Timely Cache Updating in Parallel Multi-Relay Networks

We consider a system consisting of a server, which receives updates for
$N$
files according to independent Poisson processes. The goal of the server is to deliver the latest version of the files to a user through a parallel network of
$K$
caches. We consider an update received by the user successful, if the user receives the same file version that is currently prevailing at the server. We derive an analytical expression for information freshness at the user. We observe that freshness for a file increases with increase in consolidation of rates across caches. To solve the multi-cache problem, we first solve the auxiliary problem of a single-cache system. We then rework this auxiliary solution to our parallel-cache network by consolidating rates to single routes as much as possible. This yields an approximate (sub-optimal) solution for the original problem. We provide an upper bound on the gap between the sub-optimal solution and the optimal solution. We present counterpart expressions and policies for version age of information by employing a stochastic hybrid system approach. Numerical results for both timeliness metrics show that the proposed sub-optimal policy closely follows the optimal policy.