Federated Scheduling for Stochastic Parallel Real-time Tasks

Federated scheduling is a strategy to schedule parallel real-time tasks: It allocates a dedicated cluster of cores to high-utilization task (utilization \u3e1); It uses a multiprocessor scheduling algorithm to schedule and execute all low-utilization tasks sequentially, on a shared cluster of the remaining cores. Prior work has shown that federated scheduling has the best known capacity augmentation bound of 2 for parallel tasks with implicit deadlines. In this paper, we explore the soft real-time performance of federated scheduling and address the average-case workloads instead of the worst-case values. In particular, we consider stochastic tasks -- tasks for which execution time and critical-path length are random variables. In this case, we use bounded expected tardiness as the schedulability criterion. We define a stochastic capacity augmentation bound and prove that federated scheduling algorithms guarantee the same bound of 2 for stochastic tasks. We present three federated mapping algorithms for core allocation. All of them guarantee bounded expected tardiness and provide the same capacity augmentation bound; In practice, however, we expect them to provide different performances, both in terms of the task sets they can schedule and the actual tardiness they guarantee. Therefore, we performed numerical evaluations using randomly generated task sets to understand the practical differences between the three algorithms

Parallel Real-Time Scheduling for Latency-Critical Applications

In order to provide safety guarantees or quality of service guarantees, many of today\u27s systems consist of latency-critical applications, e.g. applications with timing constraints. The problem of scheduling multiple latency-critical jobs on a multiprocessor or multicore machine has been extensively studied for sequential (non-parallizable) jobs and different system models and different objectives have been considered. However, the computational requirement of a single job is still limited by the capacity of a single core. To provide increasingly complex functionalities of applications and to complete their higher computational demands within the same or even more stringent timing constraints, we must exploit the internal parallelism of jobs, where individual jobs are parallel programs and can potentially utilize more than one core in parallel. However, there is little work considering scheduling multiple parallel jobs that are latency-critical. This dissertation focuses on developing new scheduling strategies, analysis tools, and practical platform design techniques to enable efficient and scalable parallel real-time scheduling for latency-critical applications on multicore systems. In particular, the research is focused on two types of systems: (1) static real-time systems for tasks with deadlines where the temporal properties of the tasks that need to execute is known a priori and the goal is to guarantee the temporal correctness of the tasks prior to their executions; and (2) online systems for latency-critical jobs where multiple jobs arrive over time and the goal to optimize for a performance objective of jobs during the execution. For static real-time systems for parallel tasks, several scheduling strategies, including global earliest deadline first, global rate monotonic and a novel federated scheduling, are proposed, analyzed and implemented. These scheduling strategies have the best known theoretical performance for parallel real-time tasks under any global strategy, any fixed priority scheduling and any scheduling strategy, respectively. In addition, federated scheduling is generalized to systems with multiple criticality levels and systems with stochastic tasks. Both numerical and empirical experiments show that federated scheduling and its variations have good schedulability performance and are efficient in practice. For online systems with multiple latency-critical jobs, different online scheduling strategies are proposed and analyzed for different objectives, including maximizing the number of jobs meeting a target latency, maximizing the profit of jobs, minimizing the maximum latency and minimizing the average latency. For example, a simple First-In-First-Out scheduler is proven to be scalable for minimizing the maximum latency. Based on this theoretical intuition, a more practical work-stealing scheduler is developed, analyzed and implemented. Empirical evaluations indicate that, on both real world and synthetic workloads, this work-stealing implementation performs almost as well as an optimal scheduler

Computation of risk measures in finance and parallel real-time scheduling

Many application areas employ various risk measures, such as a quantile, to assess risks. For example, in finance, risk managers employ a quantile to help determine appropriate levels of capital needed to be able to absorb (with high probability) large unexpected losses in credit portfolios comprising loans, bonds, and other financial instruments subject to default. This dissertation discusses the computation of risk measures in finance and parallel real-time scheduling. Firstly, two estimation approaches are compared for one risk measure, a quantile, via randomized quasi-Monte Carlo (RQMC) in an asymptotic setting where the number of randomizations for RQMC grows large, but the size of the low-discrepancy point set remains fixed. In the first method, for each randomization, it computes an estimator of the cumulative distribution function (CDF), which is inverted to obtain a quantile estimator, and the overall quantile estimator is the sample average of the quantile estimators across randomizations. The second approach instead computes a single quantile estimator by inverting one CDF estimator across all randomizations. Because quantile estimators are generally biased, the first method leads to an estimator that does not converge to the true quantile as the number of randomizations goes to infinity. In contrast, the second estimator does, and a central limit theorem is established for it. To get an improvement, we use conditional Monte Carlo (CMC) to obtain a smoother estimate of the distribution function, and we combine this with the second RQMC to further reduce the variance. The result is a much more accurate quantile estimator, whose mean square error can converge even faster than the canonical rate of O(1/n). Secondly, another risk measure is estimated, namely economic capital (EC), which is defined as the difference between a quantile and the mean of the loss distribution, given a stochastic model for a portfolio’s loss over a given time horizon. This work applies measure-specific importance sampling to separately estimate the two components of the EC, which can lead to a much smaller variance than when estimating both terms simultaneously. Finally, for parallel real-time tasks, the federated scheduling paradigm, which assigns each parallel task a set of dedicated cores, achieves good theoretical bounds by ensuring exclusive use of processing resources to reduce interferences. However, because cores share the last-level cache and memory bandwidth resources, in practice tasks may still interfere with each other despite executing on dedicated cores. To tackle this issue, this work presents a holistic resource allocation framework for parallel real-time tasks under federated scheduling. Under the proposed framework, in addition to dedicated cores, each parallel task is also assigned with dedicated cache and memory bandwidth resources. This work also shows the study of the characteristics of parallel tasks upon different resource allocations following a measurement-based approach and proposes a technique to handle the challenge of tremendous profiling for all resource allocation combinations under this approach. Further, it proposes a holistic resource allocation algorithm that well balances the allocation between different resources to achieve good schedulability. Additionally, this work provides a full implementation of the framework by extending the federated scheduling system with Intel’s Cache Allocation Technology and MemGuard. It also demonstrates the practicality of the proposed framework via extensive numerical evaluations and empirical experiments using real benchmark programs. In the end, the discussion about the application of risk measures for real-time scheduling is given for future work

InterCloud: Utility-Oriented Federation of Cloud Computing Environments for Scaling of Application Services

Cloud computing providers have setup several data centers at different geographical locations over the Internet in order to optimally serve needs of their customers around the world. However, existing systems do not support mechanisms and policies for dynamically coordinating load distribution among different Cloud-based data centers in order to determine optimal location for hosting application services to achieve reasonable QoS levels. Further, the Cloud computing providers are unable to predict geographic distribution of users consuming their services, hence the load coordination must happen automatically, and distribution of services must change in response to changes in the load. To counter this problem, we advocate creation of federated Cloud computing environment (InterCloud) that facilitates just-in-time, opportunistic, and scalable provisioning of application services, consistently achieving QoS targets under variable workload, resource and network conditions. The overall goal is to create a computing environment that supports dynamic expansion or contraction of capabilities (VMs, services, storage, and database) for handling sudden variations in service demands. This paper presents vision, challenges, and architectural elements of InterCloud for utility-oriented federation of Cloud computing environments. The proposed InterCloud environment supports scaling of applications across multiple vendor clouds. We have validated our approach by conducting a set of rigorous performance evaluation study using the CloudSim toolkit. The results demonstrate that federated Cloud computing model has immense potential as it offers significant performance gains as regards to response time and cost saving under dynamic workload scenarios.Comment: 20 pages, 4 figures, 3 tables, conference pape

Capacity Augmentation Bound of Federated Scheduling for Parallel DAG Tasks

We present a novel federated scheduling approach for parallel real-time tasks under a general directed acyclic graph (DAG) model. We provide a capacity augmentation bound of 2 for hard real-time scheduling; here we use the worst-case execution time and critical-path length of tasks to determine schedulability. This is the best known capacity augmentation bound for parallel tasks. By constructing example task sets, we further show that the lower bound on capacity augmentation of federated scheduling is also 2 for any m \u3e 2. Hence, the gap is closed and bound 2 is a strict bound for federated scheduling. The federated scheduling algorithm is also a schedulability test that often admits task sets with utilization much greater than 50%m