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

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.

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.

Proportionate fair (Pfair) scheduling is the only known way to optimally schedule periodic real-time task systems on multiprocessors in an on-line manner. Under Pfair scheduling, the execution of each task is broken into a sequence of quantum-length subtasks that must execute within intervals of approximately-equal lengths. This scheduling policy results in allocations that mimic those of an ideal “fluid ” scheduler, and in periodic task systems, ensures that all deadlines are met. Though Pfair scheduling algorithms hold much promise, prior to our work, research on this topic was limited in that only static systems consisting of synchronous periodic tasks were considered. My dissertation thesis is that the Pfair scheduling framework for the on-line scheduling of real-time tasks on multiprocessors can be made more flexible by allowing the underlying task model to be more general than the periodic model and by allowing dynamic task behaviors. Further, this flexibility can be efficiently achieved. Towards the goal of improving the efficiency of Pfair scheduling algorithms, we develop the PD 2 Pfair algorithm, which is the most efficient optimal Pfair scheduling algorithm devised to date. Through a series of counterexamples, we show that it is

global EDF. To our knowledge, prior work on global EDF hasfocused only on systems of independent tasks. We take an initial step here towards a generic resource-sharing framework by con-sidering simple shared objects, such as queues, stacks, and linked lists. In many applications, the predominate use of synchroniza-tion constructs is for sharing such simple objects. We analyze two synchronization methods for such objects, one based on queue-based spin locks and a second based on lock-free algorithms.

Abstract Two important trends are expected to guide the de-sign of next-generation networks. First, with the commercialization of the Internet, providers will usevalue-added services to differentiate their service offerings from other providers; such services requirethe use of sophisticated resource scheduling mechanisms in routers. Second, to enable extensibilityand the deployment of new services in a rapid and cost-effective manner, routers will be instantiated us-ing programmable network processors. In this research, our goal is to develop sophisticated multipro-cessor scheduling mechanisms that would enable networks that deploy such router platforms to provideservice guarantees to applications. Existing multiprocessor scheduling techniques are either not applicableto router platforms due to their complexity or simplistic assumptions, or are not based on rigorous for-malism, which is necessary to enable strong assertions about service guarantees. In this work, we proposeto address these limitations. This paper presents our current ideas and planned future directions. 1 Introduction Routers are the basic building blocks of wide-area networks such as the Internet. Conventionally, routers have been built using application-specific integrated circuits (ASICs) that enable highspeed packet switching. Unfortunately, ASIC designs take months to develop, and routers built using them are costly to deploy. In order to enable router extensibility in a rapid and costeffective manner, significant effort is now be*Work supported by NSF grants CCR 9972211, CCR 9988327, ITR 0082866, and CCR 0204312. ing invested in a different approach: implementing routers on programmable network processors (NPs) [1, 2, 3, 34].

We consider the implementation of a Pfair scheduler on a symmetric multiprocessor (SMP). Although SMPs are in many ways well-suited for Pfair scheduling, experimental results presented herein suggest that bus contention resulting from the simultaneous scheduling of all processors can substantially degrade performance. To correct this problem, we propose a staggered model for Pfair scheduling that strives to improve performance by more evenly distributing bus traffic over time. Additional simulations and experiments with a scheduler prototype are presented to demonstrate the effectiveness of the staggering approach. In addition, we discuss other techniques for improving performance while maintaining worst-case predictability. Finally, we present an efficient scheduling algorithm to support the proposed model and briefly explain how existing Pfair results apply to staggered scheduling.

Abstract We revisit the problem of supertasking in Pfair-scheduled multiprocessor systems. In this approach, a set of tasks, called component tasks, is assigned to a server task, called a supertask, which is then scheduled as an ordinary Pfair task. Whenever a supertask is scheduled, its processor time is allocated to its component tasks according to an internal scheduling algorithm. Hence, supertasking is an example of hierarchal scheduling.

We present several locking synchronization protocols for Pfair-scheduled multiprocessor systems. We focus on two classes of protocols. The first class is only applicable in systems in which all critical sections are short relative to the length of the scheduling quantum. In this case, efficient synchronization can be achieved by ensuring that all locks have been released before tasks are preempted. This is accomplished by exploiting the quantum-based nature of Pfair scheduling, which provides a priori knowledge of all possible preemption points. The second and more general protocol class is applicable to any system. For this class, we consider the use of a client-server model. We also discuss the viability of inheritance-based protocols in Pfair-scheduled systems.

We consider the problem of supertasking in Pfair-scheduled multiprocessor systems. In this approach, a set of tasks, called component tasks, is assigned to a server task, called a supertask, whichisthen scheduled as an ordinary Pfair task. Whenever a supertask is scheduled, its processor time is allocated to its component tasks according to an internal scheduling algorithm. Hence, supertasking is an example of hierarchal (or group-based) scheduling. In this paper, we present a generalized framework for “reweighting ” supertasks. The goal of reweighting is to assign a fraction of a processor to a given supertask so that all timing requirements of its component tasks are met. We consider the use of both fully preemptive and quantum-based scheduling within a supertask.