The Mn/Gn/1 queue with vacations and exhaustive service

Binyamin Oz; Ivo Adan; Moshe Haviv

doi:10.1016/j.ejor.2019.03.016

The M_n/G_n/1 queue with vacations and exhaustive service

Binyamin Oz, Ivo Adan, Moshe Haviv

The Hebrew University of Jerusalem

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

Abstract

We consider the M_n/G_n/1 queue with vacations and exhaustive service in which the server takes (repeated) vacations whenever it becomes idle, the service time distribution is queue length dependent, and the arrival rate varies both with the queue length and with the status of the server, being busy or on vacation. Using a rate balance principle, we derive recursive formulas for the conditional distribution of residual service or vacation time given the number of the customers in the system and the status of the server. We also derive a closed-form expression for the steady-state distribution as a function of the probability of an empty system. As an application of the above, we provide a recursive computation method for Nash equilibrium joining strategies to the observable M/G/1 queue with vacations.

Original language	English
Pages (from-to)	945-952
Number of pages	8
Journal	European Journal of Operational Research
Volume	277
Issue number	3
DOIs	https://doi.org/10.1016/j.ejor.2019.03.016
State	Published - 19 Sep 2019

Keywords

Nash equilibrium
Queueing
Rate balance
Residual lifetime
Server vacations

All Science Journal Classification (ASJC) codes

General Computer Science
Modelling and Simulation
Management Science and Operations Research
Information Systems and Management

Access to Document

10.1016/j.ejor.2019.03.016

Cite this

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title = "The Mn/Gn/1 queue with vacations and exhaustive service",

abstract = "We consider the Mn/Gn/1 queue with vacations and exhaustive service in which the server takes (repeated) vacations whenever it becomes idle, the service time distribution is queue length dependent, and the arrival rate varies both with the queue length and with the status of the server, being busy or on vacation. Using a rate balance principle, we derive recursive formulas for the conditional distribution of residual service or vacation time given the number of the customers in the system and the status of the server. We also derive a closed-form expression for the steady-state distribution as a function of the probability of an empty system. As an application of the above, we provide a recursive computation method for Nash equilibrium joining strategies to the observable M/G/1 queue with vacations.",

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AU - Adan, Ivo

AU - Haviv, Moshe

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N2 - We consider the Mn/Gn/1 queue with vacations and exhaustive service in which the server takes (repeated) vacations whenever it becomes idle, the service time distribution is queue length dependent, and the arrival rate varies both with the queue length and with the status of the server, being busy or on vacation. Using a rate balance principle, we derive recursive formulas for the conditional distribution of residual service or vacation time given the number of the customers in the system and the status of the server. We also derive a closed-form expression for the steady-state distribution as a function of the probability of an empty system. As an application of the above, we provide a recursive computation method for Nash equilibrium joining strategies to the observable M/G/1 queue with vacations.

AB - We consider the Mn/Gn/1 queue with vacations and exhaustive service in which the server takes (repeated) vacations whenever it becomes idle, the service time distribution is queue length dependent, and the arrival rate varies both with the queue length and with the status of the server, being busy or on vacation. Using a rate balance principle, we derive recursive formulas for the conditional distribution of residual service or vacation time given the number of the customers in the system and the status of the server. We also derive a closed-form expression for the steady-state distribution as a function of the probability of an empty system. As an application of the above, we provide a recursive computation method for Nash equilibrium joining strategies to the observable M/G/1 queue with vacations.

KW - Nash equilibrium

KW - Queueing

KW - Rate balance

KW - Residual lifetime

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DO - 10.1016/j.ejor.2019.03.016

M3 - مقالة

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