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 ...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.展开更多
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 sched...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.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10271110) and the Teaching and Research Award Pro-gram for Outstanding Young Teachers in Higher Education, Institu-tions of MOE, China
文摘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.
基金This research was supported by the National Natural Science Foundation of China(Nos.11271356,and 71390334).
文摘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.
