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On interchangeability for exponential single-server queues in tandem

Published online by Cambridge University Press:  14 July 2016

Masaaki Kijima  and
Naoki Makimoto
Masaaki Kijima*
Affiliation:
The University of Tsukuba, Tokyo
Naoki Makimoto*
Affiliation:
Tokyo Institute of Technology
*
∗Postal address: Graduate School of Systems Management, The University of Tsukuba, Bunkyo-ku, Tokyo 112, Japan.
∗∗Postal address: Department of Information Sciences, Tokyo Institute of Technology, Meguro-ku, Tokyo 152, Japan.
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Abstract

Consider two exponential single-server queues in tandem and suppose that service rates of customer n are λ n and μ n respectively. In this note, a simple and direct proof is given of the fact that the departure process from the tandem queue is statistically unaffected when the service rates are interchanged if λ n – μn is independent of n. The proof is based only on the memoryless property of exponential distributions.

Keywords

TANDEM QUEUEMEMORYLESS PROPERTY
Type
Short Communications
Information
Journal of Applied Probability , Volume 27 , Issue 2 , June 1990 , pp. 459 - 464
Copyright
Copyright © Applied Probability Trust 1990 

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References

[1] Anantharam, V. (1987) Probabilistic proof of the interchangeability of ·/M/1 queues in series. Queueing Systems 2, 387–392.Google Scholar
[2] Cunningham, A. A. and Dutta, S. K. (1973) Scheduling jobs with exponentially distributed processing times on two machines of a flow shop. Naval Res. Logist. Quart. 16, 69–81.Google Scholar
[3] Ku, P. S. and Niu, S. C. (1986) On Johnson's two-machine flow shop with random processing times. Operat. Res. 34, 130–136.Google Scholar
[4] Lehtonen, T. (1986) On the ordering of tandem queues with exponential servers. J. Appl. Prob. 23, 115–129.Google Scholar
[5] Stoyan, D. (1983) Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.Google Scholar
[6] Tembe, S. V. and Wolff, R. W. (1974) The optimal order of service in tandem queues. Operat. Res. 22, 824–832.Google Scholar
[7] Tsoucas, P. and Walrand, J. (1987) On the interchangeability and stochastic ordering of ·/M/1 queues in tandem. Adv. Appl. Prob. 19, 515–520.Google Scholar
[8] Weber, R. (1979) The interchangeability of ·/M/1 queues in series. J. Appl. Prob. 16, 690–695.Google Scholar