Hostname: page-component-745bb68f8f-s22k5 Total loading time: 0 Render date: 2025-02-11T23:35:59.679Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

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.)

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