Timely Multi-Goal Transmissions With an Intermittently Failing Sensor

A sensor observes a random phenomenon and transmits updates about the observed phenomenon to a remote monitor. The sensor may experience intermittent failures in which case the monitor will not receive any updates until the sensor has recovered. The monitor wants to keep a timely view of the observed process, as well as to detect any sensor failures, using the timings of the updates. We analyze this system model from a goal-oriented and semantic communication point of view, where the communication has multiple goals and multiple meanings/semantics. For the first goal, the performance is quantified by the age of information of the observed process at the monitor. For the second goal, the performance is quantified by the probability of error of the monitor's estimation of the sensor's failure status. Each arriving update packet brings both an information update and an indication about the sensor's status. The monitor estimates the failure status of the sensor by using the timings of the received updates. This estimation is subject to error, since a long period without any update receptions may be due to a low update rate or a failure of the sensor. We examine the trade-off between these two goals. We show that the probability of error of estimating a sensor failure decreases with increased update rate, however, the age of information is minimized with an intermediate update rate (not too low or high).