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 quick-release 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 quick-release 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.

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.

Multiprocessor hardware platforms are now being considered for embedded systems, due to their high computational power and little additional cost when compared to single processor systems. When scheduling real-time applications on multiprocessor platforms, a possibility is to use global scheduling, where a scheduling algorithm dynamically assign tasks to processors, and tasks can migrate from one processor to another during their execution. In this paper, we tackle the problem of schedulability analysis of sporadic tasks in global scheduling systems, where the scheduler is the Earliest Deadline First (EDF) algorithm. We provide two main contributions. First, we show that two recently proposed tests perform poorly when the task set contains heavy tasks (i.e. tasks with high utilization). We also show that neither test dominates the other. As a second contribution, we introduce a new schedulability test that improves significantly the percentage of accepted task sets, especially when considering task sets containing heavy tasks. We show the effectiveness of the proposed test through an extensive set of experiments. 1.

In soft real-time applications, tasks are allowed to miss their deadlines. Thus, less-costly scheduling algorithms can be used at the price of occasional violations of timing constraints. This may be acceptable if reasonable tardiness bounds (i.e., bounds on the extent to which deadlines may be missed) can be guaranteed. In this paper, we consider soft real-time applications implemented on multiprocessors. Pfair scheduling algorithms are the only known means of optimally scheduling hard real-time applications on multiprocessors. For this reason, we consider the use of such algorithms here. In the design of Pfair scheduling algorithms, devising schemes to correctly break ties when several tasks have the same deadline is a critical issue. Such tie-breaking schemes entail overhead that may be unacceptable or unnecessary in soft real-time applications. In this paper, we consider the earliest pseudo-deadline first (EPDF) Pfair algorithm, which avoids this overhead by using no tie-breaking information. Our main contributions are twofold. First, we establish a condition for ensuring a tardiness of at most one quantum under EPDF. This condition is very liberal and should often hold in practice. Second, we present simulation results involving randomly-generated task sets, including those that do not satisfy our condition. In these experiments, deadline misses rarely occurred, and no misses by more than one quantum ever occurred. ∗ Work supported by NSF grants CCR 9972211, CCR 9988327, ITR 0082866, and CCR 0204312. 1

This paper considers the scheduling of soft real-time sporadic task systems under global EDF on an iden-tical multiprocessor. Though Pfair scheduling is theoretically optimal for hard real-time task systems on multiprocessors, it can incur significant run-time overhead. Hence, other scheduling algorithms that are not optimal, including EDF, have continued to receive considerable attention. However, prior research on such algorithms has focussed mostly on hard real-time systems, where, to ensure that all deadlines are met, ap-proximately 50 % of the available processing capacity will have to be sacrificed in the worst case. This may be overkill for soft real-time systems that can tolerate deadline misses by bounded amounts (i.e., bounded tardiness). In this paper, we derive tardiness bounds under preemptive and non-preemptive global EDF on multiprocessors when the total utilization of a task system is not restricted and may equal the number of pro-cessors. Our tardiness bounds depend on per-task utilizations and execution costs — the lower these values, the lower the tardiness bounds. As a final remark, we note that global EDF may be superior to partitioned EDF for multiprocessor-based soft real-time systems in that the latter does not offer any scope to improve system utilization even if bounded tardiness can be tolerated.

Partitioning and global scheduling are two approaches for scheduling real-time tasks on multiprocessors. Though partitioning is sub-optimal it has traditionally been preferred; this is mainly due to the fact that well-understood uniprocessor scheduling algorithms can be used on each processor. In recent years, global scheduling algorithms based on the concept of "proportionate fairness" (Pfairness)have received considerabl attention. Pfairal)[[2#3) are of interest because they are currentl the onl known method for optimal) schedul13 periodic, sporadic, and "rate-based" task systems on mul6[]2 cessors. In addition, there has been growing practical interest in schedul32 with fairness guarantees. However, the frequency of context switching and migration in Pfair-scheduls systems has l) to some questions concerning the practicalR y of Pfair schedul#6) In this paper, we investigate this issue by comparing the PD Pfairalir)2B1 to the EDF-FF partitioning scheme, which uses "first fit" (FF)as a partitioning heuristic and theearlBB):[B2B1)l first (EDF)al):R3R# for per-processor schedul1): We present experimental resul) that show that is competitive with, and in some cases outperforms, EDF-FF. These resulL suggest that Pfair schedulR) is aviabl all1):R] e to partitioning. Furthermore, as discussed herein, Pfair scheduling provides many additional benefits, such assimpl and efficient synchronization, temporal isolL1]): faul tol1]):R6 and support for dynamic tasks.

Multicore platforms are predicted to become significantly larger in the coming years. Given that real-time workloads will inevitably be deployed on such platforms, the scalability of the scheduling algorithms used to support such workloads warrants investigation. In this paper, this issue is considered and an empirical evaluation of several global and partitioned scheduling algorithms is presented. This evaluation was conducted using a Sun Niagara multicore platform with 32 logical CPUs (eight cores, four hardware threads per core). In this study, each tested algorithm proved to be a viable choice for some subset of the workload categories considered.

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

Real-time scheduling algorithms for multiprocessor systems have been the subject of considerable recent interest. For such an algorithm to be truly useful in practice, support for semaphore-based locking must be provided. However, for many global scheduling algorithms, no such mechanisms have been proposed. Furthermore, in the partitioned case, most prior semaphore schemes are either inefficient or restrict critical sections considerably. In this paper, a new flexible multiprocessor locking scheme is presented that can be applied under both partitioning and global scheduling. This scheme allows unrestricted critical-section nesting, but has been designed to deal with the common case of short non-nested accesses efficiently.

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.