How to Schedule When You Have to Buy Your Energy

Abstract. We consider a situation where jobs arrive over time at a data center, consisting of identical speed-scalable processors. For each job, the scheduler knows how much income is lost as a function of how long the job is delayed. The scheduler also knows the fixed cost of a unit of energy. The online scheduler determines which jobs to run on which processors, and at what speed to run the processors. The scheduler's objective is to maximize profit, which is the income obtained from jobs minus the energy costs. We give a (1+ )-speed O(1)-competitive algorithm, and show that resource augmentation is necessary to achieve O(1)-competitiveness

A general framework for handling commitment in online throughput maximization

We study a fundamental online job admission problem where jobs with deadlines arrive online over time at their release dates, and the task is to determine a preemptive single-server schedule which maximizes the number of jobs that complete on time. To circumvent known impossibility results, we make a standard slackness assumption by which the feasible time window for scheduling a job is at least $1+\varepsilon$ times its processing time, for some $\varepsilon>0$. We quantify the impact that different provider commitment requirements have on the performance of online algorithms. Our main contribution is one universal algorithmic framework for online job admission both with and without commitments. Without commitment, our algorithm with a competitive ratio of $O(1/\varepsilon)$ is the best possible (deterministic) for this problem. For commitment models, we give the first non-trivial performance bounds. If the commitment decisions must be made before a job's slack becomes less than a $\delta$-fraction of its size, we prove a competitive ratio of $O(\varepsilon/((\varepsilon-\delta)\delta^2))$, for $0<\delta<\varepsilon$. When a provider must commit upon starting a job, our bound is $O(1/\varepsilon^2)$. Finally, we observe that for scheduling with commitment the restriction to the `unweighted' throughput model is essential; if jobs have individual weights, we rule out competitive deterministic 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

Competitive algorithms for due date scheduling

We consider several online scheduling problems that arise when customers request make-to-order products from a company. At the time of the order, the company must quote a due date to the customer. To satisfy the customer, the company must produce the good by the due date. The company must have an online algorithm with two components: The first component sets the due dates, and the second component schedules the resulting jobs with the goal of meeting the due dates. The most basic quality of service measure for a job is the quoted lead time, which is the difference between the due date and the release time. We first consider the basic problem of minimizing the average quoted lead time. We show that there is a (1 + ¿)-speed O( log k¿ )-competitive algorithm for this problem (here k is the ratio of the maximum work of a job to the minimum work of a job), and that this algorithm is essentially optimally competitive. This result extends to the case that each job has a weight and the objective is weighted quoted lead time. We then introduce the following general setting: there is a nonincreasing profit function pi(t) associated with each job Ji. If the customer for job Ji is quoted a due date of di, then the profit obtained from completing this job by its due date is pi(di). We consider the objective of maximizing profits. We show that if the company must finish each job by its due date, then there is no O(1)-speed poly-log-competitive algorithm. However, if the company can miss the due date of a job, at the cost of forgoing the profits from that job, then we show that there is a (1+ ¿)-speed O(1 + 1/¿)-competitive algorithm, and that this algorithm is essentially optimally competitive

Competitive algorithms for due date scheduling

We consider several online scheduling problems that arise when customers request make-to-order products from a company. At the time of the order, the company must quote a due date to the customer. To satisfy the customer, the company must produce the good by the due date. The company must have an online algorithm with two components: The first component sets the due dates, and the second component schedules the resulting jobs with the goal of meeting the due dates. The most basic quality of service measure for a job is the quoted lead time, which is the difference between the due date and the release time. We first consider the basic problem of minimizing the average quoted lead time. We show that there is a (1 + ε)-speed O(log k/ε)-competitive algorithm for this problem (here k is the ratio of the maximum work of a job to the minimum work of a job), and that this algorithm is essentially optimally competitive. This result extends to the case that each job has a weight and the objective is weighted quoted lead time. We then introduce the following general setting: there is a non-increasing profit function p i(t) associated with each job J i. If the customer for job J i is quoted a due date of d i, then the profit obtained from completing this job by its due date is p i(d i). We consider the objective of maximizing profits. We show that if the company must finish each job by its due date, then there is no O(1)-speed poly-log-competitive algorithm. However, if the company can miss the due date of a job, at the cost of forgoing the profits from that job, then we show that there is a (1 + ε)-speed O(1 + 1/ε)-competitive algorithm, and that this algorithm is essentially optimally competitive. © Springer-Verlag Berlin Heidelberg 2007.link_to_subscribed_fulltex

Competitive algorithms for due date scheduling

We consider several online scheduling problems that arise when customers request make-to-order products from a company. At the time of the order, the company must quote a due date to the customer. To satisfy the customer, the company must produce the good by the due date. The company must have an online algorithm with two components: The first component sets the due dates, and the second component schedules the resulting jobs with the goal of meeting the due dates. The most basic quality of service measure for a job is the quoted lead time, which is the difference between the due date and the release time. We first consider the basic problem of minimizing the average quoted lead time. We show that there is a (1+e)-speed $(\frac{\log k}{\epsilon})$-competitive algorithm for this problem (here k is the ratio of the maximum work of a job to the minimum work of a job), and that this algorithm is essentially optimally competitive. This result extends to the case that each job has a weight and the objective is weighted quoted lead time. We then introduce the following general setting: there is a non-increasing profit function p i (t) associated with each job J i . If the customer for job J i is quoted a due date of d i , then the profit obtained from completing this job by its due date is p i (d i ). We consider the objective of maximizing profits. We show that if the company must finish each job by its due date, then there is no O(1)-speed poly-log-competitive algorithm. However, if the company can miss the due date of a job, at the cost of forgoing the profits from that job, then we show that there is a (1+e)-speed O(1+1/e)-competitive algorithm, and that this algorithm is essentially optimally competitive