Real-time applications have deadline constraints.\ The system should provision sufficient resources for the appli- cation to meet the deadlines, and use supply and demand bound functions to analyze the schedulability of workloads. The concept of the demand bound function describes the upper bound on the resources required by the application, while the supply-bound function specifies the lower bound on the resources supplied to the tasks. If the system provides fewer resources than required, the application will experience an overload. Most work concentrates on designing systems that cannot experience short periods of overloads.

This work explores resource provisioning for control applica- tions that can tolerate overloads. It introduces analysis techniques for supply and demand bound functions that specifically consider overloads and delays in a periodic resource model. With this ex- tended model, the work addresses three problems: (1) determine the worst-case delay for a given resource demand and supply under a periodic resource model, (2) find a periodic resource supply for a given workload and worst-case tolerable delay, and (3) for a control system with a given robustness criterion, identify a periodic resource supply with a worst-case delay.