Real-time scheduling of periodic tasks with processing times and deadlines as parametric fuzzy numbers

Task scheduling is very important in real-time systems as it accomplishes the crucial goal of devising a feasible schedule of the tasks. However, the uncertainty associated with the timing constrains of the real-time tasks makes the scheduling problem difficult to formulate. This motivates the use of fuzzy numbers to model task deadlines and completion times. In this paper a method for intuitively defining smooth membership functions (MFs) for deadlines and execution times has been proposed using mixed cubic-exponential Hermite interpolation parametric curves. The effect of changes in parameterized MFs on the task schedulability and task priorities are also reported. A new technique is proposed based on the concept of dynamic slack calculation to make the existing model more practical and realistic. Examples are given to demonstrate the more satisfactory performance of the new technique.