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

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

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

[1] Brandt, A. and Sulanke, H. (1987) On the GI/M/∞ queue with batch arrivals of constant size. QUESTA 2, 187–200.Google Scholar
[2] Chaudhry, M. L. and Templeton, J. G. C. (1983) A First Course in Bulk Queues. Wiley, New York.Google Scholar
[3] Choi, B. D. and Park, K. K. (1990) The M/G/1 retrial queue with Bernoulli schedule. QUESTA 7, 219–227.Google Scholar
[4] Flatto, L. and Hahn, (1984) Two parallel queues created by arrivals with two demands I. SIAM. J. Appl. Math. 44, 1041–1053.CrossRefGoogle Scholar
[5] Holman, D. F., Chaudhry, M. L. and Kashyap, B. R. K. (1982) On the number in the system GIX/M/∞ . Sankhya 44, 294–297.Google Scholar
[6] Holman, D. F., Chaudhry, M. L. and Kashyap, B. R. K. (1983) On the service system MX/G/8. Eur. J. Operat Res. 13, 142–145.CrossRefGoogle Scholar
[7] Liu, L. (1990) Infinite Server Queues with Batch Arrivals. , University of Toronto.Google Scholar