Title: Optimization of AoII and QAoII in Multi-User Links

Abstract: We consider a network with multiple sources and a base station that send time-sensitive information to remote clients. The Age of Incorrect Information (AoII) captures the freshness of the informative pieces of status update packets at the destinations. We derive the closed-form Whittle Index formulation for a push-based multi-user network over unreliable channels with AoII-dependent cost functions. We also propose a new semantic performance metric for pull-based systems, named the Age of Incorrect Information at Query (QAoII), that quantifies AoII at particular instants when clients generate queries. Simulation results demonstrate that the proposed Whittle Index-based scheduling policies for both AoII and QAoII-dependent cost functions are superior to benchmark policies, and adopting query-aware scheduling can significantly improve the timeliness for scenarios where a single user or multiple users are scheduled at a time.