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Stationary increments of accumulation processes in queues and generalized semi-Markov schemes

Published online by Cambridge University Press:  14 July 2016

R. D. Foley ,
Georgia-Ann Klutke  and
Dieter König
R. D. Foley*
Affiliation:
Georgia Institute of Technology
Georgia-Ann Klutke*
Affiliation:
University of Texas at Austin
Dieter König*
Affiliation:
Mining Academy Freiberg
*
∗ Postal address: Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332–0205, USA.
∗∗ Postal address: Operations Research Group, Department of Mechanical Engineering, University of Texas at Austin, Austin, TX 78712, USA.
∗∗∗ Postal address: Department of Mathematics, Mining Academy Freiberg, D-O 9200 Freiberg, Germany.
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Abstract

Let Tx be the length of time to accumulate x units of a resource. In queueing, the resource could be service. We derive a sufficient condition for the process to have stationary increments where Tx is an additive functional of a Markov process. This condition is satisfied in symmetric queues and generalized semi-Markov schemes with insensitive components. As a corollary, we show that the conditional expected response time in a symmetric queue is linear in the service requirement. A similar result holds for the conditional average residence time of an insensitive component in a GSMS.

Keywords

RANDOM TIME CHANGESYMMETRIC QUEUES
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 4 , December 1991 , pp. 864 - 872
Copyright
Copyright © Applied Probability Trust 1991 

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