Affiliation:
1. Department of Mathematics, Maria Curie-Skłodowska University, 20-031 Lublin, Poland
Abstract
We investigate minimal and locally edge minimal fluid models for real-time resource-sharing networks, which are natural counterparts of pathwise minimal and locally edge minimal performance processes for the corresponding real-time stochastic systems. The models under study arise as optimizers of appropriate idleness-based criteria within a suitable family of fluid models for a given resource-sharing network. The class of minimal fluid models is fairly general, corresponding to efficient service protocols in which transmission on each route takes place in the earliest deadline first (EDF) order. For such a model, the distribution of the current lead times of the fluid mass on each route coincides with the fluid arrival measure for this route, truncated below on the current frontier level. Locally edge minimal fluid models may be regarded, in some sense, as fluid counterparts of EDF resource-sharing networks. Under mild assumptions, a locally edge minimal fluid model is uniquely determined by its data. We also show stability of such models in the strictly subcritical case. More generally, each such a subcritical model converges to the invariant manifold in finite time.
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Subject
Management Science and Operations Research,Computer Science Applications,General Mathematics
Cited by
2 articles.
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1. Local edge minimality of SRPT networks with shared resources;Mathematical Methods of Operations Research;2022-10-07
2. First Frontier Monotonicity for Fluid Models of Multiclass EDF Queueing Networks;Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering;2021