On Resilience of Multicommodity Dynamical Flow Networks

Gustav Nilsson, Giacomo Como, Enrico Lovisari

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceedingpeer-review

5 Citations (SciVal)
166 Downloads (Pure)


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.
Original languageEnglish
Title of host publication53rd IEEE Conference on Decision and Control
Publication statusPublished - 2014
Event53rd IEEE Conference on Decision and Control - Los Angeles, CA, United States
Duration: 2014 Dec 15 → …


Conference53rd IEEE Conference on Decision and Control
Country/TerritoryUnited States
CityLos Angeles, CA
Period2014/12/15 → …

Subject classification (UKÄ)

  • Control Engineering


  • Dynamical flow networks
  • multicommodity flows
  • resilience
  • distributed routing
  • heterogeneous routing


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