A DISCRETE-TIME Geo/G/1 RETRIAL QUEUE WITH SERVER BREAKDOWNS

This paper discusses a discrete-time Geo/G/1 retrial queue with the server subject to breakdowns and repairs. The customer just being served before server breakdown completes his remaining service when the server is fixed. The server lifetimes are assumed to be geometrical and the server repair time...

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Bibliographic Details
Published in:Asia-Pacific journal of operational research Vol. 23; no. 2; pp. 247 - 271
Main Authors: ATENCIA, IVAN, MORENO, PILAR
Format: Journal Article
Language:English
Published: Singapore World Scientific Publishing Co. & Operational Research Society of Singapore 01.06.2006
World Scientific Publishing Co. Pte., Ltd
Subjects:
Breakdowns
Combinatorics
Markov analysis
Operations research
Queuing theory
Recursive algorithms
Servers
Studies
Discrete-time retrial queues
recursive formulae
stochastic decomposition
unreliable server
ISSN:0217-5959, 1793-7019, 0217-5959
Online Access:Get full text
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Summary:This paper discusses a discrete-time Geo/G/1 retrial queue with the server subject to breakdowns and repairs. The customer just being served before server breakdown completes his remaining service when the server is fixed. The server lifetimes are assumed to be geometrical and the server repair times are arbitrarily distributed. We study the Markov chain underlying the considered queueing system and present its stability condition as well as some performance measures of the system in steady-state. Then, we derive a stochastic decomposition law and as an application we give bounds for the proximity between the steady-state distributions of our system and the corresponding system without retrials. Also, we introduce the concept of generalized service time and develop a recursive procedure to obtain the steady-state distributions of the orbit and system size. Finally, we prove the convergence to the continuous-time counterpart and show some numerical results.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0217-5959
1793-7019
0217-5959
DOI:10.1142/S0217595906000929