This thesis compares Bar-Gera's Method and Aashtiani's Method for solving the static traffic assignment problem with fixed demand. Specifically, it compares the computational time spent by their corresponding algorithms in thirteen networks based on real cities. It also verifies whether the assumptions made by both methods and the data used allowed such a comparison. To implement Aashtiani's algorithm, a computer code was appropriately designed. To implement Bar-Gera's algorithm, a non-open source application was used. Numerical results showed mixed results but still showed the following trends: (1) Aashtiani's algorithm seems to be faster when solving complex networks, (2) Bar-Gera's algorithm is almost always faster for very high levels of accuracy while Aashtiani's algorithm is faster for lower levels of accuracy, and (3) Bar-Gera's algorithm almost always increases its speed consistently as more accuracy is demanded. Numerical results also showed that for small networks (specifically, when the number of arcs times the number of links is less than 1.0E+7), both algorithms spent practically no more than one second, rending these networks not recommendable for carrying out future comparisons. As expected, Bar-Gera's method required less memory. This thesis also presents a unified terminology for both methods and adapted Aashtiani's formulation to this specific problem.