Analysis Of The Road Network Equilibrium And Its Application Under The Condition Of Bounded Rationality

The research on traveler’s rout choice behavior has been the key problem in the field of transportation. Travelers’decision-making behaviors in trip directly influence the distribution of traffic flow in road network. The researches on the travel behavior analysis and modeling are the foundation of future traffic planning, network design problem, decision-making of road pricing, evaluating and choosing the traffic management technology. Many recent literatures at home and abroad about travel behavior have proved that the assumptions of absolute rationality of traveler in the traditional road network equilibrium model has conflicted with more and more the experimental results and the data obtained from the survey of residents trip. In this case, the bounded rationality principle in behavioral economics provides the new approach for us to study the travelers’decision-making progress. In this paper, traveler’s rout choice process has been divided into two steps:firstly, traveler evaluates every path that can be chosen between origin and destination, and then achieve the perceive disutility of each path; secondly, traveler confirm a candidate path for trip based on the perceive disutility of each path, according to a certain decision criterion. In this paper, the assumption of absolute rationality has been substituted by bounded rationality in these two steps:in the first instance, cumulative prospect theory which com from bounded rationality has been used to model perceive disutility of the candidate path, with this perceive disutility model a road network equilibrium model has been constitute, and then which is applied in continuous network design problem; in succession, the satisfactory decision criterion which com from bounded rationality has been used to model traveler’s road choice behavior, and then the traveler’s road choice behavior model under bounded rationality condition has been used to analyses the congestion pricing. Specific studies as follows:1. Based on decision-maker’s choice process under the imprecision prospect condition in prospect theory, combine with the decision-making environment in the field of transportation, the traveler’s decision-making process has been analyzed. The perceive disutility model and the probability weighting function in traditional cumulative prospect theory are used for reference to model traveler’s subjective path disutility and subjective path disutility probability distribution function. Based on these two models, the traditional perceive path disutility model which only can be used for the condition of the path disutility is random discrete distribution is improved with the knowledge of calculus, with these improved model, the perceive path disutility can be obtained for the condition of the path disutility is random continuous distribution. 2. Focus on the traveler’s rout choice behavior in road network under the condition of path trip time is random continuous distribution as research object; traveler has been classified into different level based on the different request of credibility of path trip time. Based on the different request of path trip time credibility, the reference point of perceive path disutility function has been ascertained. On second thoughts, a road network equilibrium model based on cumulative prospect theory has been established. Combined with variational inequalities theory, a mixed behaviors network equilibrium model has been established.3. On the base of transportation network equilibrium model which is depend on cumulative prospect theory, the road network equilibrium model has been translated into an equivalent mixed integer inequality with a binary variable. We formulate the network design problem as a single-level optimization problem with equilibrium constraints. We devise a scheme to discretize the travel time function into small regions and approximate each region with a linear function. The end result is that we approximate the non-linear travel time function with a set of piecewise linear functions. Thus, the original continuous road network design problem is then completely transformed into a mixed-integer linear program. As a linear program, this mixed-integer linear program possesses the property of global optimality.4. Reference to the satisfactory decision rule which is com from bounded rationality theory, based on the analysis of traveler’s road choice behavior under the conditions of bounded rationality, the perceive path disutility has been add a slack variable. Under this condition, we analyses the road network equilibrium condition, and establish the road network equilibrium model with the satisfactory decision rule under the condition of bounded rationality. The problems of finding best and worst case bounded rationality road network equilibrium flow distributions are formulated and solved as mathematical programs with complementarily constraints.5. On the base of bounded rationality road network equilibrium model, combined with the theory of valid toll set, which consists of an infinite number of valid tolls and each valid toll can evolve the system optimum distribution when users are perfectly rational, our congestion pricing models seek a toll vector or pattern that minimizes the system travel time of the worst case tolled BRUE flow distribution, and we propose a heuristic algorithm based on penalization and a cutting plane scheme to solve them.In addition, there are abundant numerical example analyses in this paper, to prove the performance of the above models and methods, and to revealing some important properties in the route choice behaviors of various user classes and the corresponding network equilibrium pattern on the background of bounded rationality hypothesis, further to analysis the idiosyncrasy of continue road network optimum problem, as well as the effective and reliable on the congestion pricing scheme. These entire meaningful conclusions from numerical example analysis, not only enrich the harvest in the mathematical modeling, but provide for the traffic administrator in instituting the relevant policy and choosing the traffic management technology some practical reference.