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A Retrial Queuing Model with Unreliable Server in K Policy

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Abstract

The retrial queue with unreliable server with provision of temporary server has been studied. A temporary server is installed when the primary server is over loaded. It means that a fixed queue length of K-policy customers including the customer with the primary server has been build up. The primary server may breakdown while rendering service to the customers; it is sent for the repair. This type of queuing system has been investigated using matrix geometric method and obtains the probabilities of the system steady state. From the probabilities, we found some performance measures.

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References

  1. Aissani, A., and Artalejo, J.R., On the single server retrial queue subject to breakdowns.Queuing systems, 30:307–321,(1998).

    Google Scholar 

  2. Alfa, A.S. and Isotupa, K.P.S., An M/PH/K retrial queue with finite number of sources, Comput. Oper. Res., Vol.31, pp. 1455–1464, (2004).

    Article  MathSciNet  Google Scholar 

  3. Artalejo, J.R. and Corral, A.G., Retrial Queuing Systems: A Computational Approach,Springer, (2008).

    Google Scholar 

  4. Bhagat, A. and Jain, M., Unreliable M x/G/1 retrial queue with multi-optional services and impatient customers, Int.J.Oper. Res., Vol.17, pp.248–273, (2013).

    Article  MathSciNet  Google Scholar 

  5. Choudhury, G. and Ke, J.C., A batch arrival retrial queue with general retrial times under Bernoulli vacation schedule for unreliable server and delaying repair, Appl.Math. Model., Vol. 36,pp.255–269,(2012).

    Article  MathSciNet  Google Scholar 

  6. Dimitrious, I., A mixed priority retrial queue with negative arrival, unreliable server and multiple vacations.Appl.Math.Model.,Vol. 37,pp. 1295–1309. (2013).

    Article  MathSciNet  Google Scholar 

  7. Falin, G. I.and templeton, J.G.C., Retrial Queues, Chapman and Hall, (1997).

    Google Scholar 

  8. Kalyanaraman, R. and Seenivasan, M., A multi-server retrial queuing system with unreliable server, International Journal of Computational Cognation. Vol.8,NO.3,September(2010).

    Google Scholar 

  9. Krishna Kumar, B. and Madheswari, S.P., An M/M/2 queuing system with heterogeneous servers and multiple vacations, Math. Comput. Model., Vol.41,pp. 1415–1429, (2005).

    Article  Google Scholar 

  10. Kulkarni, V.G., and Choi, B.D., Retrial queues with server subject to breakdowns. Queuing Systems,7:191–208, (1990).

    Article  MathSciNet  Google Scholar 

  11. Kushner, H.J., Heavy traffic analysis of controlled Queuing and Communication Networks Springer-Verlag, New York, (2001).

    Book  Google Scholar 

  12. Leite, S.C. and Fragoso, M.D., Heavy traffic analysis of state-dependent parallel queues with trigger and an application to web search systems Perf.Eval., Vol.67, pp.913–928,(2010).

    Google Scholar 

  13. Neuts, M.F., Markov chains with applications queueing theory, which have a matrix geometric invariant probability vector, Adv. Appl. Prob., Vol.10, pp.185–212, (1978).

    Article  MathSciNet  Google Scholar 

  14. Neuts, M.F., Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. The Johns Hopkins University Press, Baltimore, 1981.

    MATH  Google Scholar 

  15. Wu, J. and Lian, Z. A single-server retrial G-queue with priority and unreliable server under Bernoulli vacation schedule.Comp.Ind.Engg.,Vol.64,pp.84–93,(2013).

    Article  Google Scholar 

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Correspondence to M. Seenivasan .

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Seenivasan, M., Indumathi, M. (2018). A Retrial Queuing Model with Unreliable Server in K Policy. In: Madhu, V., Manimaran, A., Easwaramoorthy, D., Kalpanapriya, D., Mubashir Unnissa, M. (eds) Advances in Algebra and Analysis. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-01120-8_41

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