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Competitive queueing systems with comparative rating dependent arrivals

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  • Dudin, A.N.
  • Dudin, S.A.
  • Dudina, O.S.
  • Samouylov, K.E.

Abstract

We consider the joint operation of two multi-server queueing systems. Both systems provide the same type of service and compete for customers. It is assumed that the first system is controlled by ourselves while the second one is controlled by our competitor. The arriving customers are shared between the systems depending on the comparative rating of our system. The stationary behavior of the considered model under the fixed parameters of both systems and the fixed mechanism of calculation of the rating is described by a continuous-time multi-dimensional Markov chain. The stationary distribution of this Markov chain is computed. Expressions for the key performance measures of the systems are derived. Obtained results provide an opportunity to analyse possible consequences of various managerial actions aiming to maximize the profit of our system. A numerical experiment illustrates the application of the results for making a decision about the rationality of establishing and maintaining a service system while an alternative system providing the same type of service already exists.

Suggested Citation

  • Dudin, A.N. & Dudin, S.A. & Dudina, O.S. & Samouylov, K.E., 2020. "Competitive queueing systems with comparative rating dependent arrivals," Operations Research Perspectives, Elsevier, vol. 7(C).
    • Handle: RePEc:eee:oprepe:v:7:y:2020:i:c:s221471601930260x
    DOI: 10.1016/j.orp.2020.100139
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    References listed on IDEAS

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    1. Chia-Jung Chang & Jau-Chuan Ke & Fu-Min Chang, 2018. "Unreliable retrial queue with loss and feedback under threshold-based policy," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 30(1), pages 1-20.
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    3. Baumann, Hendrik & Sandmann, Werner, 2017. "Multi-server tandem queue with Markovian arrival process, phase-type service times, and finite buffers," European Journal of Operational Research, Elsevier, vol. 256(1), pages 187-195.
    4. Dhingra, Vibhuti & Kumawat, Govind Lal & Roy, Debjit & Koster, René de, 2018. "Solving semi-open queuing networks with time-varying arrivals: An application in container terminal landside operations," European Journal of Operational Research, Elsevier, vol. 267(3), pages 855-876.
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    Cited by:

    1. Alexander Dudin & Olga Dudina & Sergei Dudin & Yulia Gaidamaka, 2022. "Self-Service System with Rating Dependent Arrivals," Mathematics, MDPI, vol. 10(3), pages 1-21, January.
    2. Mridula Jain & Anamika Jain, 2022. "Genetic algorithm in retrial queueing system with server breakdown and caller intolerance with voluntary service," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(2), pages 582-598, April.
    3. Seokjun Lee & Sergei Dudin & Olga Dudina & Chesoong Kim & Valentina Klimenok, 2020. "A Priority Queue with Many Customer Types, Correlated Arrivals and Changing Priorities," Mathematics, MDPI, vol. 8(8), pages 1-20, August.

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