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Embedded Markov chain approach to retrial queue with vacation, phase repair and multioptional services

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Abstract

The investigation deals with the steady-state behavior of a batch arrival retrial queue with multi-optional services and phase repair under Bernoulli vacation schedule. The customers enter the system in batches and are admitted following Bernoulli admission control policy. The incoming customers are forced to join the retrial group if they find the server unavailable. The customers are served in two phases viz. first essential service (FES) followed by second optional services (SOS). The server is unreliable and if fails, it is repaired in d-compulsory phases so as to become as good as before failure. The server may go for a vacation after each service completion following Bernoulli vacation schedule or it may continue serving the next customer. By applying the embedded Markov chain method, we establish the ergodicity condition for the system. The steady-state formulae for some queueing measures are established by evaluating the generating functions of queue length distribution. The cost function of the system has also been formulated. Finally, the effects of various parameters on the performance of the system have been examined numerically.

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Acknowledgments

The second author is thankful to MHRD for providing financial assistance to carry out the research.

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

    Madhu Jain & Amita Bhagat

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

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Jain, M., Bhagat, A. Embedded Markov chain approach to retrial queue with vacation, phase repair and multioptional services. OPSEARCH 52, 782–809 (2015). https://doi.org/10.1007/s12597-015-0207-8

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