Open AccessState of the Art—Networks of Queues: A Survey of Weak Convergence Results
Author(s) -
Austin J. Lemoine
Publication year - 1978
Publication title -
management science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.954
H-Index - 255
eISSN - 1526-5501
pISSN - 0025-1909
DOI - 10.1287/mnsc.24.11.1175
Subject(s) - convergence (economics) , queue , weak convergence , limit (mathematics) , markov process , computer science , state (computer science) , mathematical optimization , mathematical economics , mathematics , algorithm , economics , mathematical analysis , computer network , statistics , economic growth
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.