Informatics and Applications
2014, Volume 8, Issue 3, pp 19-27ON THE BOUNDS OF THE RATE OF CONVERGENCE AND STABILITY FOR SOME QUEUEING MODELS
- A. I. Zeifman
- A. V. Korotysheva
- K. M. Kiseleva
- V. Yu. Korolev
- S. Ya. Shorgin
Abstract
A generalization of the famous Erlang loss system has been considered, namely, a class of Markovian queueing systems with possible simultaneous arrivals and group services has been studied. Necessary and sufficient conditions of weak ergodicity have been obtained for the respective queue-length process and explicit bounds on the rate of convergence and stability have been found. The research is based on the general approach developed in the authors' previous studies for nonhomogeneous Markov systems with batch arrival and service requirements. Also, specific models with periodic intensities and different maximum size of number of arrival customers are discussed. The main limiting characteristics of these models have been computed and the effect of the maximum size of the group of arrival customers on the limiting characteristics of the queue has been studied.[+] References (18)
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[+] About this article
Title
ON THE BOUNDS OF THE RATE OF CONVERGENCE AND STABILITY FOR SOME QUEUEING MODELSJournal
Informatics and Applications2014, Volume 8, Issue 3, pp 19-27
Cover Date
2014-03-31DOI
10.14357/19922264140303Print ISSN
1992-2264Publisher
Institute of Informatics Problems, Russian Academy of SciencesAdditional Links
Key words
nonstationary Markovian queue; Erlang model; batch arrivals and group services; ergodicity; stability; boundsAuthors
A. I. Zeifman
,
,
,
A. V. Korotysheva, K. M. Kiseleva,
V. Yu. Korolev,
, and S. Ya. Shorgin
Author Affiliations
Institute of Informatics Problems, Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian
Federation
Vologda State University, 15 Lenin Str., Vologda 160000, Russian Federation
Institute of Socio-Economic Development of Territories, Russian Academy of Sciences, 56A Gorkogo Str., Vologda 160014, Russian Federation
Department of
Mathematical Statistics, Faculty of Computational Mathematics and
Cybernetics, M.V. Lomonosov Moscow State University, 1-52 Leninskiye Gory,
GSP-1, Moscow 119991, Russian Federation