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We analyze the optimal preemptive sequencing of n jobs on M + 1 parallel identical machines to minimize expected total flowtime. The running times of the jobs are independent samples from the distribution Pr(X = H) = p, Pr(X = H + T) = 1 − p, where H, T are random variables of general distribution. Preemption of a job is allowed when H is completed. This problem does not have a simple optimal solution. We show that the scheme of shortest expected remaining processing time first (SERPT) is close to optimal in two senses. The expected flowtime under SERPT and under the optimal policy differ by no more than a constant, independent of the number of jobs, and the expected number of optimal decisions that are not according to SERPT is bounded by a constant, independent of the number of jobs.

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