Research Article
First Frontier Monotonicity for Fluid Models of Multiclass EDF Queueing Networks
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@INPROCEEDINGS{10.1007/978-3-030-92511-6_8, author={Łukasz Kruk}, title={First Frontier Monotonicity for Fluid Models of Multiclass EDF Queueing Networks}, proceedings={Performance Evaluation Methodologies and Tools. 14th EAI International Conference, VALUETOOLS 2021, Virtual Event, October 30--31, 2021, Proceedings}, proceedings_a={VALUETOOLS}, year={2021}, month={12}, keywords={Earliest Deadline First Fluid model Stability}, doi={10.1007/978-3-030-92511-6_8} }- Łukasz Kruk
Year: 2021
First Frontier Monotonicity for Fluid Models of Multiclass EDF Queueing Networks
VALUETOOLS
Springer
DOI: 10.1007/978-3-030-92511-6_8
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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