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On the optimization of two-class work-conserving parameterized scheduling policies

Author

Listed:
  • Jasper Vanlerberghe

    (Ghent University (UGent))

  • Tom Maertens

    (Ghent University (UGent))

  • Joris Walraevens

    (Ghent University (UGent))

  • Stijn Vuyst

    (Ghent University (UGent))

  • Herwig Bruneel

    (Ghent University (UGent))

Abstract

Numerous scheduling policies are designed to differentiate quality of service for different applications. Service differentiation can in fact be formulated as a generalized resource allocation optimization towards the minimization of some important system characteristics. For complex scheduling policies, however, optimization can be a demanding task, due to the difficult analytical analysis of the system at hand. In this paper, we study the optimization problem in a queueing system with two traffic classes, a work-conserving parameterized scheduling policy, and an objective function that is a convex combination of either linear, convex or concave increasing functions of given performance measures of both classes. In case of linear and concave functions, we show that the optimum is always in an extreme value of the parameter. Furthermore, we prove that this is not necessarily the case for convex functions; in this case, a unique local minimum exists. This information greatly simplifies the optimization problem. We apply the framework to some interesting scheduling policies, such as Generalized Processor Sharing and semi-preemptive priority scheduling. We also show that the well-documented $$c\mu $$ c μ -rule is a special case of our framework.

Suggested Citation

  • Jasper Vanlerberghe & Tom Maertens & Joris Walraevens & Stijn Vuyst & Herwig Bruneel, 2016. "On the optimization of two-class work-conserving parameterized scheduling policies," 4OR, Springer, vol. 14(3), pages 281-308, September.
    • Handle: RePEc:spr:aqjoor:v:14:y:2016:i:3:d:10.1007_s10288-016-0312-4
    DOI: 10.1007/s10288-016-0312-4
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    References listed on IDEAS

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    1. A. Federgruen & H. Groenevelt, 1988. "M/G/c Queueing Systems with Multiple Customer Classes: Characterization and Control of Achievable Performance Under Nonpreemptive Priority Rules," Management Science, INFORMS, vol. 34(9), pages 1121-1138, September.
    2. J. Michael Harrison, 1975. "Dynamic Scheduling of a Multiclass Queue: Discount Optimality," Operations Research, INFORMS, vol. 23(2), pages 270-282, April.
    3. A. Federgruen & H. Groenevelt, 1988. "Characterization and Optimization of Achievable Performance in General Queueing Systems," Operations Research, INFORMS, vol. 36(5), pages 733-741, October.
    4. Kim, Kilhwan & Chae, Kyung C., 2010. "Discrete-time queues with discretionary priorities," European Journal of Operational Research, Elsevier, vol. 200(2), pages 473-485, January.
    5. Walraevens, Joris & Maertens, Tom & Bruneel, Herwig, 2013. "A semi-preemptive priority scheduling discipline: Performance analysis," European Journal of Operational Research, Elsevier, vol. 224(2), pages 324-332.
    6. Walraevens, Joris & Steyaert, Bart & Bruneel, Herwig, 2008. "Analysis of a discrete-time preemptive resume priority buffer," European Journal of Operational Research, Elsevier, vol. 186(1), pages 182-201, April.
    7. Walraevens, Joris & Steyaert, Bart & Bruneel, Herwig, 2004. "Performance analysis of a GI-Geo-1 buffer with a preemptive resume priority scheduling discipline," European Journal of Operational Research, Elsevier, vol. 157(1), pages 130-151, August.
    8. M. Dacre & K. Glazebrook & J. Niño‐Mora, 1999. "The achievable region approach to the optimal control of stochastic systems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 747-791.
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    Cited by:

    1. Arnaud Devos & Joris Walraevens & Dieter Fiems & Herwig Bruneel, 2020. "Analysis of a discrete-time two-class randomly alternating service model with Bernoulli arrivals," Queueing Systems: Theory and Applications, Springer, vol. 96(1), pages 133-152, October.
    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. Arnaud Devos & Joris Walraevens & Dieter Fiems & Herwig Bruneel, 2022. "Approximations for the performance evaluation of a discrete-time two-class queue with an alternating service discipline," Annals of Operations Research, Springer, vol. 310(2), pages 477-503, March.

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