Reconfigurable Intelligent Surfaces (RIS) enable dynamic electromagnetic control for 6G networks, but existing control schemes lack responsiveness to fast-varying network conditions, limiting their applicability for ultra-reliable low latency communications. This work addresses uplink delay minimization in multi-RIS scenarios with heterogeneous per-user latency and reliability demands. We propose Delay-Aware RIS Orchestrator (DARIO), an O-RAN-compliant framework that dynamically assigns RIS devices to users within short time windows, adapting to traffic fluctuations to meet per-user delay and reliability targets. DARIO relies on a novel Stochastic Network Calculus (SNC) model to analytically estimate the delay bound for each possible user-RIS assignment under specific traffic and service dynamics. These estimations are used by DARIO to formulate a Nonlinear Integer Program (NIP), for which an online heuristic provides near-optimal performance with low computational overhead. Extensive evaluations with simulations and real traffic traces show consistent delay reductions up to 95.7% under high load or RIS availability.

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