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Some analyses on the control of queues using level crossings of regenerative processes

Published online by Cambridge University Press:  14 July 2016

J. G. Shanthikumar
J. G. Shanthikumar*
Affiliation:
University of Toronto
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Abstract

Some properties of the number of up- and downcrossings over level u, in a special case of regenerative processes are discussed. Two basic relations between the density functions and the expected number of upcrossings of this process are derived. Using these reults, two examples of controlled M/G/1 queueing systems are solved. Simple relations are derived for the waiting time distribution conditioned on the phase of control encountered by an arriving customer. The Laplace-Stieltjes transform of the distribution function of the waiting time of an arbitrary customer is also derived for each of these two examples.

Keywords

QUEUEING SYSTEMSCONTROL OF QUEUESUP- AND DOWNCROSSINGSREGENERATIVE PROCESSES
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 3 , September 1980 , pp. 814 - 821
Copyright
Copyright © Applied Probability Trust 1980 

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