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Light tailed asymptotics in an unreliable $ M/G/1$ retrial queue

Author: A. Aissani
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 85 (2011).
Journal: Theor. Probability and Math. Statist. 85 (2012), 1-6
MSC (2010): Primary 60K25; Secondary 68M20, 90B22
Published electronically: January 11, 2013
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Abstract: We consider the standard unreliable $ M/G/1$ retrial queuing system with active and passive breakdowns. The explicit expressions of the probability generating functions of distribution of server state and orbit size are well known from early works. However, some problems particularly related to Cybernetic and Artificial Intellect need to save computational effort. So, we give here another look to solve this problem more simply, but under some light tailed assumptions.

References [Enhancements On Off] (What's this?)

  • 1. A. Aissani and J. R. Artalejo, On the single server retrial queue subject to breakdowns, Queuing Systems (1998), no. 30, 309-321. MR 1672139 (2000b:60212)
  • 2. V. V. Anisimov, Switching Processes in Queueing Models, Wiley, New York, 2008. MR 2437051 (2009i:60158)
  • 3. J. R. Artalejo, A classified bibliography on retrial queues: Progress in 1990-1999, TOP 7 (1999), no. 2, 187-211. MR 1737643
  • 4. J. R. Artalejo, A classified bibliography on retrial queues: Progress in 2000-2009, Mathematical and Computer Modelling 51 (2009), no. 9, 1071-1081. MR 2608893
  • 5. J. R. Artalejo and A. Gomez-Corral, Retrial Queues: An Algorithmic Approach, Springer, Berlin, 2008. MR 2416988 (2009d:60298)
  • 6. A. N. Dudin, G. A. Medvedev, and Yu. V. Melenets, Practicum on Computer in Queueing Theory, 2nd edition, Universitsetkoje Publishing Company, Minsk, 1994 (Russian); 3rd edition, OPU, Algiers, 2010. (French)
  • 7. B. V. Gnedenko and I. N. Kovalenko, Introduction to Queueing Theory, ``Nauka'', Moscow, 1969 (Russian); Birkhäuser, UK, 1989. (English) MR 0240884 (39:2229)
  • 8. J. Kim, B. Kim, and S. Ko, Tail asymptotics for the queue size distribution in an M/G/1 retrial, J. Appl. Prob. 51 (2007), no. 9, 1111-1117.
  • 9. G. I. Falin and J. G. Templeton, Retrial Queues, Chapman and Hill, New York, 1997.
  • 10. T. Kernane and A. Aissani, Stability of retrial queues with versatile retrial policy, J. Appl. Math. and Stoch. Analysis (2006), Article ID 54359. MR 2220999 (2007b:60225)
  • 11. G. A. Medvedev, Random characteristics in LAN with random access and asymetric load, Automatic Control and Computer Science 28 (1994), no. 3, 34-41.
  • 12. S. Taleb and A. Aissani, Unreliable M/G/1 retrial queue: monotonicity and comparability, Queuing Systems (1994), no. 64, 227-252. MR 2593596 (2011f:60044)

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Additional Information

A. Aissani
Affiliation: Department of Computer Science, USTHB, BP 32 El Alia, Bab Ez Zouar, 16111, Algeria

Keywords: Retrial queues, reliability, approximation, light tailed asymptotics
Published electronically: January 11, 2013
Additional Notes: This work was supported in part by the Algerian Ministry of Higher Education and Scientific Research through grant B*00220060089
The paper is based on the talk presented at the International Conference “Modern Stochastics: Theory and Applications II” held on September 7–11, 2010 at Kyiv National Taras Shevchenko University and dedicated to three anniversaries of prominent Ukrainian scientists: Anatolii Skorokhod, Volodymyr Korolyuk and Igor Kovalenko
Article copyright: © Copyright 2013 American Mathematical Society

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