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A Controlled Discrete-Time Queueing System as a Model for the Orders of Two Competing Companies

Author

Listed:
  • Mario Lefebvre

    (Department of Mathematics and Industrial Engineering, Polytechnique Montréal, C.P. 6079, Succursale Centre-ville, Montréal, QC H3C 3A7, Canada)

Abstract

We consider two companies that are competing for orders. Let X 1 ( n ) denote the number of orders processed by the first company at time n , and let τ ( k ) be the first time that X 1 ( n ) < j or X 1 ( n ) = r , given that X 1 ( 0 ) = k . We assume that { X 1 ( n ) , n = 0 , 1 , … } is a controlled discrete-time queueing system. Each company is using some control to increase its share of orders. The aim of the first company is to maximize the expected value of τ ( k ) , while its competitor tries to minimize this expected value. The optimal solution is obtained by making use of dynamic programming. Particular problems are solved explicitly.

Suggested Citation

  • Mario Lefebvre, 2024. "A Controlled Discrete-Time Queueing System as a Model for the Orders of Two Competing Companies," Games, MDPI, vol. 15(3), pages 1-8, May.
    • Handle: RePEc:gam:jgames:v:15:y:2024:i:3:p:19-:d:1404374
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    References listed on IDEAS

    as
    1. Mario Lefebvre, 2023. "A Discrete-Time Homing Problem with Two Optimizers," Games, MDPI, vol. 14(6), pages 1-10, October.
    2. P. Vijaya Laxmi & E. Girija Bhavani & K. Jyothsna, 2023. "Analysis of Markovian queueing system with second optional service operating under the triadic policy," OPSEARCH, Springer;Operational Research Society of India, vol. 60(1), pages 256-275, March.
    3. Konstantin Samouylov & Olga Dudina & Alexander Dudin, 2023. "Analysis of Multi-Server Queueing System with Flexible Priorities," Mathematics, MDPI, vol. 11(4), pages 1-22, February.
    4. 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.
    Full references (including those not matched with items on IDEAS)

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