Abstract: In this paper, the asymptotic performance of a linear closed-loop congestion control scheme is analyzed in detail. The asymptotic stability of the scheme is proved, which means the system using this control algorithm is free from oscillation in steady state. The effect of background traffic is analyzed under a Brownian assumption using stochastic difference-differential equation model. Based on those results, the issue of parameter adjustment to achieve optimal asymptotic performance in the interference of background traffic is also discussed.