Scheduling real-time, periodic jobs using imprecise results

A process is called a monotone process if the accuracy of its intermediate results is non-decreasing as more time is spent to obtain the result. The result produced by a monotone process upon its normal termination is the desired result; the error in this result is zero. External events such as timeouts or crashes may cause the process to terminate prematurely. If the intermediate result produced by the process upon its premature termination is saved and made available, the application may still find the result unusable and, hence, acceptable; such a result is said to be an imprecise one. The error in an imprecise result is nonzero. 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. This problem differs from the traditional scheduling problems since the scheduler may choose to terminate a task before it is completed, causing it to produce an acceptable but imprecise result. Consequently, the amounts of processor time assigned to tasks in a valid schedule can be less than the amounts of time required to complete the tasks. A meaningful formulation of this problem taking into account the quality of the overall result is discussed. Three algorithms for scheduling jobs for which the effects of errors in results produced in different periods are not cumulative are described, and their relative merits are evaluated

Imprecise results: Utilizing partial computations in real-time systems

In real-time systems, a computation may not have time to complete its execution because of deadline requirements. In such cases, no result except the approximate results produced by the computations up to that point will be available. It is desirable to utilize these imprecise results if possible. Two approaches are proposed to enable computations to return imprecise results when executions cannot be completed normally. The milestone approach records results periodically, and if a deadline is reached, returns the last recorded result. The sieve approach demarcates sections of code which can be skipped if the time available is insufficient. By using these approaches, the system is able to produce imprecise results when deadlines are reached. The design of the Concord project is described which supports imprecise computations using these techniques. Also presented is a general model of imprecise computations using these techniques, as well as one which takes into account the influence of the environment, showing where the latter approach fits into this model

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