Admission and routing control of multiple queues with multiple types of customers

We study the routing and admission control problem in a parallel queueing system with heterogeneous servers serving multiple types of customers. The system makes admission decision regarding whether to admit a customer upon arrival as well as routing decision of the queue to which the admitted customer is assigned. The objective is to maximize the expected profit, which includes customer-dependent revenues and holding cost and server-dependent cost. We first characterize the structure of the optimal policy for the case with two servers and two types of customers that have the same holding cost. We show that the optimal admission and routing policy has a complex non-monotone structure; however, we show that this non-monotone structure is the result of overlapping of three pairwise dominant policies that have a monotone structure. Utilizing the above structure, we propose three heuristics for the general case of multiple servers and multiple types of customers. Through a numerical study, we demonstrate the effectiveness of our heuristics, and provide conditions under which each heuristic performs well. Lastly, we provide insights on the effect of holding cost on customer rejection and the effect of fixed production cost on capacity allocation.