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Analysis of a Queueing System with Mixed Service Discipline

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Abstract

In this paper, we analyse a queueing model with two types of requests arriving in a marked Markov arrival process. Type-1 requests require a constant service rate, while type-2 requests admit a flexible service rate. Mixed service discipline is considered. It is defined as follows. The number of type-1 requests that can be processed by the system simultaneously is restricted. Type-2 requests receive service according to the classical processor sharing discipline and use all currently available (not occupied by type-1 requests) system bandwidth. Type-2 requests can be impatient and leave the system without receiving complete service. The system behavior is described by a multidimensional Markov chain. The infinitesimal generator of this chain is derived. The transparent ergodicity condition is obtained, and the stationary performance measures of the system are computed. A numerical example is presented, including consideration of the problem of choosing the optimal values of the system bandwidth and its share dedicated to the service of type-1 requests.

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Acknowledgements

The authors highly appreciate valuable comments by the anonymous reviewers account of which lead to the improvement of our manuscript.

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Author notes

  1. Sergei Dudin and Olga Dudina both contributed equally to this work.

Authors and Affiliations

  1. Belarusian State University, 4, Nezavisimosti Ave., Minsk, 220030, Belarus

    Alexander Dudin, Sergei Dudin & Olga Dudina

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  1. Alexander Dudin
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  2. Sergei Dudin
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  3. Olga Dudina
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Contributions

The individual contributions of the authors are the following: Alexander Dudin - conceptualization; methodology; formal analysis; investigation; writing, original draft preparation; supervision; writing, review and editing. Sergei Dudin - conceptualization; methodology; formal analysis; software; validation; writing, review and editing. Olga Dudina - methodology; software; validation; formal analysis; writing, review and editing. All authors reviewed the manuscript.

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Correspondence to Alexander Dudin.

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Dudin, A., Dudin, S. & Dudina, O. Analysis of a Queueing System with Mixed Service Discipline. Methodol Comput Appl Probab 25, 57 (2023). https://doi.org/10.1007/s11009-023-10042-1

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