Configuration of overloaded servers with dynamic routing

We consider overload of servers in a network with dynamic routing of messages. The system consists of $k$ servers and $\ell$ independent Poisson input flows. Messages from each flow are directed to $m$ servers, and each message is directed to a server that is the least loaded at the moment of its arrival. In such a system, configuration of overloaded servers depends on the intensity of input flows. A similar effect was considered in [1] for a system with another geometry.