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

Binyamin Oz (Corresponding author), Ivo Adan, Moshe Haviv

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

Uittreksel

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.
TaalEngels
Pagina's945-952
TijdschriftEuropean Journal of Operational Research
Volume277
Nummer van het tijdschrift3
DOI's
StatusGepubliceerd - 19 sep 2019

Vingerafdruk

Vacation
Queue
Servers
Server
Queue Length
Joining
M/G/1 Queue
Steady-state Distribution
Recursive Formula
Conditional Distribution
Nash Equilibrium
Closed-form
Customers
Vary
Dependent

Citeer dit

Oz, Binyamin ; Adan, Ivo ; Haviv, Moshe. / The Mn/Gn/1 queue with vacations and exhaustive service. In: European Journal of Operational Research. 2019 ; Vol. 277, Nr. 3. blz. 945-952
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The Mn/Gn/1 queue with vacations and exhaustive service. / Oz, Binyamin (Corresponding author); Adan, Ivo; Haviv, Moshe.

In: European Journal of Operational Research, Vol. 277, Nr. 3, 19.09.2019, blz. 945-952.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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