Sample-drop firmness analysis of TDMA-scheduled control applications

This paper proposes methods for verification of (m, k)-firmness properties of control applications running on a shared TDMA-scheduled processor. We particularly consider dropped samples arising from processor sharing. Based on the available processor budget for any sample that is ready for execution, the Finite-Point (FP) method is proposed for quantification of the maximum number of dropped samples. The FP method is further generalized using a timed automata based model to consider the variation in the period of samples. The UPPAAL tool is used to validate and verify the timed automata based model. The FP method gives an exact bound on the number of dropped samples, whereas the timed-automata analysis provides a conservative bound. The methods are evaluated considering a realistic case study. Scalability analysis of the methods shows acceptable verification times for different sets of parameters.