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  KEYWORD

Analisi e controllo di sistemi dinamici

Resilience of transportation networks

Reference persons GIACOMO COMO

Research Groups Analisi e controllo di sistemi dinamici

Description Resilience has become a key aspect in the design of critical infrastructure networks, such as transport systems. On the one hand, the ever-increasing user demand and limited growth in physical capacity forces these networks to be utilised closer and closer to their limits. On the other hand, the recent technological advancements in terms of smart sensors, high-speed communication, and real-time decision capabilities have exacerbated the large-scale interconnected nature of these systems, and increased both the potential gains associated to their optimization and their inherent systemic risks. In fact, while designed to perform well under normal operation conditions, such complex systems tend to exhibit critical fragilities in response to unforeseen disruptions. Even if simply started from small local perturbations, such disruptions have the potential to build up through cascading mechanisms driven by the interconnected dynamics of the infrastructure network, possibly leading to detrimental systemic effects. The term resilience refers to the ability of these systems “to plan and prepare for, absorb, respond to, and recover from disasters and adapt to new conditions” (definition by the US National Academy of Sciences [1]). The problem has motivated a considerable amount of research within the last few years, particularly focused on the dynamical aspects of network flows, complementing more classical static network flow optimization approaches. (See, e.g., [2] and references therein.)
In this thesis, we propose to address the problem of robustness of routing matrices in transportation networks. Routing matrices are sparse sub-stochastic matrices R whose entries represent the splitting rates, i.e, the fractions of flow moving from one cell i to another adjacent cell j. For simplicity, we will focus on the case where such routing matrices are static (rather than varying in response to feedback information as in [3,4]) and address the following question: how much do changes in R affect the value of the equilibrium of a linear compartmental system with routing matrix R and exogenous inflow u? While the question is concerned with the equilibrium of linear compartmental system dynamics, answering it proves very relevant for important nonlinear models of network traffic dynamics such as Daganzo’s Cell Transmission Model [5,6] as well as for some models of packet-switched networks [7].

[1]  Disaster Resilience: a National Imperative, The National Academies Press, 2012.
[2] G. Como, `Resilient Control of Dynamical Flow Networks’, Annual Reviews in Control, vol. 43, pp. 80-90, 2017.
[3] G. Como, K. Savla, D. Acemoglu, M.A. Dahleh, and E. Frazzoli, `Robust distributed routing in dynamical networks - Part I: Locally responsive policies and weak resilience,’ IEEE Transactions on Automatic Control 58 (2) (2013) 317–332.
[4] G.Como, E.Lovisari, and K.Savla, `Throughput optimality and overload behavior of dynamical flow networks under monotone distributed routing’, IEEE Transactions on Control of Network Systems 2 (1) (2015) 57–67.
[5]  C. Daganzo, `The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory,’ Transportation Research B 28B (4) (1994) 269–287.
[6]  C. Daganzo, `The cell transmission model, Part II: Network traffic,’ Transportation Research B 29B (2) (1995) 79–93.
[7] D. Shah and D. Wischik,`Switched networks with maximum weight policies: Fluid approximation and multiplicative state space collapse’, The Annals of Applied Probability , 22(1), pp. 70-127.


Deadline 06/08/2018      PROPONI LA TUA CANDIDATURA




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