Abstract
We consider a discrete-time Geo/G/1 retrial queue where the service time distribution has a finite exponential moment. We show that the tail of the queue size distribution is asymptotically geometric. Remarkably, the result is inconsistent with the corresponding result in the continuous-time counterpart, the M/G/1 retrial queue, where the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function.
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Artalejo, J.R.: A classified bibliography of research on retrial queues: Progress in 1990–1999. Top 7, 187–211 (1999)
Artalejo, J.R.: Accessible bibliography on retrial queues. Math. Comput. Model. 30, 1–6 (1999)
Artalejo, J.R., Gomez-Corral, A.: Retrial Queueing Systems. Springer, New York (2008)
Falin, G.I.: A survey of retrial queues. Queueing Syst. 7, 127–168 (1990)
Falin, G.I., Templeton, J.G.C.: Retrial Queues. Chapman & Hall, London (1997)
Kim, J., Kim, B., Ko, S.-S.: Tail asymptotics for the queue size distribution in M/G/1 retrial queue. J. Appl. Probab. 44, 1111–1118 (2007)
Nobel, R.D., Tijms, H.C.: Waiting-time probabilities in the M/G/1 retrial queue. Stat. Neerl. 60, 73–78 (2006)
Willmot, G.E.: A note on the equilibrium M/G/1 queue length. J. Appl. Probab. 25, 228–231 (1988)
Yang, T., Templeton, J.G.C.: A survey on retrial queues. Queueing Syst. 2, 201–233 (1982)
Yang, T., Li, H.: On the steady-state queue size distribution of the discrete-time Geo/G/1 queue with repeated customers. Queueing Syst. 21, 199–215 (1995)
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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. Tail asymptotics for the queue size distribution in a discrete-time Geo/G/1 retrial queue. Queueing Syst 61, 243–254 (2009). https://doi.org/10.1007/s11134-009-9106-0
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DOI: https://doi.org/10.1007/s11134-009-9106-0