QUASI-PRODUCT FORM TO A MULTINODE QUEUEING SYSTEM WITH A
COMMON EXPONENTIAL SETUP SERVER
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Published:1999-01
Issue:1
Volume:13
Page:103-119
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ISSN:0269-9648
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Container-title:Probability in the Engineering and Informational Sciences
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language:en
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Short-container-title:Prob. Eng. Inf. Sci.
Abstract
We consider a K-node queueing system sharing
a setup server. Each node has a node server, a waiting
position, and a service position, and it behaves as an
M/G/1/2 type queue except that each job in the waiting
position requires a setup by the setup server to move to
the service position. The service discipline of the setup
server is nonpreemptive work-conserving random selection.
The setup times have a common exponential distribution.
The main purpose of this paper is to derive the stationary
distribution for the K-node system. For each node,
we construct a corresponding setup server queue (CSQ).
The stationary distribution of the K-node system
is given by a product form of the stationary distributions
of CSQs. This result enables us to obtain the stationary
distribution of a K-node system by analyzing individual
CSQs.
Publisher
Cambridge University Press (CUP)
Subject
Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability
Cited by
1 articles.
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