Abstract
We study a three-server queueing system where servers are heterogeneous in terms of their service speed. The goal of the system operator is to find an optimal routing strategy, which assigns each customer to a server, in order to minimize all customers' expected sojourn time in the system. Using a value iteration approach, we establish that the optimal routing policy is of a threshold type. In addition, suppose the service speed of server-1 is greater than that of server-2 which is greater than that of server-3, it is found that the optimal routing threshold of server-2 when server-3 is busy, is no greater than the optimal routing threshold of server-3 or that of server-2 when server-3 is idle. Finally, we employ numerical experiments to demonstrate sensitivity analysis.
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