A Traffic Flow Assignment Model Considering The Marginal Effect And Scale Effect Of The Travel Cost

The traffic flow assignment is substantially to the discrete choice model, it is a summation of all travelers choosing roads individually. We need to consider that the travelers choose their roads based on what kind of criteria and their own characteristic related to the criteria. In this paper, we consider that the travelers choose their roads by the shortest road criteria(utility maximization) like which the multivariate Logit and Probit use. The characteristic related to the criteria is the understanding of the travel cost of roads. Based on the above analysis, this paper considers the marginal effect and scale effect of the travel cost to build traffic assignment models.Firstly, this research sort out the flow assignment model, and find that most stochastic user equilibrium models are based on the multinomial Logit model, but its independent identically distributed doesn’t match the real traffic network. Some scholars do some improvements and give models like PCL, C-Logit. But when the absolute difference between the roads is fixed, this type of models gives the same choice probability regardless of changes of the travel cost, it doesn’t match the realistic network, namely it doesn’t consider the marginal effect of the travel cost.Based on the above theoretical analysis, this research combines the Weibull distribution proposed by Castillo(2008) and changes the utility function model of the multivariate Logit model into multiplying form. This model considers the marginal effect of the travel cost. This research consider the heterogeneity of travelers and gives a multi-user multinomial Weibull model.Then, this research analyzes the scale effect of the travel cost:When the relative difference of roads is fixed, the shortest road choice probability will increase when the travel cost increases. But the multivariate Weibull model doesn’t consider this condition. This research adds a factor in the utility function of the multivariate Weibull model to consider the scale effect, and gives a new utility function and the multivariate Weibull-Logit model which both considers the marginal effect and scale effect.This research gives the corresponding route choice probability and mathematical programming for the above two models. Followed by several numerical experiments, when faces the marginal effect and scale effect of the travel cost, these two models give the flow assignment changes which meets the real traffic network. This research analyzes the influence of model parameters and traffic demand to the flow assignment. Finally, we give future research directions.