In real-time systems, timeliness of task completion is very crucial as correctness of the results depend 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. Task scheduling in real-time systems aim towards devising a feasible schedule such that timing constraints, resource constraints, precedence constraints etc are complied. The most important timing constraint of a real-time task is the deadline within which it must finish execution. Another important timing constraint is the processing time, because the processor remains busy for this duration of time. However, in the early phase of system design only an approximate idea of the tasks as well as their characteristics are known. Hence, uncertainty or impreciseness is associated with the task deadlines and processing times. This necessitates the use of fuzzy numbers to model task deadlines and processing times in real-time systems. Fuzzy deadlines and fuzzy processing times represent real-time system better, because classical real-time scheduling models suffer from the following limitations:

(i) Although separate models and solutions exist for hard real-time systems and soft real-time systems, models that may be utilized for both hard and soft real-time systems are not available. Further, in the early phase of the design, when even the source code and the tasks timing constraints are not frozen, all decisions about the task schedule have to be made. Therefore task deadlines and processing times etc. are all designer approximations. Thus, fuzzy numbers come as a natural tool to model hard and soft real-time tasks realistically. This justifies the use of fuzzy numbers for timing parameters of real-time tasks.

(ii) Deterministic models for real-time systems are always over constrained. Designs are accepted if they ensure meeting the deadlines otherwise get rejected if deadlines are missing. This happens at the time of solving the models and no information is provided regarding by how much the deadlines are actually missed. However, considerations of fuzzy numbers to model processing times and deadlines provide the designers with wider options and sufficient information to take decisions on the model design. We address these issues by developing several models for fuzzy real-time scheduling based on different fuzzy measures and membership functions. The group is also working on new optimization techniques that can be applied to the fuzzy real-time scheduling problem, to analyze schedulability conditions in the fuzzy setting. We are working for a theoretical analysis of the schedulability conditions that may be developed for real-time task sets with fuzzy timing parameters using Zadeh’s Extension Principle.