  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.
