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Author Dallery, Yves ♦ Liu, Zhen ♦ Towsley, Don
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1994
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Fork-Join queuing networks ♦ Blocking before service ♦ Concavity ♦ Duality ♦ Equivalence ♦ Marked graphs ♦ Queuing theory ♦ Symmetry ♦ Throughput
Abstract In this paper, we study quantitative as well as qualitative properties of Fork-Join Queuing Networks with Blocking (FJQN/Bs). Specifically, we prove results regarding the equivalence of the behavior of a FJQN/B and that of its duals and a strongly connected marked graph. In addition, we obtain general conditions that must be satisfied by the service times to guarantee the existence of a long-term throughput and its independence on the initial configuration. We also establish conditions under which the reverse of a FJQN/B has the same throughput as the original network. By combining the equivalence result for duals and the reversibility result, we establish a symmetry property for the throughput of a FJQN/B. Last, we establish that the throughput is a concave function of the buffer sizes and the initial marking, provided that the service times are mutually independent random variables belonging to the class of PERT distributions that includes the Erlang distributions. This last result coupled with the symmetry property can be used to identify the initial configuration that maximizes the long-term throughput in closed series-parallel networks.
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 1994-09-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 41
Issue Number 5
Page Count 40
Starting Page 903
Ending Page 942

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Source: ACM Digital Library