On the Optimality of the Whittle’s Index Policy for Minimizing the Age of Information

In this article, we consider the average age minimization problem where a central entity schedules <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> users among the <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> available users for transmission over unreliable channels. It is well-known that obtaining the optimal policy, in this case, is a difficult task. Accordingly, the Whittle’s index policy has been suggested in earlier works as a heuristic for this problem. However, the analysis of its performance remained elusive. In the sequel, we overcome these difficulties and provide rigorous results on its asymptotic optimality in the many-users regime. Specifically, we first establish its optimality in the neighborhood of a specific system’s state. Next, we extend our proof to the global case under a recurrence assumption, which we verify numerically. These findings showcase that the Whittle’s index policy has analytically provable optimality in the many-users regime for the AoI minimization problem. Finally, numerical results that showcase its performance and corroborate our theoretical findings are presented.