The structural property of network bottlenecks in maxmin fair flow control

In this letter we introduce a new conceptual framework to investigate into the underlying structure of network bottlenecks in maxmin fair flow control. It is shown that a network has a hierarchical structure with regard to its bottlenecks. The number H of network bottleneck levels is proved to be no greater than the number K of network bottleneck rates. It is also shown that there can be many bottleneck rates on each hierarchical level. So H can be much smaller than K.