Some Markovian Queuing Retrial Systems under light-traffic conditions

Date
2001
Authors
Anisimov, V. V.
Kurtulush, M.
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
Source Title
Cybernetics and Systems Analysis
Print ISSN
1060-0396
Electronic ISSN
1573-8337
Publisher
Kluwer Academic Publishers-Plenum Publishers
Volume
37
Issue
6
Pages
876 - 887
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Series
Abstract

The asymptotic behavior of the time of the first loss of a demand in Markovian single-channel and multichannel queuing retrial systems with a finite buffer and an external Markovian environment is analyzed. Two cases are studied: (a) the ratio of the input rate to the service rate tends to zero and (b) the ratio of the input rate to the service rate and the ratio of the input rate to the retrial rate tend to zero simultaneously. The method of so-called S-sets and the concept of a monotone structure introduced by Anisimov are used to prove the exponential approximation of the time of the first call loss and Poisson approximation of a flow of lost demands for both cases.

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Book Title
Keywords
Markovian queuing systems, Retrials, Light - traffic conditions, S-sets, Markovian environment
Citation
Published Version (Please cite this version)