  We study the scheduling problem in a status update system composed of an
arbitrary number of information sources with different service time
distributions and weights for the purpose of minimizing the weighted sum age of
information (AoI). In particular, we study open-loop schedulers which rely only
on the statistics (specifically, only on the first two moments) of the source
service times, in contrast to closed-loop schedulers that also make use of the
actual realizations of the service times and the AoI processes in making
scheduling decisions. Open-loop scheduling policies can be constructed off-line
and are simpler to implement compared to their closed-loop counterparts. We
consider the generate-at-will (GAW) model, and develop an analytical method to
calculate the exact AoI for the probabilistic and cyclic open-loop schedulers.
In both cases, the server initiates the sampling of a source and the ensuing
transmission of the update packet from the source to the server in an open-loop
manner; either based on a certain probability (probabilistic scheme) or
according to a deterministic cyclic pattern (cyclic scheme). We derive the
optimum open-loop cyclic scheduling policy in closed form for the specific case
of N=2 sources and propose well-performing heuristic cyclic schedulers for
general number of sources, i.e., N>2. We study the proposed cyclic schedulers
against probabilistic schedulers and several existing methods in the literature
to validate their effectiveness.
