Hostname: page-component-77c89778f8-m8s7h Total loading time: 0 Render date: 2024-07-23T18:09:23.572Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Part of: Special processes Markov 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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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