Communication networks are time-varying and hence, fair sharing of network resources among the users in such a dynamic environment is a challenging task. In this context, a time-varying network model is designed and the shortest user's route is found. In the designed network model, an end to end window-based congestion control scheme is developed with the help of internal nodes or router and the end user can get implicit feedback (RTT and throughput). This scheme is considered as fair if the allocation of resources among users minimizes overall congestion or backlog in the networks. Window update approach is based on a multi-class fluid model and is updated dynamically by considering delays (communication, propagation and queuing) and the backlog of packets in the user's routes. Convergence and stability of the window size are obtained using a Lyapunov function. A comparative study with other window-based methods is also provided.