Lagrange Relaxation Based Method for the QoS Routing Problem

In this paper a practically efficient QoS routing method is pre- sented, which provides a solution to the delay constrained least cost routing problem. The algorithm uses the concept of aggregated costs and provides an efficient method to find the optimal multiplier based on Lagrange re- laxation. This method is proven to be polynomial and it is also efficient in practice. The benefit of this method is that it also gives a lower bound on the theoretical optimal solution along with the result. The difference between the lower bound and the cost of the found path is very small proving the good quality of the result. Moreover, by further relaxing the optimality of paths, an easy way is provided to control the trade-off between the running time of the algorithm and the quality of the found paths. We present a com- prehensive numerical evaluation of the algorithm, by comparing it to a wide range of QoS routing algorithms proposed in the literature. It is shown that the performance of the proposed polynomial time algorithm is close to the optimal solution computed by an exponential algorithm. Keywords—QoS routing, delay, optimization, Lagrange relaxation