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On a tandem queueing model with identical service times at both counters, II

Published online by Cambridge University Press:  01 July 2016

O. J. Boxma
O. J. Boxma*
Affiliation:
University of Utrecht
*
∗Postal address: Mathematical Institute, University of Utrecht, Budapestlaan 6, Utrecht 3508 TA, The Netherlands.
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Abstract

This paper is devoted to the practical implications of the theoretical results obtained in Part I [1] for queueing systems consisting of two single-server queues in series in which the service times of an arbitrary customer at both queues are identical. For this purpose some tables and graphs are included. A comparison is made—mainly by numerical and asymptotic techniques—between the following two phenomena: (i) the queueing behaviour at the second counter of the two-stage tandem queue and (ii) the queueing behaviour at a single-server queue with the same offered (Poisson) traffic as the first counter and the same service-time distribution as the second counter. This comparison makes it possible to assess the influence of the first counter on the queueing behaviour at the second counter. In particular we note that placing the first counter in front of the second counter in heavy traffic significantly reduces both the mean and variance of the total time spent in the second system.

Keywords

QUEUEING THEORYTANDEM QUEUESSOJOURN TIMEASYMPTOTICSNUMERICAL RESULTS
Type
Research Article
Information
Advances in Applied Probability , Volume 11 , Issue 3 , September 1979 , pp. 644 - 659
Copyright
Copyright © Applied Probability Trust 1979 

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References

1. Boxma, O. J. (1979) On a tandem queueing model with identical service times at both counters, I. Adv. Appl. Prob. 11, 616–643.Google Scholar
2. Boxma, O. J. (1977) Analysis of Models for Tandem Queues. Ph.D. Thesis, University of Utrecht.Google Scholar
3. Boxma, O. J. (1978) On the longest service time in a busy period of the M/G/1 queue. Stock. Proc. Appl. 8, 93–100.CrossRefGoogle Scholar
4. Burke, P. J. (1964) The dependence of delays in tandem queues. Ann. Math. Statist. 35, 874–875.CrossRefGoogle Scholar
5. Kleinrock, L. (1964) Communication Nets; Stochastic Message Flow and Delay. McGraw-Hill, New York.Google Scholar
6. Krämer, W. (1973) Total waiting time distribution function and the fate of a customer in a system with two queues in series. Proc. 7th ITC Conference.Google Scholar
7. Loève, M. (1960) Probability Theory. Van Nostrand, New York.Google Scholar
8. Reich, E. (1957) Waiting times when queues are in tandem. Ann. Math. Statist. 28, 768–773.Google Scholar