Congestion control is one of the top problems in networking, and a key element for core networks to avoid congestion. The window size is used to pipelined packets on the network and is the means to manage the congestion in a network with an end-to-end approach. In the present work, we design a model for the reduction of the window in order to manage the congestion in a network. The reduction is shallow in-contrary to others approaches in which the reduction is drastic. The purpose of making the modification in the reduction algorithm of the window is to reduce the number of packets in the backbone network without affecting the end system. To do this, we test under NS2, modifying the TCP protocol code and proposing particular scenarios.