Asymptotically optimal control of many-server heterogeneous service systems with $H_{2}^{*}$ service times

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.