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An M/G/1 two phase multi-optional retrial queue with Bernoulli feedback, non-persistent customers and breakdown and repair

Author

Listed:
  • K. Lakshmi
  • Kasturi Ramanath

Abstract

This paper has been motivated by the interactive voice response system (IVRS). This system has now become a common phenomenon in our everyday life. In this paper, we consider a Poisson arrival queueing system with a single server and two essential phases of heterogeneous service. The customer who completes the first phase has a choice of k-options to choose for the second phase of service. The customer, who finds the server busy upon arrival, can either join the orbit or he/she can leave the system. After completion of both phases, the customer can decide to try again for service by joining the orbit or he/she can leave the system. The server is subject to sudden breakdowns and repairs. We assume that the breakdowns of the system can occur even when the system is idle. By using the supplementary variables technique, we have obtained the steady state probability generating functions of the orbit size and the system size. We obtain a stochastic decomposition law for the system. We present numerical results to illustrate the sensitivity of the system. We obtain some useful performance measures of the system.

Suggested Citation

  • K. Lakshmi & Kasturi Ramanath, 2014. "An M/G/1 two phase multi-optional retrial queue with Bernoulli feedback, non-persistent customers and breakdown and repair," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 19(1), pages 78-95.
    • Handle: RePEc:ids:ijores:v:19:y:2014:i:1:p:78-95
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    Citations

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    Cited by:

    1. G. Ayyappan & S. Karpagam, 2018. "An M [ X ] / G ( a , b )/1 Queueing System with Breakdown and Repair, Stand-By Server, Multiple Vacation and Control Policy on Request for Re-Service," Mathematics, MDPI, vol. 6(6), pages 1-18, June.
    2. P. Rajadurai & V. M. Chandrasekaran & M. C. Saravanarajan, 2016. "Analysis of an M[X]/G/1 unreliable retrial G-queue with orbital search and feedback under Bernoulli vacation schedule," OPSEARCH, Springer;Operational Research Society of India, vol. 53(1), pages 197-223, March.

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