The Israeli queue with infinite number of groups

Nir Perel*, Uri Yechiali

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalProbability in the Engineering and Informational Sciences
Volume28
Issue number1
DOIs
StatePublished - 2014

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