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A discrete-time queueing system with server breakdowns and changes in the repair times

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Abstract

We consider a discrete-time queueing system in which the arriving customers can decide to follow a LCFS discipline or to join the queue. Breakdowns can occur with geometrical lifetime and repair times governed by an arbitrary distribution. The repair times can exert changes governed by a geometrical law. We carry out a thorough study of the model deriving analytical results for the stationary distributions. We obtain generating functions of the number of customers in the queue and in the system. We also obtain the generating function of the repair times taking into account possible changes in the remaining repair times. The generating functions of the busy period, sojourn time in the server, sojourn time in the queue as well as some performance measures are also provided.

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Acknowledgments

The author would like to thank the referees for valuable suggestions and comments that helped to improve the presentation of this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Higher Polytechnic School, University of Málaga, 29071, Málaga, Spain

    I. Atencia

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  1. I. Atencia
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Correspondence to I. Atencia.

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The research was supported by the national spanish project TIN2012-39353-C04-01.

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Atencia, I. A discrete-time queueing system with server breakdowns and changes in the repair times. Ann Oper Res 235, 37–49 (2015). https://doi.org/10.1007/s10479-015-1940-3

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  • DOI: https://doi.org/10.1007/s10479-015-1940-3

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