Traffic assignment models and methods are under consideration of researchers all around the world. The development of this scientific field contributes both in theory and practice. In this paper, the traffic re-assignment procedure is analyzed from sensitive perspectives. This procedure is given in the form of computational techniques to cope with the network optimization problem. Numerical experiments are performed for several types of travel time functions. The results reveal that, from practical perspectives, dual algorithms are highly sensitive to parameters of travel time functions, while primal algorithms can be quite acceptable for rough computations. The obtained findings contribute to the theory and give fresh managerial insights for traffic engineers.