Abstract
In this paper we consider online scheduling of malleable parallel jobs on two identical machines, where jobs arrive over time. Each job J j has an execution time t j = p j / k j + ( k j - 1 ) c j when it is processed on k j machines, where p j > 0 and c j > 0 are the length and setup time of job J j . The objective is to minimize the makespan. For the problem with two machines, we present an online algorithm with competitive ratio of 1 + α , where α = ( 5 - 1 ) / 2 . We show that 1 + α is a lower bound on the competitive ratio of any online algorithm for the problem with m ( m ⩾ 2 ) machines. So our algorithm is optimal for the case of two machines.
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