Abstract
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.
Highlights
Open Access by Qm/online/Cmax, each machine Mi (i = 1, 2, m) has a speed si, i.e., the time used for finishing a job with size p on Mi is p/si
Q3/online/Cmax was considered by Cai and Yang [3]. They showed that the algorithm LS is an optimal online algorithm when the speed ratios (s,t ) ∈ G1 ∪ G2, where s = s2 s1, t = s3 s2
They presented a new algorithm with competitive ratio of 8 for the deterministic version, and 5.436 for its randomized variant
Summary
Definition 1: We have m parallel machines with speeds s1, s2 , , sm , respectively. Let L = {J1, J2 , , Jn} be any list of jobs, where jobs arrives online one by one and each Jj has a release time rj and a processing size of pj. Definition 2: Suppose that Jj is the current job with release time rj and size of pj. In the following we consider m parallel uniform machines with speeds s1, s2 , , sm and a job list L = {J1, J2 , , Jn} with information (rj, pj) for each job J j ∈ L , where ri and pi represent its release time and processing size, respectively.
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