The shorter queue polling model

I.J.B.F. Adan; O.J. Boxma; S. Kapodistria; V.G. Kulkarni

doi:10.1007/s10479-013-1495-0

The shorter queue polling model

I.J.B.F. Adan, O.J. Boxma, S. Kapodistria, V.G. Kulkarni

Stochastic Operations Research

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

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Abstract

We consider a two-queue polling model in which customers upon arrival join the shorter of two queues. Customers arrive according to a Poisson process and the service times in both queues are independent and identically distributed random variables having the exponential distribution. The two-dimensional process of the numbers of customers at the queue where the server is and at the other queue is a two-dimensional Markov process. We derive its equilibrium distribution using two methodologies: the compensation approach and a reduction to a boundary value problem. Keywords: Polling models; Join the shorter queue; Compensation approach; Boundary value problem

Original language	English
Pages (from-to)	167-200
Journal	Annals of Operations Research
Volume	241
Early online date	16 Nov 2013
DOIs	https://doi.org/10.1007/s10479-013-1495-0
Publication status	Published - Jun 2016

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title = "The shorter queue polling model",

abstract = "We consider a two-queue polling model in which customers upon arrival join the shorter of two queues. Customers arrive according to a Poisson process and the service times in both queues are independent and identically distributed random variables having the exponential distribution. The two-dimensional process of the numbers of customers at the queue where the server is and at the other queue is a two-dimensional Markov process. We derive its equilibrium distribution using two methodologies: the compensation approach and a reduction to a boundary value problem. Keywords: Polling models; Join the shorter queue; Compensation approach; Boundary value problem",

author = "I.J.B.F. Adan and O.J. Boxma and S. Kapodistria and V.G. Kulkarni",

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AU - Adan, I.J.B.F.

AU - Boxma, O.J.

AU - Kapodistria, S.

AU - Kulkarni, V.G.

PY - 2016/6

Y1 - 2016/6

N2 - We consider a two-queue polling model in which customers upon arrival join the shorter of two queues. Customers arrive according to a Poisson process and the service times in both queues are independent and identically distributed random variables having the exponential distribution. The two-dimensional process of the numbers of customers at the queue where the server is and at the other queue is a two-dimensional Markov process. We derive its equilibrium distribution using two methodologies: the compensation approach and a reduction to a boundary value problem. Keywords: Polling models; Join the shorter queue; Compensation approach; Boundary value problem

AB - We consider a two-queue polling model in which customers upon arrival join the shorter of two queues. Customers arrive according to a Poisson process and the service times in both queues are independent and identically distributed random variables having the exponential distribution. The two-dimensional process of the numbers of customers at the queue where the server is and at the other queue is a two-dimensional Markov process. We derive its equilibrium distribution using two methodologies: the compensation approach and a reduction to a boundary value problem. Keywords: Polling models; Join the shorter queue; Compensation approach; Boundary value problem

U2 - 10.1007/s10479-013-1495-0

DO - 10.1007/s10479-013-1495-0

M3 - Article

SN - 0254-5330

VL - 241

SP - 167

EP - 200

JO - Annals of Operations Research

JF - Annals of Operations Research

ER -

The shorter queue polling model

Abstract

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