Improving Real-Time Feasibility Analysis for Use in Linear Optimization Methods

In the design of time-critical applications, schedulability analysis can be used to define the feasibility region of tasks so that optimization techniques can find the best design solution that satisfies the deadlines. This method has been applied to obtain the optimal task implementation, priority assignment or placement of tasks onto CPUs in previous work. The definition of the feasibility region based on response time calculation requires many integer variables and is too complex for solvers. Approximation techniques have been used to define a convex subset of the feasibility region, often used in conjunction with branch and bound to compute sub-optimal solutions. In this paper, we provide an improved and simpler feasibility analysis method that allows an exact definition of the feasibility region in Mixed Integer Linear Programming (MILP) optimization methods. The encoding of the feasibility region using our method requires a significantly smaller number of binary variables and is viable for the treatment of industrial-size problems as shown by the experiments.