On resilience of multicommodity dynamical flow networks

Nilsson, Gustav; Como, Giacomo; Lovisari, Enrico

doi:10.1109/cdc.2014.7040190

Cited by 7 publications

(7 citation statements)

References 8 publications

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“…The following result is similar to the results of [10], with a modification made to take unbounded W i into account.…”

Section: ) Decentralized Algorithmsupporting

confidence: 82%

“…In this work, we study the assignment of traffic where the network includes the operator of a large fleet of autonomous vehicles among many ordinary drivers. This situation may fast become a reality, as the tenth principle of the Shared Mobility Principles for Livable Cities [2] states, 10. We support that autonomous vehicles (AVS) in dense urban areas should be operated in only shared fleets.…”

Section: Introductionmentioning

confidence: 74%

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Assignment and Control of Two- Tiered Vehicle Traffic

Nilsson

Grover

Kalabić

2018

2018 IEEE Conference on Decision and Control (CDC)

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This work considers the assignment of vehicle traffic consisting of both individual, opportunistic vehicles and a cooperative fleet of vehicles. The first set of vehicles seek a user-optimal policy and the second set seeks a fleet-optimal policy. We provide explicit sufficient conditions for the existence and uniqueness of a Nash equilibrium at which both policies are satisfied. We also propose two different algorithms to determine the equilibrium, one centralized and one decentralized. Furthermore, we present a control scheme to attain such an equilibrium in a dynamical network flow. An example is considered showing the workings of our scheme and numerical results are presented.

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“…The following result is similar to the results of [10], with a modification made to take unbounded W i into account.…”

Section: ) Decentralized Algorithmsupporting

confidence: 82%

Section: Introductionmentioning

confidence: 74%

Assignment and Control of Two- Tiered Vehicle Traffic

Nilsson

Grover

Kalabić

2018

2018 IEEE Conference on Decision and Control (CDC)

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“…Accordingly, we restrict our focus to single-destination networks. Analyzing multi-destination networks, where each vehicle is routed based on the observed congestion and must arrive at a specific destination, requires a multi-commodity model (e.g., [34]) since drivers with different destinations would respond differently to the same observations.…”

Section: System Modelmentioning

confidence: 99%

“…For example, the system could fail as shown in Section V-A, even before the demand reaches the network capacity (e.g., λ = 5 f0 ), under some congestion-aware policies such as the proportional routing. Since it follows from (27) that F * ( f, λ) ⊆ F * ( f, λ ) for any λ ≤ λ, one way to achieve the desired performance guarantee in this example is to solve (34) with the feasible set F * ( f, 6 f0 ). For this example, the resulting optimization problem has a unique solution for any…”

Section: A Optimal Capacity Allocation Via Speedmentioning

confidence: 99%

Resilient Control of Transportation Networks by Using Variable Speed Limits

Yazıcıoğlu

Roozbehani

Dahleh

2018

IEEE Trans. Control Netw. Syst.

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We investigate the use of variable speed limits for resilient operation of transportation networks, which are modeled as dynamical flow networks under local routing decisions. In such systems, some external inflow is injected to the so-called origin nodes of the network. The total inflow arriving at each node is routed to its operational outgoing links based on their current densities of traffic. The density on each link has first order dynamics driven by the difference of its incoming and outgoing flows. A link fails if it reaches its jam density. Such failures may propagate in the network and cause a systemic failure. We show that larger link capacities, i.e., the maximum flows that can be sustained by the links, are not always better for preventing systemic failures under local routing. Accordingly, we propose the use of variable speed limits to operate the links below their capacities, when necessary, to compensate for the lack of global information and coordination in routing decisions. We show that systemic failures under feasible external inflows can always be averted through a proper selection of speed limits if the routing decisions are sufficiently responsive to local congestion and the network is initially uncongested. This is an attractive feature as it provides a practical alternative to building more physical capacity or altering routing decisions that are determined by social behavior.

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“…However, as noticed in [11], when extending flow network models to multi-commodity flows, the monotonicity property is usually lost. Another example when the system's monotonicity property is lost is when a feedback controller can serve more than one queue simultaneously, and the service is split in proportion to the demand in all queues that are served simultaneously [12].…”

Section: Introductionmentioning

confidence: 99%

The Strong Integral Input-to-State Stability Property in Dynamical Flow Networks

Nilsson¹,

Coogan²

2021

Preprint

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Dynamical flow networks serve as macroscopic models for, e.g., transportation networks, queuing networks, and distribution networks. While the flow dynamics in such networks follow the conservation of mass on the links, the outflow from each link is often non-linear due to, e.g., flow capacity constraints and simultaneous service rate constraints. Such nonlinear constraints imply a limit on the magnitude of exogenous inflow that is able to be accommodated by the network before it becomes overloaded and its state trajectory diverges. This paper shows how the Strong integral Input-to-State Stability (Strong iISS) property allows for quantifying the effects of the exogenous inflow on the flow dynamics. The Strong iISS property enables a unified stability analysis of classes of dynamical flow networks that were only partly analyzable before, such as networks with cycles, multi-commodity flow networks and networks with nonmonotone flow dynamics. We present sufficient conditions on the maximum magnitude of exogenous inflow to guarantee input-tostate stability for a dynamical flow network, and we also present cases when this sufficient condition is necessary. The conditions are exemplified on a few existing dynamical flow network models, specifically, fluid queuing models with time-varying exogenous inflows and multi-commodity flow models.

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On resilience of multicommodity dynamical flow networks

Cited by 7 publications

References 8 publications

Assignment and Control of Two- Tiered Vehicle Traffic

Assignment and Control of Two- Tiered Vehicle Traffic

Resilient Control of Transportation Networks by Using Variable Speed Limits

The Strong Integral Input-to-State Stability Property in Dynamical Flow Networks

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