Deadlock avoidance and recovery techniques suffer from severe performance degradation when the network is close to or beyond saturation. Many parallel applications produce bursty traffic that may saturate the network during some intervals [25, 22, 11], and increase execution time. Therefore, the use of techniques that prevent network saturation are of crucial importance in both deadlock avoidance and recovery strategies. Several mechanisms have been proposed in the literature to reach this goal. However, some of them do not work well under all network load conditions. Others introduce some penalty when the network is not fully saturated, or complicate network and/or node implementation. In this paper, we propose a new mechanism to avoid network saturation that overcomes these drawbacks. In this mechanism, each node estimates network traffic locally by using the percentage of free virtual output channels that can be used for forwarding a message towards its destination. When this number surpasses a threshold value, network congestion is assumed to exist and message injection is forbidden.