Fair dynamic routing in large-scale heterogeneous-server systems

In a call center, there is a natural trade-off between minimizing customer wait time and fairly dividing the workload among agents of different skill levels. The relevant control is the routing policy, that is, the decision concerning which agent should handle an arriving call when more than one agent is available. We formulate an optimization problem for a call center with heterogeneous agent pools, in which each pool is distinguished by the speed at which agents in that pool handle calls. The objective is to minimize steady-state expected customer wait time subject to a ‘fairness’ constraint on the workload division.