On the Assignment of Customers to Parallel Queues

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Abstract
This paper considers routing to parallel queues in which each queue has its own single server and service times are exponential with nonidentical parameters. We give conditions on the cost function such that the optimal policy assigns customers to a faster queue when that server has a shorter queue. The queues may have finite buffers, and the arrival process can be controlled and can depend on the state and routing policy. Hence our results on the structure of the optimal policy are also true when the assigning control is in the “last” node of a network of service centers. Using dynamic programming we show that our optimality results are true in distribution.