Optimal allocation of customers in a two server queue with resequencing

The problem of optimal allocation of customers in a two server queue with heterogeneous service rates and resequencing is addressed. The resequencing constraint ensures that the customers leave the system in the order in which they entered it. It is shown that the optimal policy that minimizes the average end-to-end delay of customers in the system is independent of the number of customers in the resequencing buffer. It is also shown that the faster server should be kept busy whenever possible