The Open-Radio Access Network (O-RAN) Alliance has introduced a new architecture to enhance the 6th generation (6G) RAN. However, existing O-RAN-compliant solutions lack crucial details to perform effective control loops at multiple time scales. In this vein, we propose ORANUS, an O-RAN-compliant mathematical framework to allocate radio resources to multiple ultra Reliable Low Latency Communication (uRLLC) services at different time scales. In the near-RT control loop, ORANUS relies on a novel Stochastic Network Calculus (SNC)-based model to compute the amount of guaranteed radio resources for each uRLLC service. Unlike traditional approaches as queueing theory, the SNC-based model allows ORANUS to ensure the probability the packet transmission delay exceeds a budget, i.e., the violation probability, is below a target tolerance. ORANUS also utilizes a RT control loop to monitor service transmission queues, dynamically adjusting the guaranteed radio resources based on detected traffic anomalies. To the best of our knowledge, ORANUS is the first O-RAN-compliant solution which benefits from SNC to carry out near-RT and RT control loops. Simulation results show that ORANUS significantly improves over reference solutions, with an average violation probability 10x lower.