Task Scheduling under Uncertain Timing Constraints in Real-Time Embedded Systems

In real-time embedded systems, timeliness of task completion is a very important factor. In such systems, correctness of the output depends on the timely production of results in addition to the logical outcome of computation. Thus, tasks have explicit timing constraints besides other characteristics of general systems, and task scheduling aims towards devising a feasible schedule of the tasks such that timing constraints, resource constraints, precedence constraints, etc. are complied. In real-time embedded systems, the most important timing constraint of a task is the deadline, as tasks must be completed within this time. The next important timing constraint is the processing time, because a task occupies a processor only for this duration of time. However, in the early phase of real-time embedded systems design only an approximate idea of the tasks and their characteristics are known. As a result, uncertainty or impreciseness is associated with the task deadlines and processing times; hence, it is appropriate to use fuzzy numbers to model deadlines and processing times in real-time embedded systems. The chapter introduces a new method using mixed cubic-exponential Hermite interpolation technique for intuitively defining smooth Membership Functions (MFs) for fuzzy deadlines and processing times. The effect of changes in parameterized MFs on the task schedulability and task priorities are explained. Examples are given to demonstrate the significant features and better performance of the new technique.