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The intensity conservation law for queues with randomly changed service rate

Published online by Cambridge University Press:  14 July 2016

Masakiyo Miyazawa
Masakiyo Miyazawa*
Affiliation:
Science University of Tokyo
*
∗Postal address: Department of Information Sciences, Faculty of Science and Technology, Science University of Tokyo, Noda City, Chiba 278, Japan.
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Abstract

König et al. (1978) have derived the so-called intensity conservation law in a stationary process connected with a marked point process (PMP). That law has been shown to be useful in obtaining invariance relations in queues (cf. Franken et al. (1981)). In this paper, somewhat different versions of the intensity conservation laws are derived for a stationary process with jump points. These laws are applied to queues with randomly changed service rate. As special cases, most of equations obtained by König et al.'s law can be derived from this law. Also, we derive some inequalities between characteristic quantities in a queue with a simple type of randomly changed service rate.

Keywords

STATIONARY PROCESS WITH JUMP POINTSPOINT PROCESSQUEUE WITH RANDOM SERVICE RATE
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 2 , June 1985 , pp. 408 - 418
Copyright
Copyright © Applied Probability Trust 1985 

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