Controllability of transportation networks

Investigating the Relationship between Controller Locations and Dynamic Traffic Control in Generic Transportation Networks

“…We adopt the modeling framework previously developed in Rinaldi ( 1 ). Considering a transportation network described by a graph G ( N , L ) , with N the set of nodes and L the set of links, we can relate the evolution of cumulative vehicle numbers (CVN) at adjacent nodes, assuming first-order traffic flow dynamics bearing a triangular fundamental diagram, through a linear time-invariant dynamical system:…”

“…Marco Rinaldi 1 and Francesco Viti 1 Abstract Traffic control policies aim at reducing the negative externalities that ever-growing demand is causing on transportation networks, such as congestion and pollutant emissions. To achieve these goals, strategies coordinating and aligning the effects of several individual traffic controllers have received increasing attention in research and development in the past decades.…”

“…might simply be impossible to trigger through control actions. In our previous study (1) we have shown that placing controllers to achieve full controllability is a sufficient condition to ensure that the true global minimum of a given objective function (specifically, total cost) can be reached in the static assignment domain.…”

“…As a result of these strong nonlinearities, the choice of initial point in optimization-based approaches becomes extremely relevant, with unlucky choices potentially yielding no gain with respect to no-control assumptions. While researching this aspect, in our previous work we established how not only control settings are potentially responsible for substandard optimization results, but also how controller locations play a major role in the success of traffic control strategies ( 1 ). Indeed, to correctly steer a complex network toward desirable dynamics, a minimal subset of the network’s nodes/links must be equipped with controllers, directly dependent on the network’s topology and on the dynamics being object of control ( 22 , 23 ).…”

“…Depending on the amount, location, and type of controllers installed on a network, specific configurations of the network’s state (in relation to flows, buffered vehicles’ locations and quantities, split fractions, chosen routes, …) might simply be impossible to trigger through control actions. In our previous study ( 1 ) we have shown that placing controllers to achieve full controllability is a sufficient condition to ensure that the true global minimum of a given objective function (specifically, total cost) can be reached in the static assignment domain.…”