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This paper examines the use of the fluid limit, a mathematical tool used to analyze Age of Information (AoI) in networks, to study the long-term average AoI for scheduling optimization in multiaccess networks with transmission frequency constraints. Two types of problems that have been studied in the literature but remain unsolved are revisited under this approach, wherein multiple agents transmit over an error-prone multiaccess channel, and long-term transmission frequency constraints are considered with either a resource constraint or a minimum throughput requirement. Previous works have derived the Whittle's Index (WI) policy, max-weight policy and average AoI lower bound, however without optimality guarantee or closed-form performance analysis. This work advances the field by deriving closed-form optimal AoI and achieving scheduling policies for both problems, by utilizing the fluid limit tool and transforming the original high-dimensional Markov decision process into solving a set of partial derivative equations. As a result, threshold-based scheduling policies with closed-form threshold expressions are obtained which can be proven to be asymptotically optimal when the number of agents is large. Numerical simulations are conducted to demonstrate the performance optimality of the proposed schemes and analytical results.
Wang et al. (Mon,) studied this question.