ReTiS Lab Real Time Systems Laboratory Sensitivity Analysis in Real-Time Systems Enrico Bini Scuola Superiore Sant'Anna Why Sensitivity Analysis The scenario in Real-Time System design: � stringent constraints from the hardware (energy consumption, limited computational power…) � increasing demands from end users (new features, low prices, short response times, safety,…) � highly competitive market! Current solution: � The local guru selects a solution, based on its expertise � The solution is verified, checked, tested and, eventually, changed 1
Current practice in RT Systems Design Goal: selecting the best parameters for optimizing system performance . select initial values we must use we can use less resources more resources is the system NO NO YES YES feasible? The RT system design in the parameter space Where? param 2 ? utility ? NO ? ? function ? ? ? ? ? ? ? ? ? ? ? ? ? ? p YES 2 initial value param 1 p 1 2
The ideal design phase Problem: the design is made by attempts � Ideally we would like… � to know the feasible region param 2 utility � to know the utility function function � to perform the optimization param 1 Challenging aspects 1. To highlight variables under the designer's control. 2. Distinguish between cost and constraint . 3. Model the resource constraint (or a "suitable" approximation). 4. Model the cost (or a "suitable" error bounded function). 5. Find the optimal solution. 3
Questions? Comments? ? The Application Model A task τ i is modeled by ( C i , T i , D i ) , where: • C i is the computation time; • T i is the period; • D i is the deadline. Tasks may be scheduled by • Fixed Priority (FP), τ 1 has the highest priority; • Earliest Deadline First (EDF). 4
Results for FP Sensitivity of the computation times C i C 1 � C i are design variables � find the distance to boundary from an initial value � optimal C 2 Sensitivity of the periods T i T 1 � given C i , D i and priorities, and assuming T i as design parameters � given an initial value T 2 � find the distance to boundary Results for EDF Sensitivity of the computation times C i C 1 � C i are design variables � find the distance to boundary from an initial value � optimal C 2 Sensitivity of the periods T i T 1 � given C i , D i and priorities, and assuming T i as design parameters � given an initial value T 2 � find the distance to boundary 5
Results in Hierarchical Scheduling Sensitivity of the computation times C i C 1 � C i are design variables � find the distance to boundary from an initial value � optimal C 2 Sensitivity of the periods T i T 1 � given C i , D i and priorities, and assuming T i as design parameters � given an initial value T 2 � find the distance to boundary Qu 1. E. Bini, G. C. Buttazzo, G. M. Buttazzo, "Rate Monotonic Analysis: the Hyperbolic Bound", IEEE Transactions on Computers, 2003. 2. E. Bini, G. Buttazzo, "Schedulability Analysis of Periodic Fixed Priority Systems", IEEE Transactions on Computers, 2004. 3. G. Lipari, E. Bini, "A Methodology for Designing Hierarchical Scheduled Systems", Journal of Embedded Computing, 2004. 4. E. Bini, M. Di Natale, "Optimal Rate Selection in Fixed Priority Systems", Real-Time Systems Symposium, 2005. 5. E. Bini, M. Di Natale, G. Buttazzo "Sensitivity Analysis for Fixed- Priority Real-Time Systems", Journal of Real-Time Systems, 2007. 6. E. Bini, G. Buttazzo, "The Space of EDF Feasible Deadlines", Euromicro Conference on Real-Time Systems, 2007. 6
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