Stability of join-the-shortest-queue networks: Analysis by fluid limits

J. G. Dai, John J. Hasenbein, Bara Kim

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The standard fluid model tool is employed to investigate stability behavior in a variant of a generalized Jackson queueing network. In the network, some customers use a join-the-shortest-queue policy when entering the network or moving to the next station. Furthermore, we allow interarrival and service times to have general distributions. For networks with two stations, necessary and sufficient conditions are given for positive Harris recurrence of the network process. These conditions involve only the mean values of the network primitives. Two counterexamplesare provided to show that more information on distributions and tie-breaking probabilities is needed for networks with more than two stations, in order to characterize the stability of such systems. However, if the routing probabilities in the network satisfy a certain homogeneity condition, then it is proved that the stability behavior can be explicitly determined, again using the mean value parameters of the network.

Original languageEnglish
Title of host publicationInternational Series in Operations Research and Management Science
PublisherSpringer New York LLC
Pages461-487
Number of pages27
Volume154
DOIs
Publication statusPublished - 2011

Publication series

NameInternational Series in Operations Research and Management Science
Volume154
ISSN (Print)08848289

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ASJC Scopus subject areas

  • Management Science and Operations Research
  • Strategy and Management
  • Applied Mathematics
  • Computer Science Applications
  • Software

Cite this

Dai, J. G., Hasenbein, J. J., & Kim, B. (2011). Stability of join-the-shortest-queue networks: Analysis by fluid limits. In International Series in Operations Research and Management Science (Vol. 154, pp. 461-487). (International Series in Operations Research and Management Science; Vol. 154). Springer New York LLC. https://doi.org/10.1007/978-1-4419-6472-4_10