Study On Stochastic User Equilibrium In Two Types Of Transportation Networks

The ineciency of equilibrium is one of the attractive fields of research in transportation science and computer science. In a transportation network, the ine ciency of equilibrium is the ratio of the worst total travel time of an equilibrium assignment to the total travel time of a system optimum(SO) solution. Assuming that all the network users have perfect information about their accurate travel times, and each of them aims to minimize his own travel time, the resultant tra c assignment is the deterministic user equilibrium(DUE) assignment. If we assume that all the network users have perception errors about their travel times, and they aim to minimize their perceived travel times, the resultant tra c assignment becomes the stochastic user equilibrium(SUE)assignment. This study aims to compare the ine ciency of the SUE assignment and that of the DUE assignment, and to find whether the network is more e cient if users have more information.Firstly, we define the relative ine ciency ratio(RIR) as the ratio of the ine ciency of SUE and that of DUE, and we present the lower bound and the upper bound of the relative ine ciency ratio in general networks.Then we focus on a two-link network, in which one of the two links has a constant travel time. We propose some properties of the SUE assignment in such networks, and the necessary and su cient conditions under which the ine ciency of SUE assignment is 1 are found. Define a cross point of the two travel time functions as the flow amount that makes the travel times on the two links the same. We prove that RIR is less than 1when the total flow amount is in the proximity of the cross point, and RIR is equal to1 when the total flow amount is twice of the cross point. We determine the minimum value of RIR and the conditions under which the minimum value is achieved. The tightness of the lower bound of RIR is also guaranteed.After that we extend our study to networks of multiple parallel links. Suppose there are two types of travel time functions in the network. Some properties of SUE assignment are obtained and are further used to find the su cient conditions under which RIR is equal to 1 or less than 1. By conducting special instances, we prove that the lower bound of RIR is still tight in such networks.We further study ring networks with one origin and multiple destinations. We find a su cient condition under which RIR is less than 1. Then we focus on three types of special networks and compare RIR in these networks with 1.The major contributions of this dissertation are as follows:(1) We compare the ine ciency of SUE assignment and that of DUE assignment for the first time, and present the conditions under which accurate travel time information reduces the network e ciency;(2) In the two-link network with one link that has constant travel time,we find the minimum value of RIR;(3) The tightness of the lower bound of RIR is proved.