Resilient Control of Transportation Networks by Using Variable Speed Limits

Abstract

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.

Distributed Dynamic Pricing of Multiscale Transportation Networks

“…For every z ∈ Z λ , y z = Az is an equilibrium flow vector satisfying By z = ν. Define G(z) as in (14) and extend (12) and (20) as…”

“…In order to prove the stability result, we shall adopt a singular perturbation approach. Our strategy consists in thinking of the path preference vector z as quasi-static when we analyse the fast-scale dynamics (12), and considering the flow vector y almost equilibrated (i.e., close to y z ) when study the slow-scale dynamics (17). Then we will give a series of intermediate results that will turn out to be useful to complete the proof of Theorem 1.…”

“…The technical Lemmas aim at showing that (34) are Lyapunov functions for the fast-scale dynamics (12) with stationary path preference z.…”

“…In fact, our analysis is carried over in a fully dynamical flow network setting. In this respect, the global optimality guarantees that are obtained in this paper through decentralized feedback toll policies should be compared with other recent results on global performance and resilience of the robust distributed control of dynamical flow networks [21], [12].…”

Dynamic output feedback control for nonlinear large-scale interconnected systems

“…The previous decades have countersigned proper applications of nonlinear interconnected system methodologies ranging from biochemical applications (Motee et al , 2012) to spacecraft processes (Xua et al , 2013), double inverted pendulums (Guo and Xiong, 2018), mobile robot systems (Nazarova and Zhai, 2019), transportation networks (Yazicioglu et al , 2018), electrical power systems (Patil et al , 2019) and so forth. These processes can be described by multi-variable nonlinear models that are the field of important parametric perturbations.…”