In a stochastic user equilibrium (SUE) model, the assignment of traffic between different origins and destinations incorporates the effect of congestion through the use of capacity constraint, and also aims to model variations in drivers' perceptions or preferences, reflecting their imperfect knowledge of road network conditions. The assignment problem using a SUE model can be stated as a mathematical programming problem. This paper makes some comparisons between logit and probit methods of SUE assignment, in detail on a two-link network, and also for a more realistic numerical example of a road network, based on an actual network at Sioux Falls, USA. In the two-link network, the variability of the logit and probit parameters are compared. It is found that, for a particular value of the logit parameter, it is not easy to find the corresponding value of the probit parameter. The other main difference between the two models for this case is that the logit model does not treat correlating routes. It is shown how to construct the logit and probit algorithms to be identical in as many ways as possible, except for the difference in underlying routeing principle. This is done first for the assignment algorithm, then extended to the SUE algorithm. The results of some calibration tests on the Sioux Falls network are given.
Abstract