Average-cost PCL-indexability and quadratic-time Whittle index computation for state-capped buffered AoI scheduling

José Niño Mora

DES - Working Papers. Statistics and Econometrics. WS from Universidad Carlos III de Madrid. Departamento de Estadística

Abstract: We study age-of-information (AoI) scheduling with Bernoulli arrivals to one-packet buffers and unreliable transmissions, focusing on the long-run average criterion. A user's state is (r,d), where r is the buffered-packet age, r+d is the receiver AoI, and successful delivery reduces AoI by d. For every finite pair of coordinatewise caps and every nonnegative nondecreasing AoI cost, we analyze indexability through the framework based on partial conservation laws (PCLs). PCL-indexability entails two conditions: positive marginal work (PCLI1) and nondecreasing marginal productivity values along an adaptive-greedy active-set sweep (PCLI2). We prove unichainness, existence of an optimal row-threshold selector for every activation charge without cross-row threshold ordering, and positive Poisson-bias marginal work. For the monotonically connected row-threshold family, selector optimality and (PCLI1) imply (PCLI2) analytically, yielding exact average-cost Whittle indices without numerical monotonicity verification. We also revisit the same capped project under discounting. For any discount factor 0

Keywords: Age; Of; Information; Restless; Bandits; Whittle; Index; Partial; Conservation; Laws; Adaptive-Greedy; Algorithm; Discounted; And; Average-Cost; Criteria (search for similar items in EconPapers)
Date: 2026-10-22
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Persistent link: https://EconPapers.repec.org/RePEc:cte:wsrepe:51050

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