A bi-level approach for the optimal control of flows through a network

The operational management of traffic flows, controlled by different decision makers (that do not exchange information) through a network, gives rise to a common modeling framework that may find application within different research areas: road traffic control, hazardous materials transportation, telecommunication networks, energy systems. In this paper, a general decision architecture is considered and an application is provided to the case of the management of fleets of vehicles that transport hazardous materials (hazmat). The considered architecture takes into account the presence of different decision makers. The problem is also characterized by the presence of several (possibly conflicting) objectives. In the case of hazmat transportation, such objectives may be the reduction of economic costs and the containment of the risk (for vehicles and infrastructures). The considered model includes an upperlevel decision maker that can take decisions affecting the utility functions of the lower-level decision makers (LDMs), for example, changing the tolls for the LDMs, but leaving to such LDMs some decision capability. A specific case study is considered, relevant to the management of vehicles carrying hazmat through a critical infrastructure.