Discounted Age of Information for Networks of Constrained Devices

Remote sensing systems can exploit age of information as a performance metric to track the freshness of the data exchanged. However, sensing terminals often have a finite time span to perform their task, for example due to their limited batteries or because of mission-critical contexts. A realistic model of such scenarios ought to consider the importance of a performance metric evaluated over time, with lower weight given to future evaluations. We propose to take into account these aspects through a discounted age of information. We show how this admits some non-trivial closed form expressions, and we consider the problem of minimizing a linear combination of the discounted age of information with a transmission cost term for two different scenarios of interest, a single terminal case, and a slotted ALOHA medium access. We discuss the implications of system parameters on this metric, and its overall characterization of the resulting system performance.