The volume of higher priority Internet applications is increasing as the Internet continues to evolve. Customers require Quality of Service (QoS) guarantees with not only guaranteed bandwidth and delay but also with high availability. Our objective is for each estimated traffic flow to find a primary path with improved availability and minimum failure impact while satisfying bandwidth constraints and also minimizing network resource consumption. We devise a heuristic algorithm with four different cost functions to achieve our objective. Our approach can enhance availability of primary paths, reduce the effect of failure and also reduce the total resource consumption for both primary and backup paths.