  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.
