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Idle time utilization through service to customers in a retrial queue maintaining high system reliability*

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We consider a k-out-of-n system in which life times of components are exponentially distributed with parameter λ/i, when there are i operational components. There is a single server who repairs the failed components. In addition, service is rendered to external customers also when there are no failed components (main customers). The external customers arrive according to a BMAP. If the arriving batch of external customers finds a free server, one among them gets into service and others, if any, move to an orbit of infinite capacity. If an arriving batch sees a busy server, the whole batch moves to the orbit. The inter-retrial times are exponentially distributed with parameter α i when there are i customers in the orbit. The external customer gets service only when the server is idle and its service is assumed to be nonpreemptive. The service times of main and external customers follow arbitrary distributions B1(·) and B2(·), respectively. The stability condition and steady-state distribution are obtained. Some performance measures are computed and numerical illustrations provided.

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Authors and Affiliations

  1. Laboratory of Applied Probabilistic Analysis, Faculty of Applied Mathematics and Computer Sciences, Belarussian State University, 4, F, Independence Ave., Minsk-30, 220030, Belarus

    A. N. Dudin

  2. Department of Mathematics, Cochin University of Science & Technology, Cochin-22, India

    A. Krishnamoorthy & V. C. Narayanan

Authors
  1. A. N. Dudin
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  2. A. Krishnamoorthy
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  3. V. C. Narayanan
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Correspondence to A. N. Dudin.

Additional information

*A. Krishnamoorthy’s research supported by NBHM (DAE, Govt. of India) Research Grant; VC. Narayanan’s research supported by CSIR Fellowship.

Proceedings of the XXV International Seminar on Stability Problems for Stochastic Models, Maiori (Salerno), Italy, September 20–24, 2005.

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Dudin, A.N., Krishnamoorthy, A. & Narayanan, V.C. Idle time utilization through service to customers in a retrial queue maintaining high system reliability*. J Math Sci 191, 506–517 (2013). https://doi.org/10.1007/s10958-013-1336-3

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  • DOI: https://doi.org/10.1007/s10958-013-1336-3

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