Non-preemptive Job Scheduling Research Articles

Online Multi-Resource Social Welfare Maximization for Non-Preemptive Jobs

Multi-resource allocation is ubiquitous in datacenters. Usually, the datacenter scheduler associates each user with a utility function and then allocates multiple resources so as to maximize the social welfare, which is the sum of the utilities of the users. We refer to this problem as the Social Welfare Maximization (SWM) problem. Meanwhile, given the dynamic nature of datacenters, the scheduler is supposed to support non-preemptive scheduling, where jobs of users that are being processed would not be interrupted by the reconfiguration of resources. Non-preemptive solutions to SWM incorporating pricing considerations include dynamic pricing and bidding/auctions. However, both strategies are quite complex. Meanwhile, traditional Lagrange solutions to SWM does not support non-preemptive job scheduling. In this paper, we propose Adaptive Dominant Resource Fairness (ADRF), that provides near-optimal social welfare where each user is assigned an α-fair utility function and when 1 <; α ≤ 2. Based on ADRF, we propose Cumulative ADRF (C-ADRF), an online algorithm that greedily assigns the idle resources to the current poorest user, making it quite simple to schedule jobs from users non-preemptively. Compared with the polynomial or exponential form of time complexities in other SWM solutions, C-ADRF requires only O(log N) work, where N is the number of users. Extensive simulations using Google and Facebook cluster-data traces show an impressive behavior of C-ADRF in providing social welfare, only 3% and 2% away from the optimal social welfare, respectively.

MYOPIC POLICIES FOR NON-PREEMPTIVE SCHEDULING OF JOBS WITH DECAYING VALUE

In many scheduling applications, minimizing delays is of high importance. One adverse effect of such delays is that the reward for completion of a job may decay over time. Indeed in healthcare settings, delays in access to care can result in worse outcomes, such as an increase in mortality risk. Motivated by managing hospital operations in disaster scenarios, as well as other applications in perishable inventory control and information services, we consider non-preemptive scheduling of jobs whose internal value decays over time. Because solving for the optimal scheduling policy is computationally intractable, we focus our attention on the performance of three intuitive heuristics: (1) a policy which maximizes the expected immediate reward, (2) a policy which maximizes the expected immediate reward rate, and (3) a policy which prioritizes jobs with imminent deadlines. We provide performance guarantees for all three policies and show that many of these performance bounds are tight. In addition, we provide numerical experiments and simulations to compare how the policies perform in a variety of scenarios. Our theoretical and numerical results allow us to establish rules-of-thumb for applying these heuristics in a variety of situations, including patient scheduling scenarios.

Online scheduling of simple linear deteriorating jobs to minimize the total general completion time

Traditional scheduling assumes that the processing time of a job is fixed. Yet there are numerous situations in which the processing time increases (deteriorates) as the start time increases. In particular, lots of work has been devoted to jobs with simple linear deterioration. The processing time pj of job Jj is a simple linear function of its start time sj, precisely, pj=bjsj, where bj is the deteriorating rate. In this paper, we study the problem of online non-preemptive scheduling of jobs with arbitrary release times and simple linear deteriorating rates on a single machine to minimize the total general completion time. We present an algorithm DSDR (Delayed Smallest Deteriorating Rate) and prove that it achieves the best-possible competitive ratio (1+bmax)α for all deterministic online algorithms, where α is the general index of completion time and α>0.

Tight approximation algorithms for scheduling with fixed jobs and nonavailability

We study two closely related problems in nonpreemptive scheduling of jobs on identical parallel machines. In these two settings there are either fixed jobs or nonavailability intervals during which the machines are not available; in both cases, the objective is to minimize the makespan. Both formulations have different applications, for example, in turnaround scheduling or overlay computing. For both problems we contribute approximation algorithms with an improved ratio of 3/2. For scheduling with fixed jobs, a lower bound of 3/2 on the approximation ratio has been obtained by Scharbrodt et al. [1999]; for scheduling with nonavailability we provide the same lower bound. We use dual approximation, creation of a gap structure, and a PTAS for the multiple subset sum problem, combined with a postprocessing step to assign large jobs.

On-line scheduling revisited

We present a new on-line algorithm, MR, for non-preemptive scheduling of jobs with known processing times on m identical machines which beats the best previous algorithm for m⩾64. For m∞ its competitive ratio approaches 1+\sqrt{(1+1{\rm n} 2)/2}<1.9201. Copyright 2000 © John Wiley & Sons, Ltd.

Scheduling of independent jobs in star graph networks

In this paper, we investigate the problem of how to schedule n independent jobs on an m-dimensional star graph based network. We develop a feasibility algorithm for preemptively scheduling a given set of jobs with dimension and time requirements on a star graph network of given size with a given deadline. We show that the algorithm runs in O( n log n) time where n is the number of jobs. We also develop a simple heuristic for nonpreemptive scheduling of jobs and study its lower and upper bounds.

Note: Due-date Assignment to Multi-Job Customer Orders

The paper addresses deterministic, nonpreemptive scheduling of jobs that are immediately available for processing on a single machine. The jobs are partitioned into several multi-job customer orders. The problem is to determine a due-date for each customer order and to schedule all the jobs such that a total penalty function is minimized. The total penalty function is the sum of penalties for job earliness, penalties for job tardiness, and penalties associated with the lead times of customer orders. The main results is that there is an optimal solution in which the jobs within each customer order are processed contiguously. This is an appealing feature in terms of implementation. Efficient algorithms are presented for solving special cases of this problem.

Bounds for nonpreemptive scheduling of jobs with similar processing times on multiprocessor systems using the LPT-Algorithm

The well-known, NP-complete problem of scheduling a set ofn independent jobs nonpreemptively onm identical parallel processors to minimize the maximum finish time is considered. Let ω0 be the finish time of an optimal schedule and ω the finish time of a schedule found by the Longest Processing Time (LPT-)heuristic. We will improve the Graham-bound for the LPT-heuristic (ω/ω0 ≤ 4/3 − 1/3m) which is tight in general, by considering only jobs with similar processing times.