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We study the scheduling problem in a status update system composed of anarbitrary number of information sources with different service timedistributions and weights for the purpose of minimizing the weighted sum age ofinformation (AoI). In particular, we study open-loop schedulers which rely onlyon the statistics (specifically, only on the first two moments) of the sourceservice times, in contrast to closed-loop schedulers that also make use of theactual realizations of the service times and the AoI processes in makingscheduling decisions. Open-loop scheduling policies can be constructed off-lineand are simpler to implement compared to their closed-loop counterparts. Weconsider the generate-at-will (GAW) model, and develop an analytical method tocalculate the exact AoI for the probabilistic and cyclic open-loop schedulers.In both cases, the server initiates the sampling of a source and the ensuingtransmission of the update packet from the source to the server in an open-loopmanner; either based on a certain probability (probabilistic scheme) oraccording to a deterministic cyclic pattern (cyclic scheme). We derive theoptimum open-loop cyclic scheduling policy in closed form for the specific caseof N=2 sources and propose well-performing heuristic cyclic schedulers forgeneral number of sources, i.e., N>2. We study the proposed cyclic schedulersagainst probabilistic schedulers and several existing methods in the literatureto validate their effectiveness.

Minimizing Weighted Sum Age of Information with Open-Loop Cyclic Scheduling