Optimal control of a queueing system with two heterogeneous servers

The problem considered is that of optimally controlling a queueing system which consists of a common buffer or queue served by two servers. The arrivals to the buffer are Poisson and the servers are both exponential, but with different mean service times. It is shown that the optimal policy which minimizes the mean sojourn time of customers in the system is of threshold type. The faster server should be fed a customer from the buffer whenever it becomes available for service, but the slower server should be utilized if and only if the queue length exceeds a readily computed threshold value.