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A matrix geometric approach to the M/M/1 two-phase multi optional retrial queue with Bernoulli feedback, impatient customers and a server subject to breakdown and repair

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Abstract

In this paper, we use the matrix geometric approach to analyze the behaviour of an Interactive Voice Response System (IVRS). We model the system as an M/M/1 retrial queue with two phases of service (the second service is multi optional), Bernoulli feedback, impatient customers and the possibility of server breakdown and repair. We study the stability of the system by employing the Neuts and Rao (Queueing Syst. 7, 169–190 (1990)) truncation method and then we study the level dependent QBD (Quasi-Birth Death) model obtained by the above truncation method to obtain expressions for the performance measures of the system. Numerical illustrations are provided to study the sensitivity of the performance measures of the system to the changes in various parameters of the system.

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Acknowledgment

The authors are very grateful to the referees for their valuable suggestions to improve this paper in the present form.

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Authors and Affiliations

  1. A.M. Jain College, Meenambakkam, Chennai, Tamil Nadu, India

    K. Lakshmi

  2. School of Mathematics, Madurai Kamaraj University, Madurai-21, Tamil Nadu, India

    Kasturi Ramanath

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  1. K. Lakshmi
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  2. Kasturi Ramanath
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Correspondence to K. Lakshmi.

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Lakshmi, K., Ramanath, K. A matrix geometric approach to the M/M/1 two-phase multi optional retrial queue with Bernoulli feedback, impatient customers and a server subject to breakdown and repair. OPSEARCH 51, 36–49 (2014). https://doi.org/10.1007/s12597-013-0131-8

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