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In multi-source status update systems, sources need to be scheduled appropriately to maintain timely communication between each of the sources and the monitor. A cyclic schedule is an age-agnostic schedule in which the sources are served according to a fixed finite transmission pattern, which upon completion, repeats itself. Such a scheme has a low $O(1)$ runtime complexity, which is desirable in large networks. This paper's focus is on designing transmission patterns so as to be used in massive scale networking scenarios involving a very large number of sources, e.g., up to thousands of IoT sources, with service time requirements and weights being heterogeneous in nature. The goal is to minimize the weighted sum age of information (AoI), called weighted AoI, when transmitting users' packets over a channel susceptible to heterogeneous packet errors. The main tool we use is a stochastic modeling framework using either Markov chains (MC) or moment generating functions (MGF), by which we obtain the weighted AoI for a given transmission pattern, which is not straightforward in the presence of packet drops. Using this framework, we provide a lower bound on the weighted AoI for the particular case of two sources, and also an algorithm to attain this lower bound. Then, by using the same framework, we design a cyclic scheduler for general number of sources with reasonable complexity using convex optimization and well-established packet spreading algorithms, and comparatively evaluate the proposed algorithm and existing age-agnostic scheduling schemes for general number of sources (resp.~two sources) when the lower bound is not available (resp.~when it is available). We present extensive numerical results to validate the effectiveness of the proposed approach. |
