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

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.