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Transient analysis of a two-heterogeneous servers queue with system disaster, server repair and customers’ impatience

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Abstract

A two-heterogeneous servers queue with system disaster, server failure and repair is considered. In addition, the customers become impatient when the system is down. The customers arrive according to a Poisson process and service time follows exponential distribution. Each customer requires exactly one server for its service and the customers select the servers on fastest server first basis. Explicit expressions are derived for the time-dependent system size probabilities in terms of the modified Bessel function, by employing the generating function along with continued fraction and the identity of the confluent hypergeometric function. Further, the steady-state probabilities of the number of customers in the system are deduced and finally some important performance measures are obtained.

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Acknowledgments

The authors wish to thank the anonymous referees for their careful review and valuable suggestions that led to considerable improvement in the presentation of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Bharathidasan Institute of Technology (BIT) Campus, Anna University, Tiruchirappalli, 620024, India

    R. Sudhesh & P. Savitha

  2. Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, 110016, India

    S. Dharmaraja

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  1. R. Sudhesh
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  2. P. Savitha
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  3. S. Dharmaraja
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Correspondence to R. Sudhesh.

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Sudhesh, R., Savitha, P. & Dharmaraja, S. Transient analysis of a two-heterogeneous servers queue with system disaster, server repair and customers’ impatience. TOP 25, 179–205 (2017). https://doi.org/10.1007/s11750-016-0428-x

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  • DOI: https://doi.org/10.1007/s11750-016-0428-x

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