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Analysis of a Queueing System with Mixed Service Discipline

Author

Listed:
  • Alexander Dudin

    (Belarusian State University)

  • Sergei Dudin

    (Belarusian State University)

  • Olga Dudina

    (Belarusian State University)

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.

Suggested Citation

  • Alexander Dudin & Sergei Dudin & Olga Dudina, 2023. "Analysis of a Queueing System with Mixed Service Discipline," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-19, June.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:2:d:10.1007_s11009-023-10042-1
    DOI: 10.1007/s11009-023-10042-1
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    References listed on IDEAS

    as
    1. Mor Harchol-Balter, 2021. "Open problems in queueing theory inspired by datacenter computing," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 3-37, February.
    2. Arnaud Devos & Joris Walraevens & Dieter Fiems & Herwig Bruneel, 2021. "Heavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue," Mathematics, MDPI, vol. 9(21), pages 1-25, October.
    3. Kim, Chesoong & Dudin, Alexander & Dudina, Olga & Dudin, Sergey, 2014. "Tandem queueing system with infinite and finite intermediate buffers and generalized phase-type service time distribution," European Journal of Operational Research, Elsevier, vol. 235(1), pages 170-179.
    4. R. Núñez-Queija & O. J. Boxma, 1998. "Analysis of a multi-server queueing model of ABR," International Journal of Stochastic Analysis, Hindawi, vol. 11, pages 1-16, January.
    5. Dudin, A.N. & Dudin, S.A. & Dudina, O.S. & Samouylov, K.E., 2018. "Analysis of queueing model with processor sharing discipline and customers impatience," Operations Research Perspectives, Elsevier, vol. 5(C), pages 245-255.
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    Cited by:

    1. Sindhu S & Achyutha Krishnamoorthy & Dmitry Kozyrev, 2023. "A Two-Server Queue with Interdependence between Arrival and Service Processes," Mathematics, MDPI, vol. 11(22), pages 1-25, November.

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