On a 2-class polling model with reneging and $$k_i$$ k i -limited service

On a 2-class polling model with reneging and $$k_i$$ k i -limited service Ann Oper Res https://doi.org/10.1007/s10479-018-2915-y ORIGINAL RESEARCH On a 2-class polling model with reneging and k -limited service 1 1 Kevin Granville · Steve Drekic © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract This paper analyzes a 2-class, single-server polling model operating under a k - limited service discipline with class-dependent switchover times. Arrivals to each class are assumed to follow a Poisson process with phase-type distributed service times. Within each queue, customers are impatient and renege (i.e., abandon the queue) if the time before entry into service exceeds an exponentially distributed patience time. We model the queueing system as a level-dependent quasi-birth-and-death process, and the steady-state joint queue length distribution as well as the per-class waiting time distributions are computed via the use of matrix analytic techniques. The impacts of reneging and choice of service time distribution are investigated through a series of numerical experiments, with a particular focus on the determination of (k , k ) which minimizes a cost function involving the expected time a 1 2 customer spends waiting in the queue and an additional penalty cost should reneging take place. Keywords Polling model · k -limited service discipline · Reneging · Quasi-birth-and-death http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Operations Research Springer Journals

On a 2-class polling model with reneging and $$k_i$$ k i -limited service

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Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Business and Management; Operations Research/Decision Theory; Combinatorics; Theory of Computation
ISSN
0254-5330
eISSN
1572-9338
D.O.I.
10.1007/s10479-018-2915-y
Publisher site
See Article on Publisher Site

Abstract

Ann Oper Res https://doi.org/10.1007/s10479-018-2915-y ORIGINAL RESEARCH On a 2-class polling model with reneging and k -limited service 1 1 Kevin Granville · Steve Drekic © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract This paper analyzes a 2-class, single-server polling model operating under a k - limited service discipline with class-dependent switchover times. Arrivals to each class are assumed to follow a Poisson process with phase-type distributed service times. Within each queue, customers are impatient and renege (i.e., abandon the queue) if the time before entry into service exceeds an exponentially distributed patience time. We model the queueing system as a level-dependent quasi-birth-and-death process, and the steady-state joint queue length distribution as well as the per-class waiting time distributions are computed via the use of matrix analytic techniques. The impacts of reneging and choice of service time distribution are investigated through a series of numerical experiments, with a particular focus on the determination of (k , k ) which minimizes a cost function involving the expected time a 1 2 customer spends waiting in the queue and an additional penalty cost should reneging take place. Keywords Polling model · k -limited service discipline · Reneging · Quasi-birth-and-death

Journal

Annals of Operations ResearchSpringer Journals

Published: Jun 6, 2018

References

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