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

作　　者：LI Wen-jie MA Ran FENG Qi 

机构地区：[1]School of Mathematical Sciences, Luoyang Normal University [2]School of Mathematics and Statistics, Qingdao University [3]Department of Information and Computation Science, Zhongyuan University of Technology

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2019年第1期113-126,共14页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(11501279,11501171,11671188,and11401604);the Young Backbone Teachers of Luoyang Normal University(2018XJGGJS-10);Henan Colleges(2015GGJS-193)

摘　　要：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).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).

关 键 词：SCHEDULING ONLINE algorithm KIND RELEASE time DEADLINE 

分 类 号：O1[理学—数学]