In this paper we develop policies for scheduling dynamically arriving jobs to a broad class of parallel-processing queueing systems. We show that in heavy traffic the policies asymptotically minimize a measure of the expected system backlog, which we call system work. Our results yield succinct, closed-form expressions for optimal system work in heavy traffic.
Gans, Noah, and Garrett van Ryzin. "Optimal Dynamic Scheduling of a General Class of Parallel-Processing Queueing Systems." Advances in Applied Probability 30, no. 4 (December 1998): 1130-1156.
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