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N-policy for \({M}^{{x}}/\hbox {G}/1\) Unreliable Retrial G-Queue with Preemptive Resume and Multi-services

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Abstract

Bulk arrival retrial G-queue with impatient customers and multi-services subject to server breakdowns has been analyzed. The system allows the arrival of two types of customers: positive customers and negative customers in the system. The negative customers make the server fail if they find the server in busy state, whereas positive customers are served if the server is idle otherwise they join the virtual pool of customers called orbit. The customers from the retrial orbit try their chance again for the service. The customers have the option of obtaining more than one service. Moreover, the customers are impatient and may renege from the system with probability \((1-r)\). The server is sent for repair as soon as it breakdowns; after repair, the service process starts again. Also, the server has the provision to initiate the service when there are N customers accumulated in the system. Using supplementary variables technique and generating functions, various performance measures like reliability indices and long run probabilities have been obtained.

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References

  1. Yang, T., Templeton, J.G.C.: A survey on retrial queues. Queueing Syst. 2, 201–233 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  2. Artalejo, J.R., Falin, G.I.: Standard and retrial queueing systems: a comparative analysis. Rev. Math. Comput. 15, 101–129 (2002)

    MathSciNet  MATH  Google Scholar 

  3. Artalejo, J.R.: A classified bibliography of research on retrial queues. Progress in 1990–1999. Top 7, 187–211 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  4. Artalejo, J.R.: Accessible bibliography on retrial queues. Math. Comput. Model. 30, 1–6 (1999)

    Article  Google Scholar 

  5. Artalejo, J.R.: Accessible bibliography on retrial queues. Math. Comput. Model. 51, 1071–1081 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Wang, J., Zhou, P.: A batch arrival retrial queue with starting failures, feedback and admission control. J. Syst. Sci. Syst. Eng. 19, 306–320 (2010)

    Article  Google Scholar 

  7. Choudhury, G., Deka, M.: A single server queueing system with two phases of service subject to server breakdown and Bernoulli vacation. Appl. Math. Model. 36, 6050–6060 (2012)

    Article  MathSciNet  Google Scholar 

  8. Bhagat, A., Jain, M.: Unreliable \({M}^{X}/\text{ G }/1\) retrial queue with multi-optional services and impatient customers. Int. J. Oper. Res. 17, 248–273 (2013)

    Article  MathSciNet  Google Scholar 

  9. Wu, J., Lian, Z.: A single-server retrial G-queue with priority and unreliable server under Bernoulli vacation schedule. Comput. Ind. Eng. 64, 84–93 (2013)

    Article  Google Scholar 

  10. Wang, J., Zhang, P.: A discrete-time retrial queue with negative customers and unreliable server. Comput. Ind. Eng. 56, 1216–1222 (2009)

    Article  Google Scholar 

  11. Wang, J., Huang, Y., Do, T.V.: A single-server discrete-time queue with correlated positive and negative customer arrivals. Appl. Math. Model. 37, 6212–6224 (2013)

    Article  MathSciNet  Google Scholar 

  12. Madan, K.C.: An M/G/1 queue with second optional service. Queueing Syst. 34, 37–46 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  13. Krishnakumar, B., Vijaykumar, A., Arivudainambi, D.: An M/G/1 retrial queueing system with two-phase service and preemptive resume. Ann. Oper. Res. 113, 61–79 (2002)

    Article  MathSciNet  Google Scholar 

  14. Choudhury, G., Paul, M.: A batch arrival queue with an additional service channel under \(N\)-policy. Appl. Math. Comput. 156, 115–130 (2004)

    MathSciNet  MATH  Google Scholar 

  15. Choudhury, G., Tadj, L., Deka, K.: A batch arrival retrial queueing system with two phases of service and service interruption. Comput. Math. Appl. 59, 437–450 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  16. Jain, M., Sharma, G.C., Sharma, R.: Unreliable server M/G/1 queue with multi-optional services and multi-optional vacations. Int. J. Math. Oper. Res. 5, 145–169 (2013)

    Article  MathSciNet  Google Scholar 

  17. Gelenbe, E.: Random neural networks with negative and positive signals and product form solution. Neural Comput. 1, 502–510 (1989)

    Article  Google Scholar 

  18. Gelenbe, E.: Product-form queueing networks with negative and positive customers. J. Appl. Probab. 28, 656–663 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  19. Gelenbe, E.: The first decade of G-networks. Eur. J. Oper. Res. 126, 231–232 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  20. Harrison, P.G., Pitel, E.: Sojourn times in single server queues with negative customers. J. Appl. Probab. 30, 943–963 (1993)

    MathSciNet  MATH  Google Scholar 

  21. Harrison, P.G., Pitel, E.: The M/G/1 queue with negative customers. Adv. Appl. Prob. 28, 540–566 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  22. Shin, Y.W.: Multi-server retrial queue with negative customers and disasters. Queueing Syst. 55, 223–237 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  23. Do, T.V.: Bibliography on G-networks, negative customers and applications. Math. Comput. Model. 53, 205–212 (2011)

    Article  Google Scholar 

  24. Liu, Z., Wu, J., Yang, G.: An M/G/1 retrial G-queue with preemptive resume and feedback under \(N\)-policy subject to the server breakdowns and repairs. Comput. Math. Appl. 58, 1792–1807 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  25. Dimitriou, I.: A preemptive resume priority retrial queue with state dependent arrivals, unreliable server and negative customers. Top 21, 542–571 (2013a)

    Article  MathSciNet  MATH  Google Scholar 

  26. Dimitriou, I.: A mixed priority retrial queue with negative arrivals, unreliable server and multiple vacations. Appl. Math. Model. 37, 1295–1309 (2013b)

    Article  MathSciNet  Google Scholar 

  27. Gao, S., Wang, J.: Performance and reliability analysis of an M/G/1-G retrial queue with orbital search and non-persistent customers. Eur. J. Oper. Res. 236, 561–572 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  28. Wang, J., Cao, J., Li, J.: Reliability analysis of the retrial queue with server breakdowns and repairs. Queueing Syst. 38, 363–380 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  29. Falin, G.: An M/G/1 retrial queue with an unreliable server and general retrial times. Perform. Eval. 67, 569–582 (2010)

    Article  Google Scholar 

  30. Sherman, N.P., Kharoufeh, J.P.: An M/M/1 retrial queue with unreliable server. Oper. Res. Lett. 34, 697–705 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  31. Wang, J., Liu, B., Li, J.: Transient analysis of an M/G/1 retrial queue subject to disasters and server failures. Eur. J. Oper. Res. 189, 1118–1132 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Sciences, The Northcap University, Gurgaon, 122017, India

    Amita Bhagat

  2. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    Madhu Jain

Authors
  1. Amita Bhagat
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  2. Madhu Jain
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Correspondence to Amita Bhagat.

Additional information

The first author is thankful to Ministry of Human Resource and Development for providing financial grant to carry out the research work.

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Bhagat, A., Jain, M. N-policy for \({M}^{{x}}/\hbox {G}/1\) Unreliable Retrial G-Queue with Preemptive Resume and Multi-services. J. Oper. Res. Soc. China 4, 437–459 (2016). https://doi.org/10.1007/s40305-016-0128-0

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  • DOI: https://doi.org/10.1007/s40305-016-0128-0

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