In our previous paper, we introduced the approach to solve the multi-constrained routing problem in the over-constrained case and proposed the algorithm for the particular case of this problem when all constraints used are concave. This paper is devoted to a software implementation of this approach. We present a system for modeling the optimal network path subject to the specified constraints that reflect quality of service requirements. The system allowed us to experimentally evaluate the complexity of the proposed algorithm. Simulation results and some concluding remarks are provided in the final part of the paper.