# Robust distributed routing in dynamical networks with cascading failures

@article{Como2012RobustDR, title={Robust distributed routing in dynamical networks with cascading failures}, author={Giacomo Como and Ketan Savla and Daron Acemoglu and Munther A. Dahleh and Emilio Frazzoli}, journal={2012 IEEE 51st IEEE Conference on Decision and Control (CDC)}, year={2012}, pages={7413-7418} }

We consider a dynamical formulation of network flows, whereby the network is modeled as a switched system of ordinary differential equations derived from mass conservation laws on directed graphs with a single origin-destination pair and a constant inflow at the origin. The rate of change of the density on each link of the network equals the difference between the inflow and the outflow on that link. The inflow to a link is determined by the total flow arriving to the tail node of that link and…

## 7 Citations

### On resilience of distributed routing in networks under cascade dynamics

- Computer Science52nd IEEE Conference on Decision and Control
- 2013

A backward propagation algorithm is proposed to compute an upper bound on the margin of resilience for tree-like network topologies with breadth at most 2, and it is shown that this bound is tight for trees with the additional property of having depth at least 2.

### Throughput optimal distributed routing in dynamical flow networks

- Computer Science52nd IEEE Conference on Decision and Control
- 2013

A class of distributed routing policies is shown to be throughput optimal for single-commodity dynamical flow networks and it is proven that, if no cut capacity constraint is violated by the external inflow, then a globally asymptotically stable equilibrium exists and the network achieves maximal throughput.

### Robust Distributed Routing in Dynamical Networks–Part II: Strong Resilience, Equilibrium Selection and Cascaded Failures

- Computer ScienceIEEE Transactions on Automatic Control
- 2013

A simple convex optimization problem is proposed to solve for equilibrium flows of the unperturbed network that minimize average delay subject to strong resilience guarantees, and the use of tolls to induce such an equilibrium flow in traffic networks is discussed.

### Throughput Optimality and Overload Behavior of Dynamical Flow Networks Under Monotone Distributed Routing

- Computer ScienceIEEE Transactions on Control of Network Systems
- 2015

Under monotonicity assumptions on the routing policies, it is proven that, if the external inflow at the origin nodes does not violate any cut capacity constraints, then there exists a globally asymptotically stable equilibrium, and the network achieves maximal throughput.

### On the Induction of Cascading Failures in Transportation Networks

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- 2018

This model allows for the outright or partial failure of road cells at time zero, the effects of which can cause cascading failure in the network due to irreversible blockages resulting from congestion.

### Sheaf-theoretic framework for optimal network control.

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- 2020

This paper uses tools from sheaf theory to model and analyze optimal network control problems and their associated discrete relaxations, and provides a general bound for the error incurred by such a discretization process.

### AFRL-AFOSR-VA-TR-2015-0387 (MURI-09) DISTRIBUTED LEARNING AND INFORMATION DYNAMICS IN NETWORKED AUTONOMOUS

- Computer Science
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This project is motivated by the need to enable advanced operations of teams of autonomous vehicles to learn and adapt to uncertain and hostile environments under effective utilization of…

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