Resilient Control of Transportation Networks by Using Variable Speed Limits

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, that is, 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 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.