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.

We are developing Virtuoso, a system for distributed computing using virtual machines (VMs). Virtuoso must be able to mix batch and interactive VMs on the same physical hardware, while satisfying constraints on responsiveness and compute rates for each workload. VSched is the component of Virtuoso that provides this capability. VSched is an entirely user-level tool that interacts with the stock Linux kernel running below any type-II virtual machine monitor to schedule all VMs (indeed, any process) using a periodic real-time scheduling model. This abstraction allows compute rate and responsiveness constraints to be straightforwardly described using a period and a slice within the period, and it allows for fast and simple admission control. This paper makes the case for periodic real-time scheduling for VM-based computing environments, and then describes and evaluates VSched. It also applies VSched to scheduling parallel workloads, showing that it can help a BSP application maintain a fixed stable performance despite externally caused load imbalance.

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.

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.

Abstract — We consider several object sharing synchronization mechanisms including lock-based, lock-free, and wait-free sharing for LNREF [1], an optimal real-time scheduling algorithm on multiprocessors. We derive LNREF’s minimum-required space cost for wait-free synchronization using the space-optimal waitfree algorithm. We then establish the feasibility conditions for lock-free and lock-based sharing under LNREF, and the concomitant tradeoffs. While the tradeoff between wait-free versus the other sharing is obvious, i.e., space and time costs, we show that the tradeoff between lock-free and lock-based sharing for LNREF hinges on the cost of the lock-free retry, blocking time under lock-based. Finally, we numerically evaluate lock-free and lock-based sharing for LNREF. I.

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

Abstract Writing a new scheduler and integrating it into an existing OS is a daunting task, requiring the understanding of multiple low-level kernel mechanisms. This problem is compounded by the high degree of manual optimization of typical scheduling code, which limits code reuse and makes development prone to errors. To address these problems, we present the design of Bossa, a language specifically targeted toward the development of scheduling policies. Bossa provides high-level abstractions that are specific to the domain of scheduling. These constructs simplify the task of specifying a new scheduling policy and facilitate the static verification of critical safety properties.

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].