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An arriving decision problem in a discrete-time queueing system

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Abstract

This paper discusses a discrete-time queueing system in which an arriving customer may adopt four different strategies; two of them correspond to a LCFS discipline where displacements or expulsions occur, and in the other two, the arriving customer decides to follow a FCFS discipline or to become a negative customer eliminating the customer in the server, if any. The different choices of the involved parameters make this model to enjoy a great versatility, having several special cases of interest. We carry out a thorough analysis of the system, and using a generating function approach, we derive analytical results for the stationary distributions obtaining performance measures for the number of customers in the queue and in the system. Also, recursive formulae for calculating the steady-state distributions of the queue and system size has been developed. Making use of the busy period of an auxiliary system, the sojourn times of a customer in the queue and in the system have also been obtained. Finally, some numerical examples are given.

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Acknowledgments

We would like to thank the anonymous referees for their helpful comments.

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Authors and Affiliations

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

    Ivan Atencia, José L. Galán-García, Gabriel Aguilera-Venegas, Pedro Rodríguez-Cielos & M. Ángeles Galán-García

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  1. Ivan Atencia
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  2. José L. Galán-García
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  3. Gabriel Aguilera-Venegas
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  4. Pedro Rodríguez-Cielos
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  5. M. Ángeles Galán-García
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Correspondence to Ivan Atencia.

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Communicated by: Pavel Solin

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This work was partially supported by Grant No. TIN2015-70266-C2-1-P of the Science and Innovation Ministry of Spain.

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Atencia, I., Galán-García, J.L., Aguilera-Venegas, G. et al. An arriving decision problem in a discrete-time queueing system. Adv Comput Math 45, 1863–1879 (2019). https://doi.org/10.1007/s10444-019-09663-3

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  • DOI: https://doi.org/10.1007/s10444-019-09663-3

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