Fluid flow models in performance analysis

We review several developments in fluid flow models: feedback fluid models, linear stochastic fluid networks and bandwidth sharing networks. We also mention some promising new research directions

A Stochastic Resource-Sharing Network for Electric Vehicle Charging

We consider a distribution grid used to charge electric vehicles such that voltage drops stay bounded. We model this as a class of resource-sharing networks, known as bandwidth-sharing networks in the communication network literature. We focus on resource-sharing networks that are driven by a class of greedy control rules that can be implemented in a decentralized fashion. For a large number of such control rules, we can characterize the performance of the system by a fluid approximation. This leads to a set of dynamic equations that take into account the stochastic behavior of EVs. We show that the invariant point of these equations is unique and can be computed by solving a specific ACOPF problem, which admits an exact convex relaxation. We illustrate our findings with a case study using the SCE 47-bus network and several special cases that allow for explicit computations.Comment: 13 pages, 8 figure

A stochastic resource-sharing network for electric vehicle charging

We consider a distribution grid used to charge electric vehicles subject to voltage stability and various other constraints. We model this as a class of resource

Fluid Limits for Bandwidth-Sharing Networks in Overload.

Bandwidth-sharing networks as considered by Roberts and Massoulié [28] (Roberts JW, Massoulié L (1998) Bandwidth sharing and admission control for elastic traffic. Proc. ITC Specialist Seminar, Yokohama, Japan) provide a natural modeling framework for describing the dynamic flow-level interaction among elastic data transfers. Under mild assumptions, it has been established that a wide family of so-called a-fair bandwidth-sharing strategies achieve stability in such networks provided that no individual link is overloaded. In the present paper we focus on bandwidth-sharing networks where the load on one or several of the links exceeds the capacity. To characterize the overload behavior, we examine the fluid limit, which emerges when the flow dynamics are scaled in both space and time. We derive a functional equation characterizing the fluid limit, and show that any strictly positive solution must be unique, which in particular implies the convergence of the scaled number of flows to the fluid limit for nonzero initial states when the load is sufficiently high. For the case of a zero initial state and a zero-degree homogeneous rate allocation function, we show that there exists a linear solution to the fluid-limit equation, and obtain a fixed-point equation for the corresponding asymptotic growth rates. It is proved that a fixed-point solution is also a solution to a related strictly concave optimization problem, and hence exists and is unique. In addition, we establish uniqueness of fluid-model solutions for monotone rate-preserving networks (in particular tree networks)

Fluid Limits for Bandwidth-Sharing Networks in Overload

Bandwidth-sharing networks as considered by Roberts and Massoulié [28] (Roberts JW, Massoulié L (1998) Bandwidth sharing and admission control for elastic traffic. Proc. ITC Specialist Seminar, Yokohama, Japan) provide a natural modeling framework for describing the dynamic flow-level interaction among elastic data transfers. Under mild assumptions, it has been established that a wide family of so-called a-fair bandwidth-sharing strategies achieve stability in such networks provided that no individual link is overloaded. In the present paper we focus on bandwidth-sharing networks where the load on one or several of the links exceeds the capacity. To characterize the overload behavior, we examine the fluid limit, which emerges when the flow dynamics are scaled in both space and time. We derive a functional equation characterizing the fluid limit, and show that any strictly positive solution must be unique, which in particular implies the convergence of the scaled number of flows to the fluid limit for nonzero initial states when the load is sufficiently high. For the case of a zero initial state and a zero-degree homogeneous rate allocation function, we show that there exists a linear solution to the fluid-limit equation, and obtain a fixed-point equation for the corresponding asymptotic growth rates. It is proved that a fixed-point solution is also a solution to a related strictly concave optimization problem, and hence exists and is unique. In addition, we establish uniqueness of fluid-model solutions for monotone rate-preserving networks (in particular tree networks)