The SPI (Stepwise Path Increment) algorithm applied to solve the traffic assignment problem with fixed demand

In the traffic assignment problem with fixed demand, the travel time or link cost may depend not only on the flow on that link but also on other links (i.e., ‘non-separable’); such cases may arise at give-ways, roundabouts and so forth. In this paper a new algorithm, the ‘Stepwise Path Increments’ or SPI algorithm, is proposed to deal with such cases. Comparison with other existing algorithms namely: Smith’s and projections method is given. Results for networks tested demonstrated the potential of the SPI algorithm to achieve a good solution without the need to store all the extreme flow patterns and with a smaller number of minimum cost tree calculations than the other algorithms.