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On Resilience of Multicommodity Dynamical Flow Networks

Nilsson, Gustav LU ; Como, Giacomo LU and Lovisari, Enrico LU (2014) 53rd IEEE Conference on Decision and Control In [Host publication title missing] p.5125-5130
Abstract
Dynamical flow networks with heterogeneous routing are analyzed in terms of stability and resilience to perturbations. Particles flow through the network and, at each junction, decide which downstream link to take on the basis of the local state of the network. Differently from single-commodity scenarios, particles belong to different classes, or commodities, with different origins and destinations, each reacting differently to the observed state of the network. As such, the commodities compete for the shared resource that is the flow capacity of each link of the network. This implies that, in contrast to the single-commodity case, the resulting dynamical system is not monotone, hence harder to analyze. It is shown that, in an acyclic... (More)
Dynamical flow networks with heterogeneous routing are analyzed in terms of stability and resilience to perturbations. Particles flow through the network and, at each junction, decide which downstream link to take on the basis of the local state of the network. Differently from single-commodity scenarios, particles belong to different classes, or commodities, with different origins and destinations, each reacting differently to the observed state of the network. As such, the commodities compete for the shared resource that is the flow capacity of each link of the network. This implies that, in contrast to the single-commodity case, the resulting dynamical system is not monotone, hence harder to analyze. It is shown that, in an acyclic network, when a feasible globally asymptotically stable aggregate equilibrium exists, then each commodity also admits a unique equilibrium. In addition, a sufficient condition for stability is provided. Finally, it is shown that, differently from the single-commodity case, when this condition is not satisfied, the possible unique equilibrium may be arbitrarily fragile to perturbations of the network. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Dynamical flow networks, multicommodity flows, resilience, distributed routing, heterogeneous routing
in
[Host publication title missing]
pages
5125 - 5130
conference name
53rd IEEE Conference on Decision and Control
external identifiers
  • Scopus:84931857748
ISBN
978-1-4799-7746-8
DOI
10.1109/CDC.2014.7040190
language
English
LU publication?
yes
id
8f3e46d1-32b1-4de8-b1b5-82aa35185d04 (old id 4820629)
date added to LUP
2014-12-01 14:05:50
date last changed
2016-04-16 12:36:57
@misc{8f3e46d1-32b1-4de8-b1b5-82aa35185d04,
  abstract     = {Dynamical flow networks with heterogeneous routing are analyzed in terms of stability and resilience to perturbations. Particles flow through the network and, at each junction, decide which downstream link to take on the basis of the local state of the network. Differently from single-commodity scenarios, particles belong to different classes, or commodities, with different origins and destinations, each reacting differently to the observed state of the network. As such, the commodities compete for the shared resource that is the flow capacity of each link of the network. This implies that, in contrast to the single-commodity case, the resulting dynamical system is not monotone, hence harder to analyze. It is shown that, in an acyclic network, when a feasible globally asymptotically stable aggregate equilibrium exists, then each commodity also admits a unique equilibrium. In addition, a sufficient condition for stability is provided. Finally, it is shown that, differently from the single-commodity case, when this condition is not satisfied, the possible unique equilibrium may be arbitrarily fragile to perturbations of the network.},
  author       = {Nilsson, Gustav and Como, Giacomo and Lovisari, Enrico},
  isbn         = {978-1-4799-7746-8},
  keyword      = {Dynamical flow networks,multicommodity flows,resilience,distributed routing,heterogeneous routing},
  language     = {eng},
  pages        = {5125--5130},
  series       = {[Host publication title missing]},
  title        = {On Resilience of Multicommodity Dynamical Flow Networks},
  url          = {http://dx.doi.org/10.1109/CDC.2014.7040190},
  year         = {2014},
}