSL
Affiliation:
Department of Mathematics, Statistics and Computer Science (M/C 249) University of Illinois at Chicago, Chicago, IL 60607-7045
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the classic shortest queue problem in the heavy traffic limit. We assume that the second server works slowly and that the service rate of the first server is nearly equal to the arrival rate. Solving for the (asymptotic) joint steady state queue length distribution involves analyzing a backward parabolic partial differential equation, together with appropriate side conditions. We explicitly solve this problem. We thus obtain a two-dimensional approximation for the steady state queue length probabilities.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 10 , Issue 5 , October 1999 , pp. 497 - 509
Copyright
1999 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)