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State of the Art--Networks of Queues: A Survey of Weak Convergence Results

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  • Austin J. Lemoine

    (Control Analysis Corporation, Palo Alto, California)

Abstract

This report is a sequel to our review paper, Lemoine [Lemoine, A. J. 1977. Networks of queues-A survey of equilibrium analysis. Management sci. 24 464-481.], on the equilibrium analysis of networks of queues. In this paper we review some weak convergence results for networks of queues, which include heavy traffic limit theorems for open networks and asymptotic results for large closed Markovian systems which are generalizations of the classical repairman problem. These weak convergence results justify certain approximation schemes for processes of interest. We also discuss some important open problems in the area of weak convergence results for networks of queues.

Suggested Citation

  • Austin J. Lemoine, 1978. "State of the Art--Networks of Queues: A Survey of Weak Convergence Results," Management Science, INFORMS, vol. 24(11), pages 1175-1193, July.
    • Handle: RePEc:inm:ormnsc:v:24:y:1978:i:11:p:1175-1193
    DOI: 10.1287/mnsc.24.11.1175
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    Cited by:

    1. Edvinas Greičius & Saulius Minkevičius, 2017. "Diffusion limits for the queue length of jobs in multi-server open queueing networks," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 27(4), pages 71-84.

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