Optimizing Real-Time Decision-Making in Sensor Networks

The rapid integration of digital technologies into physical systems has given rise to cyber-physical systems, where the interaction between the computational and physical components plays a crucial role. This study explores optimal decision-making in event detection and transmission scheduling within cyber-physical systems, emphasizing the crucial aspect of efficient decision-making. We consider the problem of monitoring and reporting about a single event taking place within a finite time window achieving a reward related to the timeliness of the status update. Thus, the objective corresponds to minimizing the age of information between the instant of the event x and the status update time t, with a further penalty for a missed event. The monitoring apparatus decides when to perform the status update without knowing the value of x, but only knowing its statistical distribution. We assume a triangular probability density function for the instant of the event taking place, with a variable average. We provide an analytical derivation of the optimal choice of the status update, highlighting interesting trends, such as the saturation in the value of t as x grows close to the limit of the observation window. This proposed problem and its analytical formalization may serve as a further foundation for the general analysis of optimal monitoring of cyber-physical systems.