An expression-based method to apply Finitary Real-Time Calculus using one function call

Modern networks and embedded systems, such as those in automotive control and industrial automation, increasingly require strict timing and reliability guarantees to ensure safety and efficiency. Deterministic Network Calculus (DNC) is a theory that uses (min,+) and (max,+) algebra to compute worst-case bounds on network traffic delay and backlog, ensuring critical networks meet performance targets. It represents data movement and network service as functions of time, which are combined through mathematical operators for system analysis. Real-Time Calculus (RTC) shares the same algebraic foundation as DNC but focuses on analyzing response times in real-time systems. By modeling upper and lower bounds on arrival and service processes, RTC is widely used in the design and verification of scheduling algorithms in embedded systems, ensuring processors and controllers meet strict deadlines and prevent failures. However, RTC faces performance issues in large-scale systems with complex timing characteristics. This is due to the pseudo-periodic curves used to model workload and service, which can lead to exponential growth in stored information, making computations infeasible. Finitary RTC addresses this issue by restricting curve domains and removing unnecessary information, simplifying calculations. In this work, we modify Finitary RTC to make it independent of the RTC framework, enabling its application to a broader range of curve expressions and clarifying the algorithm for computing entire expressions. This independence allows integration into the open-source DNC library Nancy, optimizing performance when handling complex pseudo-periodic curves. The resulting extension, Nancy.FinitaryCalculus, accelerates computations and extends Nancy.Expressions, enabling users to apply the Finitary RTC algorithm with a single function call. This enhancement simplifies the user experience by eliminating repetitive code and reducing the need for in-depth knowledge of Finitary RTC theory.