Resilient Operation of Transportation Networks via Variable Speed Limits

TL;DR

This paper proposes using variable speed limits to prevent systemic failures in transportation networks modeled as dynamical flow systems, especially when local routing decisions and external inflows threaten network stability.

Contribution

It introduces a novel control strategy of variable speed limits to enhance resilience, ensuring failure prevention without needing additional physical capacity or global routing coordination.

Findings

Proper speed limit adjustments can prevent systemic failures.

Responsive local routing combined with variable speed limits enhances network resilience.

Systemic failures can be mitigated even with feasible external inflows.

Abstract

In this paper, 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 particle densities. The density on each link has first order dynamics driven by the difference of its incoming and outgoing flows. A link irreversibly 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 do not necessarily help in 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. Our main result shows 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 is much easier in practice to adjust the speed limits than to build more physical capacity or to alter routing decisions that are determined by social behavior.