Abstract: Traffic Engineering (TE) broadly relates to optimization of the performance of a network. The overlay approach has been widely used by many service providers for Traffic Engineering (TE) in large Internet backbones. In the overlay approach, logical connections are set up between edge nodes to form a full mesh virtual network on top of the physical topology. IP routing is then run over the virtual network. Instead of overlaying IP routing over the logical virtual network, the integrated approach runs shortest path IP routing natively over the physical topology. Traffic engineering needs to determine the optimal routing of traffic over the existing network infrastructure by efficiently allocating resource in order to optimize traffic performance on an IP network. Traffic engineering objectives are achieved through carefully routing logical connections over the physical links. Common objectives of traffic engineering include balancing traffic distribution across the network and avoiding congestion hot spots. This study proposes a new approach called the Bayesian approach to avoid congestion hot spots without full mesh overlaying. This approach can be illustrated with a simple network, and then present a formal analysis of the Bayesian networks and a method for finding the congestion hot spots. Once, the congestion hot spots are identified then the traffic can be distributed, so that no link in the network is either over utilized or under utilized. With this Bayesian approach the quality of the routing can be improved and congestion can be avoided.