The goal of this dissertation is to extend the Pfair scheduling approach in order to enable its efficient implementation on a real-time multiprocessor. At present, Pfair scheduling is the only known means for optimally scheduling recurrent real-time tasks on multiprocessors. In addition, there has been growing practical interest in such approaches due to their fairness guarantees. Unfortunately, prior work in this area has considered only the scheduling of independent tasks, which do not communicate with each other or share resources. The work presented herein focuses both on adding support for these actions and also on developing techniques for reducing various forms of implementation overhead, including that produced by task migrations and context switches. The thesis of this dissertation is: tasks can be efficiently synchronized in Pfair-scheduled systems and overhead due to common system events, such as context switches and migrations, can be reduced. This thesis is established through research in three areas. First, the pre-existing Pfair schedul- ing theory is extended to support the scheduling of groups of tasks as a single entity. Second, mechanisms for supporting both lock-based and lock-free synchronization are presented. Lock- based synchronization coordinates access to shared resources through the use of semaphores. On the other hand, lock-free operations are optimistically attempted and then retried if the operation fails. Last, the deployment of Pfair scheduling on a symmetric multiprocessor is considered.

A polynomial-time algorithm is presented for partitioning a collection of sporadic tasks among the processors of an identical multiprocessor platform with static-priority scheduling on each individual processor. Since the partitioning problem is easily seen to be NP-hard in the strong sense, this algorithm is not optimal. A quantitative characterization of its worst-case performance is provided in terms of sufficient conditions and resource augmentation approximation bounds. The partitioning algorithm is also evaluated over randomly generated task systems. 1

This paper addresses the problem of priority assignment in multiprocessor real-time systems using global fixed task-priority pre-emptive scheduling. In this paper, we prove that Audsley’s Optimal Priority Assignment (OPA) algorithm, originally devised for uniprocessor scheduling, is applicable to the multiprocessor case, provided that three conditions hold with respect to the schedulability tests used. Our empirical investigations show that the combination of optimal priority assignment policy and a simple compatible schedulability test is highly effective, in terms of the number of tasksets deemed to be schedulable. We also examine the performance of heuristic priority assignment policies such as Deadline Monotonic, and an extension of the TkC priority assignment policy called DkC that can be used with any schedulability test. Here we find that Deadline Monotonic priority assignment has relatively poor performance in the multiprocessor case, while DkC priority assignment is highly effective. 1.

The earliest-deadline-first (EDF) scheduling of a sporadic real-time task system on a multiprocessor may require that the total utilization of the task system, Usum, not exceed (m + 1)/2 on m processors if every deadline needs to be met. In recent work, we considered the alleviation of this under-utilization for task systems that can tolerate deadline misses by bounded amounts (i.e., bounded tardiness). We showed that if Usum ≤ m and tasks are not pinned to processors, then the tardiness of each task is bounded under both preemptive and non-preemptive EDF. The tardiness bounds that we derived are dependent upon the utilizations and execution costs of the constituent tasks, but are independent of Usum. Furthermore, any task may incur maximum tardiness. In this paper, we address the issue of supporting tasks whose tolerance to tardiness is less than that known to be possible under EDF. We propose a new scheduling policy, called EDF-hl, that is a variant of EDF, and show that under EDF-hl, any tardiness, including zero tardiness, can be ensured for a limited number of privileged tasks, and that bounded tardiness can be guaranteed to the remaining tasks if their utilizations are restricted. EDF-hl reduces to EDF in the absence of privileged tasks. The tardiness bound that we derive is a function of Usum, in addition to individual task parameters. Hence, tardiness for all tasks can be lowered by lowering Usum. An experimental evaluation of the tardiness bounds that are possible is provided. ∗ Work supported by NSF grants CNS 0309825 and CNS 0408996. The first author was also supported by an IBM Ph.D. fellowship. 1

This survey covers hard real-time scheduling algorithms and schedulability analysis techniques for homogeneous multiprocessor systems. It reviews the key results in this field from its origins in the late 1960s to the latest research published in late 2009. The survey outlines fundamental results about multiprocessor real-time scheduling that hold independent of the scheduling algorithms employed. It provides a taxonomy of the different scheduling methods, and considers the various performance metrics that can be used for comparison purposes. A detailed review is provided covering partitioned, global, and hybrid scheduling algorithms, approaches to resource sharing, and the latest results from empirical investigations. The survey identifies open issues, key research challenges, and likely productive research directions.

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This survey covers hard real-time scheduling algorithms and schedulability analysis techniques for homogeneous multiprocessor systems. It reviews the key results in this field from its origins in the late 1960’s to the latest research published in late 2009. The survey outlines fundamental results about multiprocessor realtime scheduling that hold independent of the scheduling algorithms employed. It provides a taxonomy of the different scheduling methods, and considers the various performance metrics that can be used for comparison purposes. A detailed review is provided covering partitioned, global, and hybrid scheduling algorithms, approaches to resource sharing, and the latest results from empirical investigations. The survey identifies open

In a recent work [11], we have developed an algorithm generalizing the famous Liu and Layland’s utilization bound to multiprocessor scheduling. The algorithm has the best worst-case utilization bound compared with existing algorithms. However, its average-case performance is not satisfactory as the workload of each processor is limited by Liu and Layland’s bound. In this paper, we present a new algorithm to improve the averagecase performance while keeping the best worst-case utilization bound. To determine the maximal workload assigned to each processor, we use the exact analysis i.e. Response Time Analysis (RTA) instead of the worst-case utilization threshold as in [11]. Similar to the known fact on single processors for ratemonotonic scheduling that the exact analysis RTA results in much higher average-case utilization than the worst-case bound (88% v.s. 69%), our algorithm has significantly improved average-case performance. The technical challenge is to derive the worst-case utilization bound for the new algorithm which adopts the flexible partitioning strategy with RTA. We provide a non-trivial proof showing that the algorithm guarantees also Liu and Layland’s utilization bound. Thus it dominates theoretically the state-of-the-art fixed priority scheduling algorithms for multiprocessor systems in terms of worst-case utilization bound. We have also conducted extensive experiments with randomly generated task sets to study the average-case performance of the algorithm. The experiments demonstrate that our algorithm also outperforms other existing algorithms trading lower worst-case utilization bounds for higher average utilization. 1

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