In a dynamic network environment under heavy traffic load, shortest-path routing algorithms, particularly attempt to adapt to traffic changes, frequently exhibit oscillatory behaviors and cause performance degradation. In this paper, we first analyze, the instability factors and their results in the multicast infrastructure, and then analyze the solutions leading to stability in switched networks. Subsequently, we propose a solution to the above routing problem, where the route computation is based on the actual load on the network links. We propose a fast and simple heuristic algorithm named the Cost-Delay Shortest Path (CDSP) algorithm, which attempts to strike a balance between the different QoS parameters. The CDSP algorithm is based on a simple path exponential selection function taking simultaneously both the cost and delay into consideration and allowing the network load to be distributed in an optimal way.