THE ISRAELI QUEUE WITH INFINITE NUMBER OF GROUPS

Nir Perel · Uri Yechiali

49 citations0/0 files storedProbability in the Engineering and Informational Sciences

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Advanced Queuing Theory Analysis Optimization and Search Problems Age of Information Optimization

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.

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References

1999Introduction to Matrix Analytic Methods in Stochastic Modeling 1984Matrix-Geometric Solutions to Stochastic Models 1985Analysis of polling systems 2011Applications of polling systems 2005Analysis and control of polling systems

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