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Analysis of a Queue with General Service Demands and Multiple Servers with Variable Service Capacities

Author

Listed:
  • Michiel De Muynck

    (SMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University (UGent), Sint-Pietersnieuwstraat 41, B-9000 Gent, Belgium)

  • Herwig Bruneel

    (SMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University (UGent), Sint-Pietersnieuwstraat 41, B-9000 Gent, Belgium)

  • Sabine Wittevrongel

    (SMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University (UGent), Sint-Pietersnieuwstraat 41, B-9000 Gent, Belgium)

Abstract

We present the study of a non-classical discrete-time queuing system in which the customers each request a variable amount of service, called their “service demand”, from a system with multiple servers, each of which can provide a variable amount of service, called their “service capacity”, in each time slot. The service demands are independent from customer to customer and follow a general distribution, whereas the service capacities follow a phase-type distribution and are independent from server to server and from slot to slot. Since an exact analytical analysis for this general queuing system is infeasible, we propose several approximations for the key performance characteristics in this system such as the mean system content and the mean customer delay in steady state. The accuracy of each of these approximations is compared to simulations using several numerical examples.

Suggested Citation

  • Michiel De Muynck & Herwig Bruneel & Sabine Wittevrongel, 2023. "Analysis of a Queue with General Service Demands and Multiple Servers with Variable Service Capacities," Mathematics, MDPI, vol. 11(4), pages 1-21, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:953-:d:1066748
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    References listed on IDEAS

    as
    1. J. J. Kim & M. L. Chaudhry & V. Goswami & A. D. Banik, 2021. "A New and Pragmatic Approach to the GIX/Geo/c/N Queues Using Roots," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 273-289, March.
    2. Isaac Grosof & Mor Harchol-Balter & Alan Scheller-Wolf, 2022. "WCFS: a new framework for analyzing multiserver systems," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 143-174, October.
    3. Michiel Muynck & Sabine Wittevrongel & Herwig Bruneel, 2017. "Analysis of discrete-time queues with general service demands and finite-support service capacities," Annals of Operations Research, Springer, vol. 252(1), pages 3-28, May.
    4. Mohan L. Chaudhry & James J. Kim & Abhijit D. Banik, 2019. "Analytically Simple and Computationally Efficient Results for the GI X / Geo / c Queues," Journal of Probability and Statistics, Hindawi, vol. 2019, pages 1-18, September.
    5. Evsey Morozov & Michele Pagano & Irina Peshkova & Alexander Rumyantsev, 2020. "Sensitivity Analysis and Simulation of a Multiserver Queueing System with Mixed Service Time Distribution," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
    6. Michiel Muynck & Herwig Bruneel & Sabine Wittevrongel, 2020. "Analysis of a queue with general service demands and correlated service capacities," Annals of Operations Research, Springer, vol. 293(1), pages 73-99, October.
    7. Herwig Bruneel & Sabine Wittevrongel & Dieter Claeys & Joris Walraevens, 2016. "Discrete-time queues with variable service capacity: a basic model and its analysis," Annals of Operations Research, Springer, vol. 239(2), pages 359-380, April.
    8. Gao, Peixia & Wittevrongel, Sabine & Walraevens, Joris & Moeneclaey, Marc & Bruneel, Herwig, 2009. "Calculation of delay characteristics for multiserver queues with constant service times," European Journal of Operational Research, Elsevier, vol. 199(1), pages 170-175, November.
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