The upper bound of packet transmission capacity in local static routings
  We propose a universal analysis for static routings on networks and describe the congestion characteristics by the theory. The relation between average transmission time and transmission capacity is described by inequality T0Rc0<=1. For large scale sparse networks, the non-trivial upper bond of transmission capacity Rc0 is limited by Rc0<=1/< 1/k > in some approximate conditions. the theoretical results agree with simulations on BA Networks. 
Zhe He, Rui-Jie Xu, Si-Wu Liu, Bing-Hong Wang
cs.NI cond-mat.stat-mech