Queueing network models with two classes of customers

Some peculiar properties of multi-class product-form closed queueing networks with two classes of customers are presented. In particular, we show that in a network with two stations there exists a combination of customer classes such that the stations are equally utilized regardless of the population size. Such an equiutilization point is shown to be an optimal operational point at which the system operates at maximum power. Furthermore, it is shown that the equiutilization point belongs to a set of customer populations that lead both stations to saturate simultaneously as the population increases. The edges of such a common saturation sector are also derived and the limit values of the performance measures when the population increases to infinity are obtained