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The queue GI/Hm/s in continuous time

Published online by Cambridge University Press:  14 July 2016

Jos H. A. De smit
Jos H. A. De smit*
Affiliation:
Twente University of Technology
*
∗Postal address: Department of Applied Mathematics, Twente University of Technology, P.O. Box 217, 7500 AE Enschede, The Netherlands.
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Abstract

This is an extension of our previous paper [4] on the queue GI/Hm/s. In that paper we have derived results for the actual waiting time, the number of customers in the system at arrival epochs and the number of customers during a busy cycle. Here we obtain results for the virtual waiting time and the number of customers in the system at arbitrary times.

Keywords

MULTISERVER QUEUEHYPEREXPONENTIAL SERVICE TIMESVIRTUAL WAITING TIMEQUEUE LENGTH IN CONTINUOUS TIME
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 1 , March 1985 , pp. 214 - 222
Copyright
Copyright © Applied Probability Trust 1985 

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References

[1] Cohen, J. W. (1982) The Single Server Queue. North-Holland, Amsterdam.Google Scholar
[2] De Smit, J. H. A. (1973) Some general results for many server queues. Adv. Appl. Prob. 5, 153–169.Google Scholar
[3] De Smit, J. H. A. (1973) On the many server queue with exponential service times. Adv. Appl. Prob. 5, 170–182.Google Scholar
[4] De Smit, J. H. A. (1983) The queue GI/M/s with customers of different types or the queue GI/Hm/s. Adv. Appl. Prob. 15, 392–419.CrossRefGoogle Scholar
[5] De Smit, J. H. A. (1983) A numerical solution for the multi-server queue with hyperexponential service times. Operat. Res. Letters 2, 217–224.Google Scholar