We consider the intra-sporadic task model, which is a generalization of the sporadic task model motivated by recent work on Pfair scheduling. The intra-sporadic model is essentially a quantum-based, multiprocessor variant of the uniprocessor rate-based execution model of Jeffay and Goddard. In the intra-sporadic 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 intra-sporadic task system is feasible on M processors i its total utilization is at most M . We also gave an optimal algorithm for scheduling intra-sporadic tasks on two processors. In this paper, we show that the PD² Pfair algorithm can be used to schedule any intra-sporadic 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 intra-sporadic tasks can be optimally scheduled on systems of more than two processors.

We consider the issue of deadline tardiness under global multiprocessor scheduling algorithms. We present a general tardiness-bound derivation that is applicable to a wide variety of such algorithms (including some whose tardiness behavior has not been analyzed before). Our derivation is very general: job priorities may change rather arbitrarily at runtime, capacity restrictions may exist on certain processors, and, under certain conditions, non-preemptive regions are allowed. Our results show that, with the exception of static-priority algorithms, most global algorithms considered previously have bounded tardiness. In addition, our results provide a simple means for checking whether tardiness is bounded under newly-developed algorithms. 1

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.

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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

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 schedule task sets with total utilization greater than 3M+1

The earliest-pseudo-deadline-first (EPDF) Pfair algorithm is more efficient than other known Pfair scheduling algorithms, but is not optimal for scheduling recurrent real-time task systems on more than two identical processors. Although not optimal, EPDF may be preferable for real-time systems instantiated on less-powerful platforms, those with soft timing constraints, or those whose task composition can change at run-time. In prior work, Srinivasan and Anderson established a sufficient per-task utilization restriction for ensuring a tardiness of at most q quanta, where q ≥ 1, under EPDF. They also conjectured that under this algorithm, a tardiness bound of one quantum applies to task systems that are not subject to any restriction other than the obvious restrictions, namely, that the total system utilization not exceed the available processing capacity and per-task utilizations not exceed 1.0. In this paper, we present counterexamples that show that their conjecture is false and present sufficient per-task utilization restrictions that are more liberal than theirs. For ensuring a tardiness bound of one quantum, our restriction presents an improvement of 50 % over the previous one. Key words: soft real-time, multiprocessors, Pfairness, scheduling, tardiness bounds

Abstract not found