Parametric Timing Analysis

Embedded systems often have real-time constraints. Traditional timing analysis statically determines the maximum execution time of a task or a program in a real-time system. These systems typically depend on the worst-case execution time of tasks in order to make static scheduling decisions so that tasks can meet their deadlines. Static determination of worst-case execution times imposes numerous restrictions on real-time programs, which include that the maximum number of iterations of each loop must be known statically. These restrictions can significantly limit the class of programs that would be suitable for a real-time embedded system. This paper describes work-in-progress that uses static timing analysis to aid in making dynamic scheduling decisions. For instance, different algorithms with varying levels of accuracy may be selected based on the algorithm's predicted worst-case execution time and the time allotted for the task. We represent the worst-case execution time of a function or a loop as a formula, where the unknown values affecting the execution time are parameterized. This parametric timing analysis produces formulas that can then be quickly evaluated at run-time so dynamic scheduling decisions can be made with little overhead. Benefits of this work include expanding the class of applications that can be used in a real-time system, improving the accuracy of dynamic scheduling decisions, and more effective utilization of system resources.