Resilience of Input Metering in Dynamic Flow Networks

TL;DR

This paper analyzes the robustness of input metering policies in dynamic flow networks, especially transportation systems, under disturbances, introducing new theoretical tools to estimate network resilience and proposing methods to identify stable operating points.

Contribution

It introduces the concept of monotone-invariant points for assessing resilience in FIFO-based flow networks, including those with cycles, which was not addressed in prior work.

Findings

Inner-estimates for regions of attraction of equilibria and periodic orbits

Application of monotone systems theory to flow networks

Two methods for identifying monotone-invariant points

Abstract

In this paper, we study robustness of input metering policies in dynamic flow networks in the presence of transient disturbances and attacks. We consider a compartmental model for dynamic flow networks with a First-In-First-Out (FIFO) routing rule as found in, e.g., transportation networks. We model the effect of the transient disturbance as an abrupt change to the state of the network and use the notion of the region of attraction to measure the resilience of the network to these changes. For constant and periodic input metering, we introduce the notion of monotone-invariant points to establish inner-estimates for the regions of attraction of free-flow equilibrium points and free-flow periodic orbits using monotone systems theory. These results are applicable to, e.g., networks with cycles, which have not been considered in prior literature on dynamic flow networks with FIFO routing. Finally, we propose two approaches for finding suitable monotone-invariant points in the flow networks with FIFO rules.