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 consisting of two heterogeneous parallel servers. The service times of the two servers have an increasing hazard rate. The arrival process is a general renewal 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 expected discounted holding cost. We show some monotonicity properties of the optimal policy. Then we show that the optimal policy routes an arriving customer to the fastest server whenever this server has the lowest workload.