Note--Some Results on Sojourn Times in Acyclic Jackson Networks

B. Simon and R. D. Foley
Additional contact information
B. Simon: Bell Laboratories, Holmdel, New Jersey
R. D. Foley: Virginia Polytechnic Institute and State University

Management Science, 1979, vol. 25, issue 10, 1027-1034

Abstract: Lemoine (Lemoine, A. 1977. Networks of queues--a survey of equilibrium analysis. Management Sci. 24 464-481.) studies sojourn times in acyclic, Jackson networks as part of his survey of equilibrium results. In his paper, he argues that a particular customer has a sojourn time at node i that is independent of his remaining sojourn time in the network given that the customer transfer from node i to node j. This assumption is then used to derive a set of equations involving the Laplace-Stieltjes transform of the sojourn times at each node from which several properties of sojourn times are determined. In a private communication, Mitrani (Mitrani, I. 1978. A critical note on a result of Lemoine. Private communication.) argues that the independence assumption is in error and provides a heuristic argument based on a four node, acyclic, Jackson network. From this, Mitrani concludes that the sojourn time in such networks is still an unsolved problem. We make Mitrani's argument rigorous, using some new results on sojourn times in Jackson networks.

Keywords: networks; of; queues (search for similar items in EconPapers)
Date: 1979
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://dx.doi.org/10.1287/mnsc.25.10.1027 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:25:y:1979:i:10:p:1027-1034

Access Statistics for this article

More articles in Management Science from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().