Optimal routing to two parallel heterogeneous servers with resequencing

The optimal routing problem is considered under the class of fixed-position routing policies, that route customers to the faster server from the head of the service queue, and to the slower server from position J. The cost function is taken as the long-run average holding cost of the customers in the system. It is shown that an optimal stationary policy exists and is of the following type: the faster service is kept active as long as the service queue is not empty. The decision whether or not to route a customer to the slower server is independent of the state of the resequencing queue