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Queueing Systems

, Volume 58, Issue 3, pp 155–160 | Cite as

The M/M/1 retrial queue with retrials due to server failures

  • G. I. Falin
Article

Abstract

Sherman and Kharoufeh (Oper. Res. Lett. 34:697–705, [2006]) considered an M/M/1 type queueing system with unreliable server and retrials. In this model it is assumed that if the server fails during service of a customer, the customer leaves the server, joins a retrial group and in random intervals repeats attempts to get service. We suggest an alternative method for analysis of the Markov process, which describes the functioning of the system, and find the joint distribution of the server state, the number of customers in the queue and the number of customers in the retrial group in steady state.

Keywords

Retrials Unreliable server Steady state 

Mathematics Subject Classification (2000)

60K25 90B22 

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References

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    Sherman, N.P., Kharoufeh, J.P., Abramson, M.: An M/G/1 retrial queue with unreliable server for streaming multimedia applications. Probab. Eng. Inf. Sci. (in press) Google Scholar
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    Tweedie, R.L.: Sufficient conditions for regularity, recurrence and ergodicity of Markov processes. In: Math. Proceedings of the Cambridge Philosophical Society, vol. 78, part 1 (1975) Google Scholar
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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Probability Theory, Mechanics and Mathematics FacultyMoscow State UniversityMoscowRussian Federation

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