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This paper considers a class of parallel server systems that are known as N-systems. In an N-system, there are two customer classes that are catered by servers in two pools. Servers in one of the pools are cross-trained and can serve customers from both classes whereas all the servers in the other pool can only serve one of the customer classes. A customer reneges from his queue if his waiting time in the queue exceeds his patience. The objective is to minimize the total cost that includes a linear holding cost and a reneging cost. The authors prove that, when the service speed is pool-dependent, but not class-dependent, a ci-type greedy policy is asymptotically optimal in many-server heavy traffic.
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