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Fast Scheduling of Periodic Tasks on Multiple Resources
 In Proceedings of the 9th International Parallel Processing Symposium
"... 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 t ..."
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Cited by 101 (15 self)
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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 ...
Mixed Pfair/ERfair Scheduling of Asynchronous Periodic Tasks
, 2001
"... Pfair Scheduling was proposed by... In this paper, we introduce a workconserving variant of Pfair scheduling called "earlyrelease" fair (ERfair) scheduling. We also present a new scheduling algorithm called PD² and show that it is optimal for scheduling any mix of earlyrelease and nonearly ..."
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Cited by 94 (44 self)
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Pfair Scheduling was proposed by... In this paper, we introduce a workconserving variant of Pfair scheduling called "earlyrelease" fair (ERfair) scheduling. We also present a new scheduling algorithm called PD² and show that it is optimal for scheduling any mix of earlyrelease and nonearlyrelease asynchronous, periodic tasks. In contrast, almost all prior work on Pfair scheduling has been limited to synchronous systems. PD²is an optimization of an earlier deadlinebased algorithm of Baruah, Gehrke, and Plaxton called PD; PD² uses a simpler tiebreaking scheme than PD to disambiguate equal deadlines. We present a series of counterexamples that suggest that, in general, the PD² tiebreaking mechanism cannot be simplified. In contrast to this, we show that no tiebreaking information is needed on twoprocessor systems.
PriorityDriven Scheduling of Periodic Task Systems on Multiprocessors
, 2001
"... The scheduling of systems of periodic tasks upon multiprocessor platforms is considered. ..."
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Cited by 91 (15 self)
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The scheduling of systems of periodic tasks upon multiprocessor platforms is considered.
Scheduling with dynamic voltage/speed adjustment using slack reclamation in multiprocessor realtime systems
 IEEE TRANS. ON PARALLEL AND DISTRIBUTED SYSTEMS
, 2003
"... The high power consumption of modern processors becomes a major concern because it leads to decreased mission duration (for batteryoperated systems), increased heat dissipation, and decreased reliability. While many techniques have been proposed to reduce power consumption for uniprocessor systems ..."
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Cited by 87 (7 self)
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The high power consumption of modern processors becomes a major concern because it leads to decreased mission duration (for batteryoperated systems), increased heat dissipation, and decreased reliability. While many techniques have been proposed to reduce power consumption for uniprocessor systems, there has been considerably less work on multiprocessor systems. In this paper, based on the concept of slack sharing among processors, we propose two novel poweraware scheduling algorithms for task sets with and without precedence constraints executing on multiprocessor systems. These scheduling techniques reclaim the time unused by a task to reduce the execution speed of future tasks and, thus, reduce the total energy consumption of the system. We also study the effect of discrete voltage/speed levels on the energy savings for multiprocessor systems and propose a new scheme of slack reservation to incorporate voltage/speed adjustment overhead in the scheduling algorithms. Simulation and tracebased results indicate that our algorithms achieve substantial energy savings on systems with variable voltage processors. Moreover, processors with a few discrete voltage/speed levels obtain nearly the same energy savings as processors with continuous voltage/speed, and the effect of voltage/speed adjustment overhead on the energy savings is relatively small.
Quickrelease Fair Scheduling
 In Proceedings of the 12th Euromicro Conference on RealTime Systems
, 2003
"... In prior work on multiprocessor fairness, efficient techniques with provable properties for reallocating spare processing capacity have been elusive. In this paper, we address this shortcoming by proposing a new notion of multiprocessor fairness, called quickrelease fair (QRfair) scheduling, which ..."
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Cited by 84 (35 self)
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In prior work on multiprocessor fairness, efficient techniques with provable properties for reallocating spare processing capacity have been elusive. In this paper, we address this shortcoming by proposing a new notion of multiprocessor fairness, called quickrelease fair (QRfair) scheduling, which is a derivative of Pfair scheduling that allows efficient allocation of spare capacity. Under QRfair scheduling, each task is specified by giving both a minimum and a maximum weight (i.e., processor share). The goal is to schedule each task (as the available spare capacity changes) at a rate that is (i) at least that implied by its minimum weight and (ii) at most that implied by its maximum weight. Our contributions are fourfold. First, we present a quickrelease variant of the PD Pfair scheduling algorithm called PD . Second, we formally prove that the allocations of PD always satisfy (i) and (ii). Third, we consider the problem of defining maximum weights in a way that encourages a fair distribution of spare capacity. Fourth, we present results from extensive simulation experiments that show the efficacy of PD in allocating spare capacity.
Optimal Ratebased Scheduling on Multiprocessors
 In Proceedings of the 34th ACM Symposium on Theory of Computing
, 2001
"... We consider the intrasporadic task model, which is a generalization of the sporadic task model motivated by recent work on Pfair scheduling. The intrasporadic model is essentially a quantumbased, multiprocessor variant of the uniprocessor ratebased execution model of Jeffay and Goddard. In the i ..."
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Cited by 76 (37 self)
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We consider the intrasporadic task model, which is a generalization of the sporadic task model motivated by recent work on Pfair scheduling. The intrasporadic model is essentially a quantumbased, multiprocessor variant of the uniprocessor ratebased execution model of Jeffay and Goddard. In the intrasporadic model, a task is specified by an average rate of execution, and there is no restriction on instantaneous execution rates. Such exibility is useful in applications in which some processing steps may be highly jittered. In previous work, we showed that an intrasporadic task system is feasible on M processors i its total utilization is at most M . We also gave an optimal algorithm for scheduling intrasporadic tasks on two processors. In this paper, we show that the PD² Pfair algorithm can be used to schedule any intrasporadic task system that is feasible on M processors. Because the sporadic model is a special case of the intrasporadic model, our work shows that PD² is also optimal for scheduling sporadic tasks on a multiprocessor. This paper is the first to show that sporadic or intrasporadic tasks can be optimally scheduled on systems of more than two processors.
Surplus Fair Scheduling: A ProportionalShare CPU Scheduling Algorithm for Symmetric Multiprocessors
"... In this paper, we present surplus fair scheduling (SFS), a proportionalshare CPU scheduler designed for symmetric multiprocessors. We first show that the infeasibility of certain weight assignments in multiprocessor environments results in unfairness or starvation in many existing proportionalshar ..."
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Cited by 69 (7 self)
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In this paper, we present surplus fair scheduling (SFS), a proportionalshare CPU scheduler designed for symmetric multiprocessors. We first show that the infeasibility of certain weight assignments in multiprocessor environments results in unfairness or starvation in many existing proportionalshare schedulers. We present a novel weight readjustment algorithm to translate infeasible weight assignments to a set of feasible weights. We show that weight readjustment enables existing proportionalshare schedulers to significantly reduce, but not eliminate, the unfairness in their allocations. We then present surplus fair scheduling, a proportionalshare scheduler that is designed explicitly for multiprocessor environments. We implement our scheduler in the Linux kernel and demonstrate its efficacy through an experimental evaluation. Our results show that SFS can achieve proportionate allocation, application isolation and good interactive performance, albeit at a slight increase in scheduling overhead. We conclude from our results that a proportionalshare scheduler such as SFS is not only practical but also desirable for server operating systems.
Resource partitioning among realtime applications
 In Proceedings of Euromicro Conference on RealTime Systems
, 2003
"... When executing different realtime applications on a single processor system, one problem is how to compose these applications and guarantee at the same time that their timing requirements are not violated. A possible way of composing applications is through the resource reservation approach. Each a ..."
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Cited by 68 (13 self)
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When executing different realtime applications on a single processor system, one problem is how to compose these applications and guarantee at the same time that their timing requirements are not violated. A possible way of composing applications is through the resource reservation approach. Each application is handled by a dedicated server that is assigned a fraction of the processor. Using this approach, the system can be seen as a twolevel hierarchical scheduler. A considerable amount of work has been recently addressed to the analysis of this kind of hierarchical systems. However, a question is still unanswered: given a set of realtime tasks to be handled by a server, how to assign the server parameters so that the task set is feasible? In this paper, we answer to the previous question for the case of fixed priority local scheduler by presenting a methodology for computing the class of server parameters that make the task set feasible. 1.
Pfair Scheduling: Beyond Periodic Task Systems
 In Proc. of the 7th International Conference on RealTime Computing Systems and Applications
, 2000
"... In this paper, we consider variants of Pfair and ERfair scheduling in which subtasks may be released late, i.e., there may be separation between consecutive windows of the same task. We call such tasks intrasporadic tasks. There are two main contributions of this paper. First, we show the existence ..."
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Cited by 64 (30 self)
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In this paper, we consider variants of Pfair and ERfair scheduling in which subtasks may be released late, i.e., there may be separation between consecutive windows of the same task. We call such tasks intrasporadic tasks. There are two main contributions of this paper. First, we show the existence of a Pfair (and hence ERfair) schedule for any intrasporadic task system whose utilization is at most the number of available processors. Second, we give a polynomialtime algorithm that is optimal for scheduling intrasporadic tasks in a Pfair or ERfair manner on systems of one or two processors.
A categorization of realtime multiprocessor scheduling problems and algorithms
 HANDBOOK ON SCHEDULING ALGORITHMS, METHODS, AND MODELS
, 2004
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