Optimal online algorithms for scheduling on two identical machines under a grade of service

This work is aimed at investigating the online scheduling problem on two parallel and identical machines with a new feature that service requests from various customers are entitled to many different grade of service (GoS) levels, so each job and machine are labelled with the GoS levels, and each job can be processed by a particular machine only when its GoS level is no less than that of the machine. The goal is to minimize the makespan. For non-preemptive version, we propose an optimal online al-gorithm with competitive ratio 5/3. For preemptive version, we propose an optimal online algorithm with competitive ratio 3/2.

Online scheduling of jobs with kind release times and deadlines on a single machine

This paper studies online scheduling of jobs with kind release times on a single machine. Here "kind release time" means that in online setting, no jobs can be released when the machine is busy. Each job J has a kind release time r(J) ≥ 0, a processing time p(J) > 0 and a deadline d(J) > 0. The goal is to determine a schedule which maximizes total processing time( p(J)E(J)) or total number( E(J)) of the accepted jobs. For the first objective function p(J)E(J), we first present a lower bound 2(1/2), and then provide an online algorithm LEJ with a competitive ratio of 3. This is the first deterministic algorithm for the problem with a constant competitive ratio. When p(J) ∈ {1, k}, k > 1 is a real number, we first present a lower bound min{(1 + k)/k, 2 k/(1 + k)}, and then we show that LEJ has a competitive ratio of1 + k/k. In particular, when all the k length jobs have tight deadlines, we first present a lower bound max{4/(2 + k), 1}(for p(J)E(J)) and 4/3(for E(J)). Then we prove that LEJ is k/k-competitive for p(J)E(J) and we provide an online algorithm H with a competitive ratio of 2 k/( k + 1) for the second objective function E(J).

Online scheduling of two type parallel jobs on identical machines

In this paper we consider an online scheduling of parallel jobs with preemption on identical machines, where jobs arrive over time. The objective is to minimize the makespan. For the problem that jobs have only two possible widths mj = 1 or m, we present an optimal online algorithm by using ＂temporary schedule＂.

Online algorithms for scheduling with machine activation cost on two uniform machines

In this paper we investigate a variant of the scheduling problem on two uniform machines with speeds 1 and s. For this problem, we are given two potential uniform machines to process a sequence of independent jobs. Machines need to be activated before starting to process, and each machine activated incurs a fixed machine activation cost. No machines are initially activated, and when a job is revealed, the algorithm has the option to activate new machines. The objective is to minimize the sum of the makespan and the machine activation cost. We design optimal online algorithms with competitive ratio of (2s+1)/(s+1) for every s≥1.

A heuristic MBLS algorithm for the two semi-online parallel machine scheduling problems with deterioration jobs

The combination of online or semi-online with deterioration jobs has never been researched in scheduling problems. In this paper, two semi-online parallel machine scheduling problems with linear deterioration processing time are considered. In the first problem, it is assumed that the deterioration rates of jobs are known in an interval, that is, bj ∈[0, α], where 0 〈α≤ 1 and bj denotes the linear deterioration rate. In the second problem, it is assumed that the largest deterioration rate of jobs is known in advance, that is, b = max1≤j≤n {bj }. For each of the two problems, a heuristic MBLS algorithm is worked out and its worst-case ratio is analyzed. At the same time, the worst-case ratio of the list （LS） algorithm is investigated and it is proved that all the ratios are tight.

Performance Prediction Based Workload Scheduling in Co-Located Cluster

Cloud service providers generally co-locate online services and batch jobs onto the same computer cluster,where the resources can be pooled in order to maximize data center resource utilization.Due to resource competition between batch jobs and online services,co-location frequently impairs the performance of online services.This study presents a quality of service(QoS)prediction-based schedulingmodel(QPSM)for co-locatedworkloads.The performance prediction of QPSM consists of two parts:the prediction of an online service’s QoS anomaly based on XGBoost and the prediction of the completion time of an offline batch job based on randomforest.On-line service QoS anomaly prediction is used to evaluate the influence of batch jobmix on on-line service performance,and batch job completion time prediction is utilized to reduce the total waiting time of batch jobs.When the same number of batch jobs are scheduled in experiments using typical test sets such as CloudSuite,the scheduling time required by QPSM is reduced by about 6 h on average compared with the first-come,first-served strategy and by about 11 h compared with the random scheduling strategy.Compared with the non-co-located situation,QPSM can improve CPU resource utilization by 12.15% and memory resource utilization by 5.7% on average.Experiments show that the QPSM scheduling strategy proposed in this study can effectively guarantee the quality of online services and further improve cluster resource utilization.

Better Algorithm of Ordinal Online Schedule for Jobs with Similar Sizes on Two Machines

Ordinal online schedule for jobs with similar sizes in on two parallel machines system is considered. Firstly it is proved that the worst case performance ratio of the existing algorithm P2 cannot be improved even if the job processing times are known in for any . Then a better algorithm named S is developed and its worst case performance ratio is given for? .

Hierarchical On-line Scheduling of Multiproduct Batch Plants with a Combined Approach of Mathematical Programming and Genetic Algorithm

In this contribution we present an online scheduling algorithm for a real world multiproduct batch plant. The overall mixed integer nonlinear programming (MINLP) problem is hierarchically structured into a mixed integer linear programming (MILP) problem first and then a reduced dimensional MINLP problem, which are optimized by mathematical programming (MP) and genetic algorithm (GA) respectively. The basis idea relies on combining MP with GA to exploit their complementary capacity. The key features of the hierarchical model are explained and illustrated with some real world cases from the multiproduct batch plants.

On-Line Scheduling for Jobs with Arbitrary Release Times on Parallel Related Uniform Machines

A parallel related uniform machine system consists of m machines with different processing speeds. The speed of any machine is independent on jobs. In this paper, we consider online scheduling for jobs with arbitrary release times on the parallel uniform machine system. The jobs appear over list in terms of order. An order includes the processing size and releasing time of a job. For this model, an algorithm with competitive ratio of 12 is addressed in this paper.

Better Algorithm for Order On-Line Scheduling on Uniform Machines

In this paper, we consider online scheduling for jobs with arbitrary release times on the parallel uniform machine system. An algorithm with competitive ratio of 7.4641 is addressed, which is better than the best existing result of 12.

Optimizing Vaccine Access: A Web-Based Scheduling System with Geo-Tagging Integration and Decision Support for Local Health Centers

The system created aims to produce an online vaccination appointment scheduling system with geo-tagging integration and a decision-support mechanism for neighborhood health clinics. With a decision support mechanism that suggests the essential vaccines based on their account details, it is made to meet the unique vaccination needs of each patient. The system includes immunizations that are accessible locally, and patients and midwives can manage their own corresponding information through personal accounts. Viewers of websites can visualize the distribution of vaccines by purok thanks to geotagging. The Agile Scrum Methodology was modified by the researchers for early delivery, change flexibility, and continual system improvement in order to accomplish the study’s main goal. In order to assess the system’s acceptability in terms of functional adequacy, performance efficiency, compatibility, usability, reliability, security, maintainability, and portability, it was designed in accordance with the ISO 25010 Product Software Quality Standards. Following the assessment, the system was given an average total weighted mean score of 4.62, which represents a verbal interpretation of “strongly agree”. This score demonstrates that the evaluators were in agreement that the system met the requirements of ISO 25010 for Product Software Quality Standards.

Online scheduling of image satellites based on neural networks and deep reinforcement learning

In the ‘‘Internet Plus" era, space-based information services require effective and fast image satellite scheduling. Most existing studies consider image satellite scheduling to be an optimization problem to solve with searching algorithms in a batch-wise manner. No real-time speed method for satellite scheduling exists. In this paper, with the idea of building a real-time speed method, satellite scheduling is remodeled based on a Dynamic and Stochastic Knapsack Problem(DSKP), and the objective is to maximize the total expected profit. No existing algorithm could be able to solve this novel scheduling problem properly. With inspiration from the recent achievements in Deep Reinforcement Learning(DRL) in video games, AlphaGo and dynamic controlling,a novel DRL-based method is applied to training a neural network to schedule tasks. The numerical results show that the method proposed in this paper can achieve relatively good performance with real-time speed and immediate respond style.

Heuristics for Online Scheduling on Identical Parallel Machines with Two GoS Levels

This paper considers the online scheduling problem on m(m≥3)parallel machines(the first k machines with grade 1 and the remaining m-k machines with grade 2)with two Go S levels and makespan as the objective function.The jobs arrive over time with grade 1 or 2 and an arrival job can be assigned to a machine only when the grade of the job is no less than the grade of the machine.Three cases are considered:(i)For k=1,the authors present an online algorithm with competitive ratio of9/5.(ii)For 1<k<m-1,an online algorithm with competitive ratio of 2.280 is proposed.(iii)For k=m-1,an online algorithm is presented with competitive ratio of 2.All the three algorithms are based on greedy algorithm with a similar structure.At last,numerical instances are given and the average competitive ratios of the instances show good performance of the proposed algorithms.

An Optimal Online Algorithm for Fractional Scheduling on Uniform Machines with Three Hierarchies

This paper is concerned with the fractional version of online hierarchical scheduling problem on uniform machines.In the problem,the jobs and machines have several different hierarchies and each job can be arbitrarily split between the machines with hierarchies not above the hierarchy of the job.The objective is to minimize the makespan.The authors present an optimal algorithm for the problem with three hierarchies.

Online Scheduling on Bounded Batch Machines to Minimize the Maximum Weighted Completion Time

We investigate the online scheduling problem on identical parallel-batch machines to minimize the maximum weighted completion time.In this problem,jobs arrive over time and the processing times(of the jobs)are identical,and the batch capacity is bounded.For this problem,we provide a best possible online algorithm with a competitive ratio of(√5+1)/2.Moreover,when restricted to dense-algorithms,we present a best possible dense-algorithm with a competitive ratio of 2.

Online Over Time Scheduling on Parallel-Batch Machines:A Survey

Online scheduling is a rapidly developed branch in scheduling theory.In this paper,we present an extensive survey for online over time scheduling on parallel-batch machines.Some open problems are proposed for further research.

An Optimal Online Algorithm for Scheduling on Two Parallel Machines with GoS Eligibility Constraints

We consider the online scheduling problem on two parallel machines with the Grade of Service(GoS)eligibility constraints.The jobs arrive over time,and the objective is to minimize the makespan.We develop a(1+α)-competitive optimal algorithm,whereα≈0.555 is a solution ofα^(3)−2α^(2)−α+1=0.

Semi-Online Algorithms for Scheduling with Machine Cost

In this paper, we consider the following semi-online List Model problem with known total size. We are given a sequence of independent jobs with positive sizes, which must be assigned to be processed on machines. No machines are initially provided, and when a job is revealed the algorithm has the option to purchase new machines. By normalizing all job sizes and machine cost, we assume that the cost of purchasing one machine is 1. We further know the total size of all jobs in advance. The objective is to minimize the sum of the makespan and the number of machines to be purchased. Both non-preemptive and preemptive versions are considered. For the non-preemptive version, we present a new lower bound 6/5 which improves the known lower bound 1.161. For the preemptive version, we present an optimal semi-online algorithm with a competitive ratio of 1 in the case that the total size is not greater than 4, and an algorithm with a competitive ratio of 5/4 otherwise, while a lower bound 1.0957 is also presented for general case.

Online Scheduling on Two Uniform Unbounded Parallel-Batch Machines to Minimize Makespan

We study an online(over time)scheduling problem on two uniform unbounded parallel-batch machines with processing speed 1 and v(0<≤1),respectively,to minimize the makespan.We first show that no online algorithm can have a competitive ratio less than 1+αL,whereαL=(√5−1)/2≈0.618 if 0≤1/2,andαL=α2(v)is the positive root ofα^(3)+3α^(2)+(3−1/v)α−1/v=0 if1/2≤1.This lower bound is still valid when all jobs have the same processing times.Then,we provide an online algorithm with a competitive ratio at most min{(√5+1)/2,√2/v}.When the jobs have the same processing times,we present the best possible online algorithm with a competitive ratio 1+αL.

Preemptive Semi-Online Scheduling with Tightly-Grouped Processing Times

This paper investigates a preemptive semi-online scheduling problem onm identical parallel machines wherem=2,3. It is assumed that all jobs have their processing times in betweenp andrp (p > 0,r ≥1). The goal is to minimize the makespan. Best possible algorithms are designed for anyr≥1 whenm=2,3. Keywords semi-online - scheduling - preemption - competitive ratio Regular PaperThis research is supported by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE. China, and the National Natural Science Foundation of China (Grant Nos. 10271110 and 60021201).Yong He received his B.S., M.S., and Ph.D. degrees all from Zhejiang University in 1989, 1992, 1996, respectively. He is currently a professor and Ph.D. supervisor at Department of Mathematics, Zhejiang University. His current research interests include combinatorial and network optimization, scheduling theory, computational biology, mathematical modeling, etc.Yi-Wei Jiang received his B.S. degree from Zhejiang University in 2002. He is currently a Ph.D. candidate of Zhejiang University. His current interests include scheduling theory and online algorithms.