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First Frontier Monotonicity for Fluid Models of Multiclass EDF Queueing Networks

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Performance Evaluation Methodologies and Tools (VALUETOOLS 2021)

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Abstract

We investigate fluid models of subcritical Earliest Deadline First (EDF) multiclass queueing networks with soft deadlines. For any such model, we show that after a time proportional to the size of the initial condition, the left endpoint of the cumulative fluid mass lead time distribution, called the first frontier, is nondecreasing. Moreover, in the strictly subcritical case, the first frontier actually increases as long as there is fluid mass in the system. Stability of strictly subcritical EDF fluid models and weak stability of subcritical EDF fluid models follow from the above findings as corollaries.

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Authors and Affiliations

  1. Institute of Mathematics, Maria Curie-Skłodowska University, Lublin, Poland

    Łukasz Kruk

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  1. Łukasz Kruk
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Correspondence to Łukasz Kruk .

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Editors and Affiliations

  1. Tsinghua University, Beijing, China

    Qianchuan Zhao

  2. Sun Yat-sen University, Guangzhou, China

    Li Xia

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Kruk, Ł. (2021). First Frontier Monotonicity for Fluid Models of Multiclass EDF Queueing Networks. In: Zhao, Q., Xia, L. (eds) Performance Evaluation Methodologies and Tools. VALUETOOLS 2021. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 404. Springer, Cham. https://doi.org/10.1007/978-3-030-92511-6_8

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  • DOI: https://doi.org/10.1007/978-3-030-92511-6_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-92510-9

  • Online ISBN: 978-3-030-92511-6

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