Optimal control of two parallel infinite-server queues

The problem of the optimal admission and routing of customers to a network of two infinite server queues in parallel is considered. The service times in the two queues are exponential with a common rate. The arrival process is Poisson. There is a nonnegative cost associated with rejecting a customer and a cost of holding a customer in each queue. This holding cost is a nondecreasing convex function of the number of customers in that queue and is different for each queue. It is shown that the optimal control policy has admission monotonicity and routing monotonicity properties