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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

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