We address the problem of the performance analysis of the stochastic fair sharing (SFS) algorithm for fair link sharing. The SFS scheme has been proposed to carry out a fair link sharing and fair sharing among virtual private networks. Depending upon the current utilization and provisioned capacities of the classes, the SFS admission control algorithm decides which sessions to accept and which to reject. In this letter, we undertake the performance evaluation of the SFS scheme analytically. We explore the tradeoff between fairness and the blocking probability by varying the trunk reservation parameter. The results show that the analytical performance measure agrees well with the simulation results.