Lagrange Index based Scheduling for Minimizing Age of Updates from Heterogeneous Sources

Modern sensing systems generate heterogeneous updates ranging from small status packets to large data objects. We study a single-hop wireless uplink network where sensors generate updates at will, each consisting of a sensor dependent number of packets. Under a strict medium-access constraint and non-preemptive (no-switching) transmissions, decision stages become action-dependent and stochastic. We formulate the problem as a restless multi-armed bandit (RMAB) with semi-Markov decision process (SMDP) dynamics and develop a Lagrange index based heuristic for minimizing weighted average AoI cost. For the weighted AoI setting, we utilize the structural properties of the heuristic to enable efficient index computation. Numerical results demonstrate consistent performance gains over existing non-preemptive scheduling policies, providing a practical solution for heterogeneous freshness-aware systems.