We consider a queueing system with several identical servers, each with its own queue. Identical customers arrive according to some stochastic process and as each customer arrives it must be assigned to some server's queue. No jockeying amongst the queues is allowed. We are interested in assigning the arriving customers so as to maximize the the number of customers which complete their service by a certain time. If each customer's service time is a random variable with a non-decreasing hazard rate then the strategy that does this is one that assigns each arrival to the shortest queue.
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