Robust cooperative monitoring problem

The cooperative monitoring problem refers to the placement and configuration of passive monitoring points (or monitors) to jointly realize a task of monitoring time-varying traffic flows. Given a traffic monitoring task, e.g., monitor a traffic flow percentage, the objective consists in minimizing the total monitoring cost to realize this task. We formulate the corresponding problem as a mixed-integer linear program (MILP). This formulation can also be dualized to determine the gain obtained when increasing the number of monitoring points (i.e., the monitoring installation cost) and the fraction of monitored traffic (i.e., the monitoring configuration cost). As traffic flows are subject to uncertainty, we extend the MIP formulations developed in [1] to their robust counter-part when the uncertainty in traffic demands is modeled by means of box+polyhedral and box+ellipsoidal perturbation sets.