QUASI-PRODUCT FORM TO A MULTINODE QUEUEING SYSTEM WITH A COMMON EXPONENTIAL SETUP SERVER

Authors:
Genji Yamazaki
Affiliations:
Department of Production and Information Systems, Tokyo Metropolitan Institute of Technology, Hino-city, Tokyo 191, Japan
Venue:
Probability in the Engineering and Informational Sciences
Year:
1999

Citing 1
Cited 1

Open, Closed, and Mixed Networks of Queues with Different Classes of Customers

Journal of the ACM (JACM)

QUASI-PRODUCT FORM TO A MULTINODE QUEUEING SYSTEM SHARING A STATE-DEPENDENT SETUP SERVER

Probability in the Engineering and Informational Sciences

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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.