Algorithmic analysis of the Geo/Geo/c retrial queue

In this paper, we consider a discrete-time queue of Geo/ Geo/ c type with geometric repeated attempts. It is known that its continuous counterpart, namely the M/ M/ c queue with exponential retrials, is analytically intractable due to the spatial heterogeneity of the underlying Markov chain, caused...

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Bibliographic Details
Published in:European journal of operational research 2008-09, Vol.189 (3), p.1042-1056
Main Authors: Artalejo, Jesus R., Economou, Antonis, Gómez-Corral, Antonio
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Busy period
Exact sciences and technology
Geo/ Geo/ c queue
Markov analysis
Matrix-analytic methods
Operational research and scientific management
Operational research. Management science
Queueing
Queuing theory
Queuing theory. Traffic theory
Retrials
Stationary distribution
Studies
Waiting time
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Summary:In this paper, we consider a discrete-time queue of Geo/ Geo/ c type with geometric repeated attempts. It is known that its continuous counterpart, namely the M/ M/ c queue with exponential retrials, is analytically intractable due to the spatial heterogeneity of the underlying Markov chain, caused from the retrial feature. In discrete-time, the occurrence of multiple events at each slot increases the complexity of the model and raises further computational difficulties. We propose several algorithmic procedures for the efficient computation of the main performance measures of this system. More specifically, we investigate the stationary distribution of the system state, the busy period and the waiting time. Several numerical examples illustrate the analysis.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2007.01.060