Assignment of Customers to Servers in a Heterogeneous Queuing System with Switching

We consider a discrete time queuing system composed of a set of servers in parallel in which both customers and servers may be of several types. Customers in service may be switched from one server to another at the beginning of each period. We consider dynamic assignment rules and derive conditions that ensure that it is optimal (in a very strong sense) always to assign customers with longer service times to faster servers.