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Transient solution for a finite capacity M/Ga,b/1 queueing system with vacations to the server

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Abstract

In this paper we consider a single server queueing system with Poisson input, general service and a waiting room that allows only a maximum of ‘b’ customers to wait at any time. A minimum of ‘a’ customers are required to start a service and the server goes for a vacation whenever he finds less than ‘a’ customers in the waiting room after a service. If the server returns from a vacation to find less than ‘a’ customers waiting, he begins another vacation immediately. Using the theory of regenerative processes we derive expressions for the time dependent system size probabilities at arbitrary epochs.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Cochin University of Science and Technology, 682 022, Cochin, India

    M. J. Jacob & T. P. Madhusoodanan

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  1. M. J. Jacob
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  2. T. P. Madhusoodanan
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Jacob, M.J., Madhusoodanan, T.P. Transient solution for a finite capacity M/Ga,b/1 queueing system with vacations to the server. Queueing Syst 2, 381–386 (1987). https://doi.org/10.1007/BF01150049

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  • DOI: https://doi.org/10.1007/BF01150049

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