ON THE TRAFFIC ASSIGNMENT PROBLEM WITH FLOW DEPENDENT COSTS - I AND II.

THE AUTHOR REFERS TO A PAPER BY LE BLANC ET AL (1975) WHICH PRESENTED A VERY EFFICIENT MATHEMATICAL ALGORITHM METHOD TO SOLVE THE MULTI COMMODITY USER - EQUILIBRIATED NETWORK FLOW DISTRIBUTION PROBLEM WITH FLOW DEPENDENT-COSTS. THIS METHOD IS CONSIDERED TO BE SIMILAR IN COMPUTATIONAL REQUIREMENTS TO THE ITERATED CAPACITY RESTRAINED TECHNIQUE BUT TO BE MATHEMATICALLY PROVEN TO CONVERGE. THIS PAPER SHOWS HOW TO GENERALIZE THE ALGORITHM TO NETWORKS WITH LINK CAPACITIES, AND A SIMPLE MODIFICATION TO LE BLANC'S ORIGINAL ALGORITHM HAS BEEN INTRODUCED WHICH MAKES POSSIBLE THE STUDY OF CAPACITATED NETWORKS. THE MODIFICATION IS CONSIDERED TO BE MATHEMATICALLY SOUND, AND NOT TO ADD ANY SIGNIFICANT COMPUTATIONAL BURDEN TO THE ALGORITHM. ITS APPLICATION IS ILLUSTRATED BY AN EXAMPLE IN WHICH LE BLANC'S NOTATION HAS BEEN USED. IN THE SECOND PART OF THIS PAPER THE PREVIOUS RESULTS ARE GENERALIZED BY SHOWING HOW TO INCORPORATE LINK CAPACITIES INTO ANY EQUILIBRIUM TRAFFIC ASSIGNMENT ALGORITHM. THIS IS DONE BY DEFINING AN EQUIVALENT UNCAPACITATED TRAFFIC EQUILIBRIUM PROBLEM (EP). AS AN EXAMPLE, THE PERFORMANCE OF THE CONVEX-SIMPLEX METHOD USED BY NGUYEN (1974) ON EP IS EXAMINED, AND IT IS SHOWN HOW THIS CAN BE EASILY MODIFIED TO DEAL WITH CAPACITATED NETWORKS.