# Resilient distributed routing in dynamical flow networks

**Giacomo Como**, Lund University, Sweden

**Abstract:**

We study the resilience properties of dynamical flow networks with distributed routing. Dynamical flow networks are modeled as systems of ordinary differential equations derived from mass conservation laws on directed graphs. Distributed routing policies regulate the way the total outflow at each non-destination node gets split among its outgoing links using local information on the current state of the network, while the outflow of a link depends on the current particle density on that link through a flow function. Disturbances are modelled as (possibly adversarial) reductions of the link flow capacities. In the case where maximum density capacities are finite, our model allows for the possibility of cascading failures. We characterize a class of optimally robust distributed policies and show that, if the routing policies are allowed to use local information only from the links immediately downstream, then the margin of resilience is in general strictly smaller than the min-cut capacity of the network, while there is no such a loss if the policies are allowed to use local information also from the links immediately upstream. These results provide guidelines, e.g., in the design of robust local feedback mechanisms in transportation networks.

#### Presentation Slides

**Biography:**

Giacomo Como is an Assistant Professor at the Department of Automatic Control, Lund University, Sweden. He received the B.Sc., M.S., and Ph.D. degrees in Applied Mathematics from Politecnico di Torino, Italy, in 2002, 2004, and 2008, respectively. In 2006-2007, he was a Visiting Assistant in Research at the Department of Electrical Engineering, Yale University. From 2008 to 2011, he was a Postdoctoral Associate at the Laboratory for Information and Decision Systems, Massachusetts Institute of Technology. His current research interests include the mathematics of control and information theory, and networks.