Optimal routing of customers to two parallel heterogeneous servers: The case of IHR service times

We consider here the optimal routing of customers, arriving to a system con sisting of two heterogeneous parallel servers. The service times of the two servers have an increasing hazard rate. The arrival process is a general r enewal process. The cost of holding x customers in the system per time unit is a nondecreasing and convex function. The objective is to minimize the e xpected discounted holding cost. We show some monotonicity properties of th e optimal policy. Then we show that the optimal policy routes an arriving c ustomer to the fastest server whenever this server has the lowest workload.