The shorter queue polling model

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-dimensi...

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Bibliographic Details
Published in:Annals of operations research 2016-06, Vol.241 (1-2), p.167-200
Main Authors: Adan, Ivo J. B. F., Boxma, Onno J., Kapodistria, Stella, Kulkarni, Vidyadhar G.
Format: Article
Language:English
Subjects:
Boundary value problems
Business and Management
Combinatorics
Compensation
Costs
Customer services
Customers
Distribution of goods
Management research
Markov processes
Mathematical analysis
Operations research
Operations Research/Decision Theory
Queues
Queuing
Queuing theory
Random variables
Servers
Studies
Telecommunications systems
Theory of Computation
Two dimensional
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Summary: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.
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-013-1495-0