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.
Original language | English |
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Pages (from-to) | 47-55 |
Number of pages | 9 |
Journal | Queueing Systems |
Volume | 57 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2007 Sep |
Keywords
- GI/M/1 type Markov chain
- Loss probability
- Matrix-valued function
- Maximal eigenvalue
- Stationary distribution
ASJC Scopus subject areas
- Statistics and Probability
- Computer Science Applications
- Management Science and Operations Research
- Computational Theory and Mathematics