Path Finding and Traffic Equilibrium in Stochastic Networks Considering Link Travel Time Correlations

The focus of this dissertation is on the user equilibrium traffic assignment problem in stochastic networks. The path finding problem, which is the main sub-problem in the reliability-based traffic equilibrium problem, is also addressed. The main contribution of this study is to consider link travel time correlations in a dynamic stochastic network for the path finding sub-problem and as a result for the traffic equilibrium problem.;A Monte Carlo simulation-based approach is developed to solve path finding problems in static stochastic networks. This approach demonstrates the importance of considering link travel time correlations in path finding problems in which link travel time reliability measures are considered. This solution method is applied to two different path finding problems, namely the shortest path problem considering on-time arrival reliability (SPOTAR) and the minimum travel time budget path problem (MTTBP). The former minimizes the travel time budget considering a certain probability of on-time arrival and the latter minimizes travel time budget defined as a sum of mean travel time and scaled standard deviation of travel time. To consider correlation in the second problem, standard deviation of travel time is defined based on the covariance matrix of network link travel times. This simulation-based approach for the path finding problem is tested for both static and dynamic networks in this dissertation. The results are compared with existing methods in the literature on static networks and demonstrate the importance of considering correlation in the path finding problem.;Furthermore, most of the studies on stochastic networks in the literature are based on the hypothetical link travel time distributions. Thus this study also identifies network-wide time-dependent link travel time distributions and correlation structure. To this end a simulation-based dynamic traffic assignment tool is applied to simulate different travel times depending on demand level, weather conditions, and incidents information according to real-world data.;Finally, this dissertation designs and implements a framework for the reliability-based user equilibrium problem. First a definition and a mathematical formulation are presented for this problem, and then a column generation based solution with an iterative-based algorithm is applied to solve this problem by minimizing a defined gap function. In this framework, spatial and temporal correlations of link travel times are considered for different classes of users in terms of their valuation of reliability. Two different reliability rules, defining utility for the users, are applied to the path finding problem (SPOTAR and MTTBP). Furthermore, two solution algorithms are presented to relate link flows to link travel time distributions, and temporal and spatial link travel time correlations, namely scenario-based and analytical solution algorithms. The former simulates the latest path flow assignment several times under different scenarios (such as incidents and weather conditions) to update link travel time distributions and correlations, and the latter simulates the latest path flow assignment just once without considering any specific scenario and uses an analytical formulation to relate mean link travel times to standard deviation of travel times and correlations. Finally three different assignment approaches are also tested for the reliability-based user equilibrium, namely random, gap weighted, and gap weighted with sorted destinations. The methodology is tested for different scenarios on a medium-size test sub-network of Chicago, and implemented on the large scale network of Chicago.