The Israeli Queue with a general group-joining policy

Nir Perel; Uri Yechiali

doi:10.1007/s10479-015-1942-1

The Israeli Queue with a general group-joining policy

Nir Perel, Uri Yechiali^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We consider a single-server multi-queue system with unlimited-size batch service where the next queue to be served is the one with the most senior customer (the so called ‘Israeli Queue’). We study a Markovian system with state-dependent group-joining policy and derive results for various performance measures, such as steady-state distribution of the number of groups in the system, sojourn times, group sizes, and lengths of busy periods. Closed-form expressions are obtained for both the Uniform and the Geometric joining policies. Numerical results are presented.

Original language	English
Pages (from-to)	179-212
Number of pages	34
Journal	Annals of Operations Research
Volume	317
Issue number	1
DOIs	https://doi.org/10.1007/s10479-015-1942-1
State	Published - Oct 2022

Keywords

Busy periods
Group sizes
Israeli Queue
Queueing
Sojourn times
Unlimited-size batch service

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10.1007/s10479-015-1942-1

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title = "The Israeli Queue with a general group-joining policy",

abstract = "We consider a single-server multi-queue system with unlimited-size batch service where the next queue to be served is the one with the most senior customer (the so called {\textquoteleft}Israeli Queue{\textquoteright}). We study a Markovian system with state-dependent group-joining policy and derive results for various performance measures, such as steady-state distribution of the number of groups in the system, sojourn times, group sizes, and lengths of busy periods. Closed-form expressions are obtained for both the Uniform and the Geometric joining policies. Numerical results are presented.",

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AB - We consider a single-server multi-queue system with unlimited-size batch service where the next queue to be served is the one with the most senior customer (the so called ‘Israeli Queue’). We study a Markovian system with state-dependent group-joining policy and derive results for various performance measures, such as steady-state distribution of the number of groups in the system, sojourn times, group sizes, and lengths of busy periods. Closed-form expressions are obtained for both the Uniform and the Geometric joining policies. Numerical results are presented.

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KW - Group sizes

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KW - Sojourn times

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The Israeli Queue with a general group-joining policy

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Keywords

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