Given a set of n tasks and m resources, where each task x has a rational weight x:w = x:e=x:p; 0 < x:w < 1, a periodic schedule is one that allocates a resource to a task x for exactly x:e time units in each interval [x:p k; x:p (k + 1)) for all k 2 N. We de ne a notion of proportionate progress, called P-fairness, and use it to design an e cient algorithm which solves the periodic scheduling problem. Keywords: Euclid's algorithm, fairness, network ow, periodic scheduling, resource allocation.

Given n periodic tasks, each characterized by an execution requirement and a period, and m identical copies of a resource, the periodic scheduling problem is concerned with generating a schedule for the n tasks on the m resources. We present an algorithm that schedules every feasible instance of the periodic scheduling problem, and runs in O(minfm lg n; ng) time per slot scheduled. 1 Introduction Given a set \Gamma of n tasks, where each task x is characterized by two integer parameters x:e and x:p, and m identical copies of a resource, a periodic schedule is one that allocates a resource to each task x in \Gamma for exactly x:e time units in each interval [k \Delta x:p; (k+1) \Delta x:p) for all k in N, subject to the following constraints: Constraint 1: A resource can only be allocated to a task for an entire "slot" of time, where for each i in N slot i is the unit interval from time i to time i + 1. Constraint 2: No task may be allocated more than one copy of the resource ...

In this paper, we consider the preemptivescheduling of hard-real-time sporadic task systems on one processor. Wefirstgive necessary and sufficient conditions for a sporadic task system to be feasible (i.e., schedulable). The conditions cannot, in general, be tested efficiently (unless P = NP). They do, however, lead to a feasibilitytestthat runs in efficient pseudo-polynomial time for a very large percentage of sporadic task systems. 1 Introduction Scheduling theory as it applies to hard-real-time environments --- environments where the missing of a single deadline may have disastrous consequences --- seems to currently be enjoying a renaissance. Hardreal -time scheduling problems may concern either fixed-duration tasks or recurring tasks that must be completed within a certain time frame. The problems most studied within the recurring category involve periodically recurring tasks [LL73, LM80, LM81, LW82,Mok83, BHR90]. Aperiodically or sporadically recurring tasks have also been stud...

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In applications ranging from video reception to telecommunications and packet communication to aircraft control, tasks enter periodically and have fixed response time constraints, but missing a deadline is acceptable, provided most deadlines are met. We call such tasks "occasionally skippable". We look at the problem of uniprocessor scheduling of occasionally skippable periodic tasks in an environment having periodic tasks. We show that making optimal use of skips is NP-hard. We then look at two algorithms called Skip-Over Algorithms (one a variant of earliest deadline first and one of rate monotonic scheduling) that exploit skips. We give schedulability bounds for both. 1 Introduction 1.1 Basic Assumptions and Definitions We consider a uni-processor system in which preemption is possible at any time and costs nothing. All tasks are periodic but they may enter the system at any time. A task is characterized by its computation requirements and period; the deadline of a task equals it...

Recent advances in wireless technology have brought us closer to the vision of pervasive computing where sensors/actuators can be connected through a wireless network. Due to cost constraints and the dynamic nature of sensor networks, it is undesirable to assume the existence of base stations connected by a wired backbone. In this paper, we present a network architecture suitable for sensor networks along with a medium access control protocol based on Earliest Deadline First. The key idea consists of exploiting the periodic nature of the traffic in sensor networks. Hence, medium access control can be achieved using implicit prioritization instead of relying on control packets. The robustness of our protocol is proved in spite of packets loss and its effectiveness is shown by experimental results.

* We present a task model for the real-time execution of eventdriven tasks in which no a priori characterization of the actual arrival rates of events is known; only the expected arrival rates of events is known. The model, called rate-based execution (RBE), is a generalization of Mok's sporadic task model [14]. The RBE model is motivated naturally by distributed multimedia and digital signal processing applications. We derive necessary and sufficient conditions for determining the feasibility of an RBE task set and demonstrate that earliest deadline first (EDF) scheduling is an optimal scheduling algorithm for both preemptive and nonpreemptive execution environments, as well as hybrid environments wherein RBE tasks access shared resources. Our analysis of RBE tasks demonstrates a fundamental distinction between deadline based scheduling methods and static priority based methods. We show that for deadlinebased scheduling methods, feasibility is solely a function of the distribution o...

AbstractÐAn increasing number of real-time applications, related to multimedia and adaptive control systems, require greater flexibility than classical real-time theory usually permits. In this paper, we present a novel scheduling framework in which tasks are treated as springs with given elastic coefficients to better conform to the actual load conditions. Under this model, periodic tasks can intentionally change their execution rate to provide different quality of service and the other tasks can automatically adapt their periods to keep the system underloaded. The proposed model can also be used to handle overload conditions in a more flexible way and to provide a simple and efficient mechanism for controlling a system's performance as a function of the current load. Index TermsÐReal-time scheduling, overload management, rate adaptation. 1

This paper concerns the problem of scheduling sets of preemptable, periodic tasks on multiple resources. We consider a task model that allows arbitrary mixes of fixed and migratable tasks, and prove the existence of an optimal pfair scheduler in this model. Fixed tasks must always be scheduled on a given resource, while migratable tasks can be scheduled on different resources at different times. A pfair scheduler produces a periodic schedule in which the times each task is allocated a processor are approximately evenly spread throughout its period. This work extends work of Baruah et al, who proved a similar result for systems in which all tasks are migratable.

We give a comprehensive summary of our recent research on the feasibility problems for various types of hard-real-time preemptive task systems on one processor. We include results on periodic, sporadic, and hybrid task systems. While many of the results herein have appeared elsewhere, this is the first paper presenting a holistic view of the entire problem.