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Discrete-time GI/G/1 retrial queues with time-controlled vacation policies

Discrete-time GI/G/1 retrial queues with time-controlled vacation policies A discrete-time GI/G/1 retrial queue with Bernoulli retrials and time-controlled vacation policies is investigated in this paper. By representing the inter-arrival, service and vacation times using a Markov-based approach, we are able to analyze this model as a level-dependent quasi-birth-and-death (LDQBD) process which makes the model algorithmically tractable. Several performance measures such as the stationary probability distribution and the expected number of customers in the orbit have been discussed with two different policies: deterministic time-controlled system and random time-controlled system. To give a comparison with the known vacation policy in the literature, we present the exhaustive vacation policy as a contrast between these policies under the early arrival system (EAS) and the late arrival system with delayed access (LAS-DA). Significant difference between EAS and LAS-DA is illustrated by some numerical examples. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Discrete-time GI/G/1 retrial queues with time-controlled vacation policies

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References (45)

Publisher
Springer Journals
Copyright
Copyright © 2013 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-013-0244-0
Publisher site
See Article on Publisher Site

Abstract

A discrete-time GI/G/1 retrial queue with Bernoulli retrials and time-controlled vacation policies is investigated in this paper. By representing the inter-arrival, service and vacation times using a Markov-based approach, we are able to analyze this model as a level-dependent quasi-birth-and-death (LDQBD) process which makes the model algorithmically tractable. Several performance measures such as the stationary probability distribution and the expected number of customers in the orbit have been discussed with two different policies: deterministic time-controlled system and random time-controlled system. To give a comparison with the known vacation policy in the literature, we present the exhaustive vacation policy as a contrast between these policies under the early arrival system (EAS) and the late arrival system with delayed access (LAS-DA). Significant difference between EAS and LAS-DA is illustrated by some numerical examples.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Nov 29, 2013

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