Statistical Guarantee Optimization for AoI in Single-Hop and Two-Hop Systems with Periodic Arrivals

Age of Information (AoI) has proven to be a useful metric in networked systems where timely information updates are of importance. In the literature, minimizing "average age" has received considerable attention. However, various applications pose stricter age requirements on the updates which demand knowledge of the AoI distribution. Furthermore, the analysis of AoI distribution in a multi-hop setting, which is important for the study of Wireless Networked Control Systems (WNCS), has not been addressed before. Toward this end, we study the distribution of AoI in a WNCS with two hops and devise a problem of minimizing the tail of the AoI distribution with respect to the frequency of generating information updates, i.e., the sampling rate of monitoring a process, under first-come-first-serve (FCFS) queuing discipline. We argue that computing an exact expression for the AoI distribution may not always be feasible; therefore, we opt for computing upper bounds on the tail of the AoI distribution. Using these upper bounds we formulate Upper Bound Minimization Problems (UBMP), namely, Chernoff-UBMP and alpha-relaxed Upper BoundMinimization Problem (alpha-UBMP), where alpha > 1 is an approximation factor, and solve them to obtain "good" heuristic rate solutions. We demonstrate the efficacy of our approach by solving the proposed UBMPs for three service distributions: geometric, exponential, and Erlang. Simulation results show that the rate solutions obtained are near-optimal for minimizing the tail of the AoI distribution for the considered distributions.