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This paper describes three algorithms for scheduling preemptive, imprecise tasks on a processor to minimize the total error. Each imprecise task consists of a mandatory task followed by an optional task. Some of the tasks are on-line; they arrive after the processor begins execution. The algorithms assume that when each new on-line task arrives, its mandatory task and the portions of all the mandatory tasks yet to be completed at the time can be feasibly scheduled to complete by their deadlines. The algorithms produce for such tasks feasible schedules whose total errors are as small as possible. The three algorithms are designed for three types of task systems: (1) when every task is on-line and is ready upon its arrival, (2) when every on-line task is ready upon arrival but there are also off-line tasks with arbitrary ready times, and (3) when on-line tasks have arbitrary ready times. Their running times are 0 (n logn ), 0 (n log n ), and 0 ( n log2 n ), respectively.

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PERTS is a prototyping environment for real-time systems. It is being built incrementally and will contain basic building blocks of operating systems for time-critical applications, tools and performance models for the analysis, evaluation and measurement of real-time systems, and a simulation/emulation environment.It is designed to support the use and evaluation of new design approaches, experimentations with alternative system building blocks, and the analysis and performance profiling of prototype real-time systems. I. INTRODUCTION While existing approaches, techniques and tools for the design, prototyping and development of software systems are effective for many application domains, they often do not address the difficulties in building hard real-time computing systems. A hard real-time computing system, hereafter simply called a real-time system, is one in which most tasks have hard timing constraints. Here, the term task refers to a basic unit of work. A task may be a granule of computation, a unit of data transmission, a file access, or an I/O operation, etc. The simplest timing constraint imposed on a task is its deadline, the point in time by which the task is required to complete. The result produced by a task with a deadline is correct only if it is available by the deadline, in addition to being functionally correct. A late result is of little or no use. Applications supported by real-time systems include command and control, guidance and navigation, flight control, object identification, autonomous vehicle control, and intelligent manufacturing.approach would begin with models and optimality criteria that explicitly account for the constraints and possibilities of trading off between various figures of merit, and then design the application and the underlying system to achieve the desired tradeoffs. Such an approach would lead to more flexible, easy-)_ This work has been partially supported by ONR Contract Nos. NOOO14-89-J-1181, and N000-92-J-1815. 372L https://ntrs.nasa.gov/search.