Asymptotic analysis for loss probability of queues with finite GI/M/1 type structure

Authors:
Jeongsim Kim;Bara Kim
Affiliations:
Department of Mathematics Education, Chungbuk National University, Chungbuk, Republic of Korea 361-763;Department of Mathematics and Telecommunication Mathematics Research Center, Korea University, Seoul, Republic of Korea 136-701
Venue:
Queueing Systems: Theory and Applications
Year:
2007

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Tail asymptotics of the waiting time and the busy period for the $${{\varvec{M/G/1/K}}}$$ queues with subexponential service times

Queueing Systems: Theory and Applications

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Abstract

This paper discusses the asymptotic behavior of the loss probability for general queues with finite GI/M/1 type structure such as GI/M/c/K, SM/M/1/K and GI/MSP/1/K queues. We find an explicit expression for the asymptotic behavior of the loss probability as K tends to infinity. With the result, it is shown that the loss probability tends to 0 at a geometric rate.