This paper presents recent new findings on the network resource utilization bias phenomenon in the context of TCP-friendly rate control (TFRC) protocol based data flows. It has been found that data flows with lower data rate could yield more than twice of the link utilization than flows with higher data rates under the circumstance that multiple dta flows compete network resource in a shared bottleneck link, e.g. the access link bandwidth is greater than the bottleneck bandwidth. The study is carried out through extensive numerical experiments and a set of key results are presented. In this paper, we highlight and analysis the underlying reasons of the obtained results, and proposed a solution and assessed its performance through simulations. The aspects which could be further improved in the proposed solution have also been discussed.