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A TIME-DEPENDENT STUDY OF THE KNOCKOUT QUEUE

Published online by Cambridge University Press:  28 March 2013

Brian Fralix
Brian Fralix*
Affiliation:
Department of Mathematical Sciences Clemson, University Clemson, SC E-mail: bfralix@clemson.edu
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Abstract

We examine the time-dependent behavior of a birth–death process, whose birth rates and death rates are decreasing and increasing, respectively, with respect to the current state. Such models can be used to describe Markovian queueing systems with exponential reneging, where potential arrivals balk with a certain probability that depends on the number of customers observed upon arrival. Our results are derived by interpreting the birth–death process as the queue-length process of what we refer to as the “knockout queue.”

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 3 , July 2013 , pp. 309 - 317
Copyright
Copyright © Cambridge University Press 2013 

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