NDLI: Equivalence, reversibility, symmetry and concavity properties in fork-join queuing networks with blocking

Content Provider	ACM Digital Library
Author	Dallery, Yves Liu, Zhen Towsley, Don
Copyright Year	1994
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.
Starting Page	903
Ending Page	942
Page Count	40
File Format	PDF
ISSN	00045411
e-ISSN	1557735X
DOI	10.1145/185675.185776
Journal	Journal of the ACM (JACM)
Volume Number	41
Issue Number	5
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1994-09-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Fork-Join queuing networks Blocking before service Concavity Duality Equivalence Marked graphs Queuing theory Symmetry Throughput
Content Type	Text
Resource Type	Article
Subject	Hardware and Architecture Information Systems Control and Systems Engineering Artificial Intelligence Software

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