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THE ISRAELI QUEUE WITH INFINITE NUMBER OF GROUPS

Published online by Cambridge University Press:  19 November 2013

Nir Perel  and
Uri Yechiali
Nir Perel
Affiliation:
Department of Statistics and Operations Research, School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, Israel. E-mail: perelnir@post.tau.ac.il; uriy@post.tau.ac.il
Uri Yechiali
Affiliation:
Department of Statistics and Operations Research, School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, Israel. E-mail: perelnir@post.tau.ac.il; uriy@post.tau.ac.il
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Abstract

The so called “Israeli Queue” is a single server polling system with batch service of an unlimited size, where the next queue to be visited is the one in which the first customer in line has been waiting for the longest time. The case with finite number of queues (groups) was introduced by Boxma, Van der Wal and Yechiali [3]. In this paper we extend the model to the case with a (possibly) infinite number of queues. We analyze the M/M/1, M/M/c, and M/M/1/N—type queues, as well as a priority model with (at most) M high-priority classes and a single lower priority class. In all models we present an extensive probabilistic analysis and calculate key performance measures.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 28 , Issue 1 , January 2014 , pp. 1 - 19
Copyright
Copyright © Cambridge University Press 2013 

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