Coordination mechanisms for selfish scheduling

In machine scheduling, a set of jobs must be scheduled on a set of machines so as to minimize some global objective function, such as the makespan, which we consider in this paper. In practice, jobs are often controlled by independent, selfishly acting agents, which each select a machine for processing that minimizes the (expected) completion time. This scenario can be formalized as a game in which the players are job owners, the strategies are machines, and a player’s disutility is the completion time of its jobs in the corresponding schedule. The equilibria of these games may result in larger-than-optimal overall makespan. The price of anarchy is the ratio of the worst-case equilibrium makespan to the optimal makespan. In this paper, we design and analyze scheduling policies, or coordination mechanisms, for machines which aim to minimize the price of anarchy of the corresponding game. We study coordination mechanisms for four classes of multiprocessor machine scheduling problems and derive upper and lower bounds on the price of anarchy of these mechanisms. For several of the proposed mechanisms, we also prove that the system converges to a pure-strategy Nash equilibrium in a linear number of rounds. Finally, we note that our results are applicable to several practical problems arising in communication networks.     

Programming support and scheduling for communicating parallel tasks

Task-based programming models are beneficial for the development of parallel programs for several reasons. They provide a decoupling of the specification of parallelism from the scheduling and mapping to execution resources of a specific hardware platform, thus allowing a flexible and individual mapping. For platforms with a distributed address space, the use of parallel tasks, instead of sequential tasks, adds the additional advantage of a structuring of the program into communication domains that can help to reduce the overall communication overhead.     

On scheduling tasks with exponential service times and in-tree precedence constraints

Summary In this paper we extend the work of Chandy and Reynolds in which they considered the problem of scheduling tasks on two identical processors. The processing times of the tasks are independent, identically distributed exponential random variables. The tasks are subject to in-tree precedence constraints. Chandy and Reynolds have shown that the expected value of the makespan is minimized if and only if the scheduling policy is Highest-Level-First (HLF). We extend their result by showing that a policy maximizes the probability that all tasks finish by some time t0 if and only if the policy is HLF. Additionally, we show that a policy maximizes the probability that the sum of the finishing times of all the tasks is less than some value s0 if and only if the policy is HLF.This work has been partially supported by a Lady Davis Fellowship at the Technion, Haifa Israel; by the Research Institute for Advanced Computer Science at the NASA Ames Research Center, Moffett Field CA; and by NSF Grant MCS 80-04257.     

On approximation of the bulk synchronous task scheduling problem

The bulk synchronous task scheduling problem (BSSPO) is known as an effective task scheduling problem for distributed memory machines. We present a proof of NP-completeness of the decision counterpart of BSSPO, even in the case of makespan of at most five. This implies nonapproximability of BSSPO, meaning that there is no approximation algorithm with performance guarantee smaller than 6/5 unless P = NP. We also give an approximation algorithm with a performance guarantee of two for BSSPO in several restricted cases.     

Multi-queue scheduling of two tasks

Summary Scheduling in the central server queueing model, consisting of a CPU server and m I/O servers, is considered for the case of two customers. Optimal (maximal CPU utilization) CPU and I/O schedules are obtained. The best CPU schedule depends on the I/O schedule in effect; and is either Longest or Shortest-Expected-Remaining-Processing-Time-First. However, for certain I/O schedules the CPU schedule is immaterial. The best I/O schedule is always to process the longer CPU customer first.     

Quasi-static scheduling of communicating tasks

Good scheduling policies for distributed embedded applications are required for meeting hard real time constraints and for optimizing the use of computational resources. We study the quasi-static scheduling problem in which (uncontrollable) control flow branchings can influence scheduling decisions at run time. Our abstracted distributed task model consists of a network of sequential processes that communicate via point-to-point buffers. In each round, the task gets activated by a request from the environment. When the task has finished computing the required responses, it reaches a pre-determined configuration and is ready to receive a new request from the environment. For such systems, we prove that determining the existence of a scheduling policy that guarantees upper bounds on buffer capacities is undecidable. However, we show that the problem is decidable for the important subclass of “data-branching” systems in which control flow branchings are exclusively due to data-dependent internal choices made by the sequential components. This decidability result exploits ideas derived from the Karp and Miller coverability tree for Petri nets as well as the existential boundedness notion of languages of message sequence charts.     

复合并行机排序问题的启发式算法研究

为有效解决复合并行机排序的极小化最大完成时间问题,提出了分支定界算法和改进的启发式动态规划算法。利用分支定界算法的3个工具:分支模型、边界和优先规则,构建出分支搜索树。按优先规则进行定界搜索,从而减小了问题求解规模。将原始作业转换为虚拟作业,根据Johnson法则,求解出原问题的最优排序。改进的动态规划算法复杂度分析和计算实验表明,这两个算法可靠性高并且可以解决实际问题。     

Using job-shop scheduling tasks for evaluating collocated collaboration

Researchers have begun to explore tools that allow multiple users to collaborate across multiple devices in collocated environments. These tools often allow users to simultaneously place and interact with information on shared displays. Unfortunately, there is a lack of experimental tasks to evaluate the effectiveness of these tools for information coordination in such scenarios. In this article, we introduce job-shop scheduling as a task that could be used to evaluate systems and interactions within computer-supported collaboration environments. We describe properties that make the task useful, as well as evaluation measures that may be used. We also present two experiments as case studies to illustrate the breadth of scenarios in which this task may be applied. The first experiment shows the differences when users interact with different communicative gesturing schemes, while the second demonstrates the benefits of shared visual information on large displays. We close by discussing the general applicability of the tasks.     

On the complexity of fixed-priority scheduling of periodic, real-time tasks

We consider the complexity of determining whether a set of periodic, real-time tasks can be scheduled on m 1 identical processors with respect to fixed-priority scheduling. It is shown that the problem is NP-hard in all but one special case. The complexity of optimal fixed-priority scheduling algorithm is also discussed.     

Allocation and scheduling of precedence-related periodic tasks

This paper discusses a static algorithm for allocating and scheduling components of periodic tasks across sites in distributed systems. Besides dealing with the periodicity constraints, (which have been the sole concern of many previous algorithms), this algorithm handles precedence, communication, as well as replication requirements of subtasks of the tasks. The algorithm determines the allocation of subtasks of periodic tasks to sites, the scheduled start times of subtasks allocated to a site, and the schedule for communication along the communication channel(s). Simulation results show that the heuristics and search techniques incorporated in the algorithm are very effective     

A new algorithm for scheduling periodic, real-time tasks

We consider the problem of preemptively scheduling a set of periodic, real-time tasks on a multiprocessor computer system. We give a new scheduling algorithm, the so-called Slack-Time Algorithm, and show that it is more effective than the known Deadline Algorithm. We also give an (exponential-time) algorithm to decide if a task system is schedulable by the Slack-Time or the Deadline Algorithm. The same algorithm can also be used to decide if a task system is schedulable by any given fixed-priority scheduling algorithm. This resolves an open question posed by Leung and Whitehead. Finally, it is shown that the problem of deciding if a task system is schedulable by the Slack-Time, the Deadline, or any given fixed-priority scheduling algorithm is co-NP-hard for each fixedm.     

A new algorithm for scheduling periodic,real-time tasks

Algorithmica - We consider the problem of preemptively scheduling a set of periodic, real-time tasks on a multiprocessor computer system. We give a new scheduling algorithm, the so-called...     

Online scheduling of moldable parallel tasks

In this paper, we study an online scheduling problem with moldable parallel tasks on m processors. Each moldable task can be processed simultaneously on any number of processors of a parallel computer, and the processing time of a moldable task depends on the number of processors allotted to it. Tasks arrive one by one. Upon arrival of each task, the scheduler has to determine both the number of processors and the starting time for the task. Moreover, these decisions cannot be changed in the future. The objective is to attain a schedule such that the longest completion time over all tasks, i.e., the makespan, is minimized. First, we provide a general framework to show that any \(\rho \)-bounded algorithm for scheduling of rigid parallel tasks (the number of processors for a task is fixed a prior) can be extended to yield an algorithm for scheduling of moldable tasks with a competitive ratio of \(4\rho \) if the ratio \(\rho \) is known beforehand. As a consequence, we achieve the first constant competitive ratio, 26.65, for the moldable parallel tasks scheduling problem. Next, we provide an improved algorithm with a competitive ratio of at most 16.74.     

Feedback fuzzy-DVS scheduling of control tasks

To consider the energy-aware scheduling problem in computer-controlled systems is necessary to improve the control performance, to use the limited computing resource sufficiently, and to reduce the energy consumption to extend the lifetime of the whole system. In this paper, the scheduling problem of multiple control tasks is discussed based on an adjustable voltage processor. A feedback fuzzy-DVS (dynamic voltage scaling) scheduling architecture is presented by applying technologies of the feedback control and the fuzzy DVS. The simulation results show that, by using the actual utilization as the feedback information to adjust the supply voltage of processor dynamically, the high CPU utilization can be implemented under the precondition of guaranteeing the control performance, whilst the low energy consumption can be achieved as well. The proposed method can be applied to the design in computer-controlled systems based on an adjustable voltage processor.     

Power-aware scheduling algorithms for sporadic tasks in real-time systems

In this paper, we consider the canonical sporadic task model with the system-wide energy management problem. Our solution uses a generalized power model, in which the static power and the dynamic power are considered. We present a static solution to schedule the sporadic task set, assuming worst-case execution time for each sporadic tasks release, and propose a dynamic solution to reclaim the slacks left by the earlier completion of tasks than their worst-case estimations. The experimental results show that the proposed static algorithm can reduce the energy consumption by 20.63%–89.70% over the EDF* algorithm and the dynamic algorithm consumes 2.06%–24.89% less energy than that of the existing DVS algorithm.     

Stretching algorithm for global scheduling of real-time DAG tasks

Real-Time Systems - Parallelism is becoming more important nowadays due to the increasing use of multiprocessor systems. A Directed Acyclic Graph (DAG) is a general model of parallel tasks with...     

Deterministic preemptive scheduling of real-time tasks

Algorithms for the preemptive scheduling of deterministic, real-time tasks can have applications in providing quality-of-service guarantees to packet flows in multichannel optical networks     

Multiprocessor online scheduling of hard-real-time tasks

The problems of hard-real-time task scheduling in a multiprocessor environment are discussed in terms of a scheduling game representation of the problem. It is shown that optimal scheduling without a priori knowledge is impossible in the multiprocessor case even if there is no restriction on preemption owing to precedence or mutual exclusion constraints. Sufficient conditions that permit a set of tasks to be optimally scheduled at run time are derived