Optimal dynamic allocation of heterogeneous servers under the condition of total overload: the discounted case

The authors consider the following model. There are M servers with exponential service times and no waiting space. There are N customer types which arrive according to independent Poisson processes. Each time a customer of type i is placed in a server of type j, a reward r(i,j) is produced. The authors determine, in the discounted case, the optimal policy to operate this system when the arrival rates are very large