Queues with heterogeneous servers and uninformed customers: who works the most?

In this paper, we consider systems that can be modelled by $M\mid M\mid n$ queues with heterogeneous servers and non informed customers. Considering any two servers: we show that the probability that the fastest server is busy is smaller than the probability that the slowest server is busy. Moreover, we show that the effective rate of service done by the fastest server is larger than effective rate of service done by the slowest server.