Scheduling periodic jobs using imprecise results

One approach to avoid timing faults in hard, real-time systems is to make available intermediate, imprecise results produced by real-time processes. When a result of the desired quality cannot be produced in time, an imprecise result of acceptable quality produced before the deadline can be used. The problem of scheduling periodic jobs to meet deadlines on a system that provides the necessary programming language primitives and run-time support for processes to return imprecise results is discussed. Since the scheduler may choose to terminate a task before it is completed, causing it to produce an acceptable but imprecise result, the amount of processor time assigned to any task in a valid schedule can be less than the amount of time required to complete the task. A meaningful formulation of the scheduling problem must take into account the overall quality of the results. Depending on the different types of undesirable effects caused by errors, jobs are classified as type N or type C. For type N jobs, the effects of errors in results produced in different periods are not cumulative. A reasonable performance measure is the average error over all jobs. Three heuristic algorithms that lead to feasible schedules with small average errors are described. For type C jobs, the undesirable effects of errors produced in different periods are cumulative. Schedulability criteria of type C jobs are discussed.