Analyzing Age of Information in Multiaccess Networks with Time-Varying Channels: A Fluid Limits Approach

In this paper, we adopt the fluid limits approach to analyze the age of information (AoI) in a wireless multi-access network where users share the channel and transmissions are unreliable. We prove the convergence of the AoI occupancy measure to the fluid limit, represented by a partial differential equation (PDE). Furthermore, we demonstrate the global convergence to the equilibrium of the PDE, i.e., the stationary AoI distribution. Within this framework, we first consider the case of i.i.d. channel conditions and generate-at-will statuses for users. We demonstrate that a previously established AoI lower bound in the literature is asymptotically accurate, and a straightforward threshold-based access policy can be asymptotically optimal. Next, we consider the case where the channel states are time-varying, i.e., the Gilbert-Elliott channel model. We assume partial channel state information (CSI) is available due to channel probing singals. Theoretical analysis reveals that only a fraction of CSI is required to approach the optimal performance. Additionally, we numerically evaluate the performance of the proposed policy and the existing Whittle's index policy under time-varying channels. Simulation results demonstrate that the proposed policy outperforms the Whittle's index policy since the latter cannot adapt to time-varying channels.