Tail asymptotics for the queue size distribution in the MAP/G/1 retrial queue
- Authors
- Kim, Bara; Kim, Jeongsim; Kim, Jerim
- Issue Date
- 9월-2010
- Publisher
- SPRINGER
- Keywords
- MAP/G/1 retrial queue; Tail asymptotics; Queue size distribution; Karamata Tauberian theorem
- Citation
- QUEUEING SYSTEMS, v.66, no.1, pp.79 - 94
- Indexed
- SCIE
SCOPUS
- Journal Title
- QUEUEING SYSTEMS
- Volume
- 66
- Number
- 1
- Start Page
- 79
- End Page
- 94
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/115723
- DOI
- 10.1007/s11134-010-9179-9
- ISSN
- 0257-0130
- Abstract
- We consider a MAP/G/1 retrial queue where the service time distribution has a finite exponential moment. We derive matrix differential equations for the vector probability generating functions of the stationary queue size distributions. Using these equations, Perron-Frobenius theory, and the Karamata Tauberian theorem, we obtain the tail asymptotics of the queue size distribution. The main result on light-tailed asymptotics is an extension of the result in Kim et al. (J. Appl. Probab. 44:1111-1118, 2007) on the M/G/1 retrial queue.
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