Online Scheduling on Two Parallel Identical Machines Under a Grade of Service Provision  

作　　者：Shuang Cai Ke Liu 

机构地区：[1]Data Department,Beijing Kingsoft Cloud Network Technology Co.,Ltd.,Beijing,100086,China [2]Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing,100190,China [3]University of Chinese Academy of Sciences,Beijing,100190,China

出　　处：《Journal of the Operations Research Society of China》2022年第4期689-702,共14页中国运筹学会会刊（英文）

基　　金：This research was supported by the National Natural Science Foundation of China(Nos.11271356,and 71390334).

摘　　要：In this paper,we investigate online scheduling problems on two parallel identical machines under a grade of service provision with makespan as the objective function.The jobs arrive over time and each job can be scheduled only when it has already been arrived.We consider three different versions:(i)the two machines cannot be idle at the same time until all arrived jobs have been processed;(ii)further to the first problem,jobs are processed on a first-come,first-serviced basis;(iii)each job must be assigned to one of the two machines as soon as it arrives.Respectively for three online scheduling problems,optimal online algorithms are proposed with competitive ratio(√5+1)/2,(√5+1)/2 and 5/3.

关 键 词：Online scheduling Parallel machines A grade of service provision GOS 

分 类 号：O22[理学—运筹学与控制论]