On the integration of an effective assignment algorithm with path and path-flow management in a combined trip distribution and traffic assignment algorithm.

The combined trip distribution and assignment problem could be described as a search for a set of demands - given by a double constrained distribution model - which is stable under the times generated by a user equilibrium assignment of these trip rates. So the natural criteria of convergence are given by the changes of the minimum origin- destination travel (O/D) times and the user equilibrium conditions. Since the two standard algorithms (by S. Evans, M. Florian et. al.) for this problem are link flow orientated, no direct verification of the above introduced natural convergence tests could be used. This failure establishes the starting-point for the new algorithm to be presented. In the first part of this paper, a new path orientated assignment algorithm is introduced and a proof of its convergence is lined out. To show its fast convergence rate, the algorithm is tested with a realistic network. These results will be compared to the results gained with Frank-Wolfe Type algorithms. It is shown that the new algorithm converges faster than the Frank- Wolfe Type algorithms. Beyond this, it becomes evident, that the observed travel time fault for used routes could be tested and predetermined. The second part of this paper deals with the integration of the above assignment algorithm in an algorithm for solving the combined model. In conclusion, all algorithms will be tested on a dataset consisting of 21 cells and 293 links on a PC. The results show that the new algorithm calculates a solution that has a maximum deviation of the exact solution (calculated with 10000 Evans iterations) of less than 1 per cent in the link flows and none in the demands. This means a speeding up of a factor 100. In addition, the link flow distribution is generated by a path flow distribution which has the property, that between all O/D pairs only routes are used, that have a maximum deviation of 0.001 sec in relation to the minimum travel times. The needed storage of the new algorithm is only 10 per cent higher than for the other algorithms.