Some Markovian Queuing Retrial Systems under Light-Traffic Conditions

Authors:
V. V. Anisimov;M. Kurtulush
Affiliations:
Taras Shevchenko University, Kiev, Ukraine. Bilkent University, Ankara, Turkey;Bilkent University, Ankara, Turkey
Venue:
Cybernetics and Systems Analysis
Year:
2001

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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 iS-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.