Asymptotic analysis for loss probability of queues with finite <Emphasis Type="Italic">GI</Emphasis>/<Emphasis Type="Italic">M</Emphasis>/1 type structure |
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Authors: | Jeongsim Kim Bara Kim |
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Institution: | (1) Department of Mathematics Education, Chungbuk National University, 12, Gaeshin-dong, Heungduk-ku, Cheongju, Chungbuk, 361-763, Republic of Korea;(2) Department of Mathematics and Telecommunication Mathematics Research Center, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul, 136-701, Republic of Korea |
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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.
This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology
Research Center) support program supervised by the IITA (Institute of Information Technology Assessment). |
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Keywords: | GI/M/1 type Markov chain Stationary distribution Loss probability Maximal eigenvalue Matrix-valued function |
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