Minimal and Locally Edge Minimal Fluid Models for Resource-Sharing Networks

• 成果类型: Article
• 署名作者: Kruk, Lukasz
• 署名单位: Maria Curie-Sklodowska University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2020.1110
• 发表日期: 2021
• 页码: 1513-1551
• 关键词: multiclass queuing-networks; state-space collapse; edf networks; STABILITY; LIMITS; CONVERGENCE; equilibria; algorithm; tracking; policies

摘要

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.