After being proposed by Jain, Chiu, and Hawe in 1984, the fairness score function F(x) has been widely adopted to evaluate the fairness of the network resource distribution. The fairness score function F(x) possesses some nice properties. However, in some cases, it will give obviously unreasonable fairness scores. Chen and Zhang (2005) proposed another fairness score function G(x) which better fits the real world situation. Another fairness score function G~*(x;w) is considered to treat the case that the users have different priority levels. It can be shown that G~*(x;w) preserves all the meritorious properties that the existing score functions possess. Statistical test for monitoring the fairness of the network resource distribution is discussed in this paper.
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