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The authors consider a system of parallel queues where tasks are assigned (dispatched) to one of the available servers upon arrival. The dispatching decision is based on the full state information, i.e., on the sizes of the new and existing jobs. They are interested in minimizing the so-called mean slowdown criterion corresponding to the mean of the sojourn time divided by the processing time. Assuming no new jobs arrive, the Shortest-Processing-Time-Product (SPTP) schedule is known to minimize the slowdown of the existing jobs.
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