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Tail asymptotics of the queue size distribution in the M/M/m retrial queue
- Authors
- Kim, Jerim; Kim, Jeongsim; Kim, Bara
- Issue Date
- 8월-2012
- Publisher
- ELSEVIER SCIENCE BV
- Keywords
- M/M/m retrial queue; Queue size distribution; Censored Markov process; Tail asymptotics; Karamata Tauberian theorem; Riemann-Lebesgue lemma
- Citation
- JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, v.236, no.14, pp.3445 - 3460
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
- Volume
- 236
- Number
- 14
- Start Page
- 3445
- End Page
- 3460
- ISSN
- 0377-0427
- Abstract
- We consider an M/M/m retrial queue and investigate the tail asymptotics for the joint distribution of the queue size and the number of busy servers in the steady state. The stationary queue size distribution with the number of busy servers being fixed is asymptotically given by a geometric function multiplied by a power function. The decay rate of the geometric function is the offered load and independent of the number of busy servers, whereas the exponent of the power function depends on the number of busy servers. Numerical examples are presented to illustrate the result. (C) 2012 Elsevier B.V. All rights reserved.
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