Abstract
Optimal control of many-server heterogenous service systems with service times that have a special hyper-exponential distribution, denoted by $H_{2}^{*}$ , which is a mixture of an exponential distribution and a unit point mass at 0, is considered. A static priority policy that assigns priorities to server pools based on their service time distributions is proposed. This policy is shown to be asymptotically optimal in the many-server heavy-traffic regime in minimizing the total number of customers.
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