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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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) and the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2008-314-C00031).
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Kim, B., Kim, J. & Kim, J. Tail asymptotics for the queue size distribution in the MAP/G/1 retrial queue. Queueing Syst 66, 79–94 (2010). https://doi.org/10.1007/s11134-010-9179-9
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DOI: https://doi.org/10.1007/s11134-010-9179-9