### A schedulable utilization bound for the multiprocessor epdf pfair algorithm

- Real-Time Systems
, 2008

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### Resource Reservation in Real-Time Operating Systems- a joint industrial and academic position

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### PDCS'07 (2007)" A Rapid Heuristic for Scheduling Non-Preemptive Dependent Periodic Tasks onto Multiprocessor

, 2009

"... We address distributed real-time applications represented by systems of non-preemptive dependent periodic tasks. This system is described by an acyclic directed graph. Because the distribution and the scheduling of these tasks onto a multiprocessor is an NP-hard problem we propose a greedy heuristic ..."

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We address distributed real-time applications represented by systems of non-preemptive dependent periodic tasks. This system is described by an acyclic directed graph. Because the distribution and the scheduling of these tasks onto a multiprocessor is an NP-hard problem we propose a greedy heuristic to solve it. Our heuristic sequences three algorithms: assignment, unrolling, and scheduling. The tasks of the same, or multiple, periods are assigned to the same processor according to a mixed sort. Then, the initial graph of tasks is unrolled, i.e. each task is repeated according to the ratio between its period and the least common multiple of all periods of tasks. Finally, the tasks of the unrolled graph are distributed and scheduled onto the processors where they have been assigned. Then, we give the complexity of this heuristic, and we illustrate it with an example. A performance analysis comparing our heuristic with an optimal Branch and Cut algorithm concludes that our heuristic is effective in terms of scheduling success ratio and speed. 1

### DIET-ethic: Fair Scheduling of Optional Computations in

, 2012

"... HPC platforms require users to submit a pre-determined number of computation requests (also called jobs). Unfortunately, this is cumbersome when some of the computations are optional, i.e., they are not critical, but their completion would improve results. For example, given a deadline, the number o ..."

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HPC platforms require users to submit a pre-determined number of computation requests (also called jobs). Unfortunately, this is cumbersome when some of the computations are optional, i.e., they are not critical, but their completion would improve results. For example, given a deadline, the number of requests to submit for a Monte Carlo experiment is difficult to choose. The more requests are completed, the better the results are, however, submitting too many might overload the platform. Conversely, submitting too few requests may leave resources unused and misses an opportunity to improve the results. This paper introduces and solves the problem of scheduling optional computations. An architecture which auto-tunes the number of requests is proposed, then implemented in the DIET GridRPC middleware. Real-life experiments show that several metrics are improved, such as user satisfaction, fairness and the number of completed requests. Moreover, the solution is shown to be scalable. Key-words: HPC; GridRPC; malleable applications; Grid’5000

### Abstract Mixed Pfair/ERfair Scheduling of Asynchronous Periodic Tasks ⋆

"... Pfair scheduling was proposed by Baruah, Cohen, Plaxton, and Varvel as a nonwork-conserving way of optimally and efficiently scheduling periodic tasks on a multiprocessor. In this paper, we introduce a work-conserving variant of Pfair scheduling called “early-release ” fair (ERfair) scheduling. We a ..."

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Pfair scheduling was proposed by Baruah, Cohen, Plaxton, and Varvel as a nonwork-conserving way of optimally and efficiently scheduling periodic tasks on a multiprocessor. In this paper, we introduce a work-conserving variant of Pfair scheduling called “early-release ” fair (ERfair) scheduling. We also present a new scheduling algorithm called PD 2 and show that it is optimal for scheduling any mix of earlyrelease and non-early-release asynchronous, periodic tasks. In contrast, almost all prior work on Pfair scheduling has been limited to synchronous systems. PD 2 is an optimization of an earlier deadline-based algorithm of Baruah, Gehrke, and Plaxton called PD; PD 2 uses a simpler tie-breaking scheme than PD to disambiguate equal deadlines. We present a series of counterexamples that suggest that, in general, the PD 2 tie-breaking mechanism cannot be simplified. In contrast to this, we show that no tie-breaking information is needed on two-processor systems.

### We consider the scheduling of recurrent (i.e., periodic, sporadic, or rate-based) real-time task systems on multi-

"... The earliest-pseudo-deadline-first (EPDF) Pfair scheduling algorithm is less expensive than some other known Pfair algorithms, but is not optimal for scheduling recurrent real-time tasks on more than two processors. In prior work, sufficient per-task weight (i.e., utilization) restrictions were esta ..."

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The earliest-pseudo-deadline-first (EPDF) Pfair scheduling algorithm is less expensive than some other known Pfair algorithms, but is not optimal for scheduling recurrent real-time tasks on more than two processors. In prior work, sufficient per-task weight (i.e., utilization) restrictions were established for ensuring that tasks either do not miss their deadlines or have bounded tardiness when scheduled under EPDF. Implicit in these restrictions is the assumption that the total system utilization may equal the total available processing capacity (i.e., the total number of processors). This paper considers an orthogonal issue, namely, determining a sufficient restriction on the total utilization of a task set for it to be schedulable (i.e., a schedulable utilization bound) under EPDF, assuming that there are no per-task weight restrictions. We prove that a task set with total utilization at most 3M+1 4 is correctly scheduled under EPDF on M processors, regardless of how large each task’s weight is. At present, we do not know whether this value represents the worst-case for EPDF, but we do provide a counterexample that shows that it cannot be improved to exceed 86 % of the total processing capacity. The schedulable utilization bound we derive is expressed in terms of the maximum weight of any task, and hence, if this value is known, may be used to

### Abstract Discrete Optimization Efficient scheduling of periodic information

, 2003

"... In many mission-critical applications such as police and homeland security-related information systems, automated monitoring of relevant information sources is essential. Such monitoring results in a large number of periodic queries, which can significantly increase the load on a server that hosts i ..."

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In many mission-critical applications such as police and homeland security-related information systems, automated monitoring of relevant information sources is essential. Such monitoring results in a large number of periodic queries, which can significantly increase the load on a server that hosts information services. If the execution of these queries is not carefully scheduled on the server, high peak load might occur, leading to degraded service quality. We investigate this query scheduling problem with the objective of minimizing the serverÕs peak load. We state an optimization-based formulation and show that this problem is NP-hard in the strong sense. Subsequently, several greedy heuristic approaches are developed and compared via a computational study with respect to solution quality and computational efficiency. Ó 2005 Elsevier B.V. All rights reserved.

### An Efficient Algorithm to Reduce the Inflations in Multi-Supertask Environment by Using a Transient Behavior Prediction Method

, 2005

"... SUMMARY The supertask approach was proposed by Moir and Ramamthy as a means of supporting non-migratory tasks in Pfair-scheduled systems. In this approach, tasks bound to the same processor are combined into a single server task, called a supertask, which is scheduled as an ordinary Pfair task. When ..."

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SUMMARY The supertask approach was proposed by Moir and Ramamthy as a means of supporting non-migratory tasks in Pfair-scheduled systems. In this approach, tasks bound to the same processor are combined into a single server task, called a supertask, which is scheduled as an ordinary Pfair task. When a supertask is scheduled, one of its component tasks is selected for execution. In previous work, Holman et al. showed that component-task deadlines can be guaranteed by inflating each supertask’s utilization. In addition, their experimental results showed that the required inflation factors should be small in practice. Consequently, the average inflation produced by their rules is much greater than that actually required by the supertasks. In this paper, we first propose a notion of Transient Behavior Prediction for supertasks, which predicts the latest possible finish time of subtasks that belong to supertasks. On the basis of the notion, we present an efficient schedulability algorithm for Pfair supertasks in which the deadlines of all component tasks can be guaranteed. In addition, we propose a task merging process which combines the unschedulable supertasks with some Pfair tasks; hence, a newly supertask can be scheduled in the system. Finally, we propose the new reweighting functions that can be used when the previous two methods fail. Our reweighting functions produce smaller inflation factor than the previous work does. To demonstrate the efficacy of the supertasking approach, we present the experimental evaluations of our algorithm, which decreases substantially a number of reweights and the size of inflation when there are many supertasks in the Pfair-scheduled systems. key words: supertasks, real-time scheduling, Pfair, EPDF 1.

### A Rapid Heuristic for Scheduling Non-Preemptive Dependent Periodic Tasks onto Multiprocessor

"... We address distributed real-time applications represented by systems of non-preemptive dependent periodic tasks. This system is described by an acyclic directed graph. Because the distribution and the scheduling of these tasks onto a multiprocessor is an NP-hard problem we propose a greedy heuristic ..."

Abstract
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We address distributed real-time applications represented by systems of non-preemptive dependent periodic tasks. This system is described by an acyclic directed graph. Because the distribution and the scheduling of these tasks onto a multiprocessor is an NP-hard problem we propose a greedy heuristic to solve it. Our heuristic sequences three algorithms: assignment, unrolling, and scheduling. The tasks of the same, or multiple, periods are assigned to the same processor according to a mixed sort. Then, the initial graph of tasks is unrolled, i.e. each task is repeated according to the ratio between its period and the least common multiple of all periods of tasks. Finally, the tasks of the unrolled graph are distributed and scheduled onto the processors where they have been assigned. Then, we give the complexity of this heuristic, and we illustrate it with an example. A performance analysis comparing our heuristic with an optimal Branch and Cut algorithm concludes that our heuristic is effective in terms of scheduling success ratio and speed. 1