Currently, a large number of ALM algorithms have been proposed to build the overlay networks and transmit data through spanning trees over the overlay networks. However, few works focus on the congestion of spanning tree, the key to the performance of application. This paper studies the impact of spanning tree congestion on ALM performance and proposes a model to quantify and evaluate the congestion. A statistical link model is introduced to describe congestion occurring in ALM networks and a dependency-degree factor is presented to express the dependence between adjacent links. Furthermore, two schemes, the inter-level redundant links (INTER-RL) scheme and the intra-level redundant links (INTRA-RL) scheme, are proposed to enhance the resilience of ALM spanning trees against congestion. Simulation results indicate that the proposed statistical model well describes the congestion in ALM networks and two redundant link schemes both significantly boost the robustness of ALM even in tough network environments.