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Sojourn times in vacation and polling systems with Bernoulli feedback

Published online by Cambridge University Press:  14 July 2016

T. Takine ,
H. Takagi  and
T. Hasegawa
T. Takine*
Affiliation:
Kyoto University
H. Takagi*
Affiliation:
IBM Research Division
T. Hasegawa*
Affiliation:
Kyoto University
*
∗Postal address: Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, Kyoto 606, Japan.
∗∗Postal address: IBM Tokyo Research Laboratory, 5–9, Sanbancho, Chiyodaku, Tokyo 102, Japan.
∗Postal address: Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, Kyoto 606, Japan.
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Abstract

We study sojourn times in M/G/1 multiple vacation systems and multiqueue cyclic-service (polling) systems with instantaneous Bernoulli feedback. Three service disciplines, exhaustive, gated, and 1-limited, are considered for both M/G/1 vacation and polling systems. The Laplace-Stieltjes transforms of the sojourn time distributions in the three vacation systems are derived. For polling systems, we provide explicit expressions for the mean sojourn times in symmetric cases. Furthermore a pseudo-conservation law with respect to the mean sojourn times is derived for a polling system with a mixture of the three service disciplines.

Keywords

QUEUESPSEUDO-CONSERVATION LAWS
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 2 , June 1991 , pp. 422 - 432
Copyright
Copyright © Applied Probability Trust 1991 

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