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A Discrete-Time Geo/G/1 retrial queue with the server subject to starting failures

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Abstract

This paper studies a discrete-time Geo/G/1 retrial queue where the server is subject to starting failures. We analyse the Markov chain underlying the regarded queueing system and present some performance measures of the system in steady-state. Then, we give two stochastic decomposition laws and find a measure of the proximity between the system size distributions of our model and the corresponding model without retrials. We also develop a procedure for calculating the distributions of the orbit and system size as well as the marginal distributions of the orbit size when the server is idle, busy or down. Besides, we prove that the M/G/1 retrial queue with starting failures can be approximated by its discrete-time counterpart. Finally, some numerical examples show the influence of the parameters on several performance characteristics.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, E.T.S.I. de Telecomunicación, Universidad de Málaga, Málaga, 29071, Spain

    I. Atencia

  2. Departamento de Economía, Métodos Cuantitativos, e Historia Económica, Facultad de Ciencias Empresariales, Universidad Pablo de Olavide, Sevilla, 41013, Spain

    P. Moreno

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  1. I. Atencia
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  2. P. Moreno
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Correspondence to I. Atencia.

Additional information

This work is supported by the DGINV through the project BFM2002-02189.

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Atencia, I., Moreno, P. A Discrete-Time Geo/G/1 retrial queue with the server subject to starting failures. Ann Oper Res 141, 85–107 (2006). https://doi.org/10.1007/s10479-006-5295-7

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  • DOI: https://doi.org/10.1007/s10479-006-5295-7

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