Robust Distributed Routing in Dynamical Networks with Cascading Failures

TL;DR

This paper analyzes the resilience of dynamical networks with finite capacity links and cascading failures under distributed routing policies, highlighting the impact of flow disruptions and spill-backs on network robustness.

Contribution

It introduces a novel model with discontinuous flow functions at maximum capacity, capturing spill-backs and analyzing network resilience under perturbations.

Findings

Finite capacity links can cause spill-backs affecting network flow

Discontinuous flow functions model realistic capacity constraints

Resilience depends on how flow reductions impact overall network stability

Abstract

Robustness of routing policies for networks is a central problem which is gaining increased attention with a growing awareness to safeguard critical infrastructure networks against natural and man-induced disruptions. Routing under limited information and the possibility of cascades through the network adds serious challenges to this problem. This abstract considers the framework of dynamical networks introduced in our earlier work [1,2], where the network is modeled by a system of ordinary differential equations derived from mass conservation laws on directed acyclic graphs with a single origin-destination pair and a constant inflow at the origin. The rate of change of the particle density on each link of the network equals the difference between the inflow and the outflow on that link. The latter is modeled to depend on the current particle density on that link through a flow function. The novel modeling element in this paper is that every link is assumed to have finite capacity for particle density and that the flow function is modeled to be strictly increasing as density increases from zero up to the maximum density capacity, and is discontinuous at the maximum density capacity, with the flow function value being zero at that point. This feature, in particular, allows for the possibility of spill-backs in our model. In this paper, we present our results on resilience of such networks under distributed routing, towards perturbations that reduce link-wise flow functions.