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Cyber-physical systems (CPS) are physical and engineered systems whose operations are controlled, coordinated and monitored, by (mostly) resource-constrained computing and communication elements. Applications of CPS can be found in diverse, yet critical, areas like transportation, critical infrastructures, healthcare and industrial control. Many applications in the CPS domain have components of mixed criticalities which possess real-time requirements, and need schedulability validation. The literature of scheduling algorithms commonly relies on sufficient tests to determine if a set of mixed-criticality tasks is schedulable on a single processor. The drawback of these safe tests is their pessimism, a matter that could be solved if an exact schedulability analysis is used. This talk is spent to an algorithm for exact worst-case response time characterization of mixed-criticality sporadic real-time tasks executing according to a given fixed-priority scheduler. We also discuss an interesting result that if an exact schedulability test is used, the Audsley’s optimal priority assignment algorithm is not applicable to the mixed-criticality case. A feasibility interval for some specific setup of the system model is also provided.