Scheduling real-time, periodic jobs using imprecise results

Abstract

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