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The Mk/M/∞ queue with heterogeneous customers in a batch

Part of: Special processes Operations research and management science Markov processes

Published online by Cambridge University Press:  14 July 2016

Bong Dae Choi  and
Kwang Kyu Park
Bong Dae Choi*
Affiliation:
Korea Advanced Institute of Science and Technology
Kwang Kyu Park*
Affiliation:
Korea Advanced Institute of Science and Technology
*
∗Postal address: Department of Mathematics, Korea Advanced Institute of Science and Technology, P.O. Box 150, Cheongryang, Seoul, Korea.
∗Postal address: Department of Mathematics, Korea Advanced Institute of Science and Technology, P.O. Box 150, Cheongryang, Seoul, Korea.
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Abstract

We consider the Mk/M/∞ queue with k heterogeneous customers in a batch where the customer of type i in a batch requires an exponential service time with parameter µi. In steady state, the joint generating function of the number of customers of type i being served in the system is derived explicitly by solving a partial differential equation.

Keywords

JOINT GENERATING FUNCTIONBATCH SERVICE

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Short Communications
Information
Journal of Applied Probability , Volume 29 , Issue 2 , June 1992 , pp. 477 - 481
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

Supported by a grant from Korea Science and Engineering Foundation 1990–1993.

References

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