Abstract
It is well known that the expected waiting time for customers routed to several parallel queues decreases dramatically when customers are routed to the shortest of two randomly chosen queues, rather than being arbitrarily assigned to one of the queues, and that the further improvement when there are three queues to choose from is much less than the improvement when moving from one to two queues (the power of two [5]). We consider the power of two effect when a subset of customers are flexible, and can choose the shortest of two queues, while the remainder are dedicated, and have no routing choice. We show that the stationary expected waiting time is decreasing and convex in the proportion of flexible customers. Our results show that having a small proportion of flexible customers has nearly as much benefit as having full power of two choices.
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