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Author McKenna, James
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1987
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract Striking progress has been made recently in obtaining expressions for the sojourn time distribution function (STDF) of a job at a $\textit{c}-server,$ first-come, first-serve (FCFS) center in a closed, product-form queuing network. These results have more recently been extended, and expressions have been obtained for the joint distribution function (DF) of the sojourn times of a job at a sequence of single-server, FCFS centers lying on an “overtake-free” path. However, these formulas present considerable computational problems in the case of large, closed queuing networks. In this paper, asymptotic techniques developed by Mitra and McKenna for the calculation of the partition function of large, product-form closed queuing networks are applied to the sojourn time problem. Asymptotic expansions are obtained for the STDF of a job at $\textit{c}-server,$ FCFS center in closed, product-form queuing networks. Similar expansions are obtained for the joint DF of the sojourn times of a job at a sequence of single server, FCFS centers lying on an “overtake-free” path. In addition, integral expressions are obtained for the STDF of a job at a single server, FCPS center in a closed, product-form queuing network in which all the centers are load independent. These integral expressions also yield useful asymptotic expansions. Finally, integral expressions are also obtained for the joint DF of the sojourn times of a job at the centers of an “overtake-free” path in such a network.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1987-10-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 34
Issue Number 4
Page Count 19
Starting Page 985
Ending Page 1003


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Source: ACM Digital Library