Integrating Activity Scheduling and Travel Choices in a Dynamic Network Equilibrium Framework: Concepts, Algorithms and Application

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The purpose of the dissertation is to develop a framework for equilibration of activity-trip chain demand in an integrated system of activity scheduling and travel choices within a dynamic network equilibrium framework. Activity-based modeling systems generate detailed activity chain schedules for individuals, which have to be assigned to transportation networks. Most of the implementations of activity-based models have been separate from the dynamic traffic assignment models. However, representation of detailed individual activity schedules throughout the assignment procedure, and capturing the resulting network performance measures in generating activity schedules, would lead to schedules consistent with real dynamics of transportation networks. Most of the studies on the integration of the activity-based modeling systems with dynamic traffic assignment systems have focused on the applications. The literature lacks a theoretical basis and rigorous analytical treatment for the integrated model; moreover, important mathematical properties of the model are not adequately investigated. This dissertation aims at bridging the gap by presenting a household activity schedule adjustment model coupled with dynamic traffic assignment, where individuals’ choices are made within a user equilibrium framework. The proposed framework provides achievement of faster algorithmic convergence for the integration of activity-based and dynamic traffic assignment models by serving as an inner adjustment process. The equilibrium problem is formulated as a fixed-point equilibrium problem, which provides a basis for investigation of the solution properties. The input variables to the model are the individuals’ detailed activity schedules (obtained from an activity-based model) which could be translated as the time-dependent origin-destination demands, while the output variables are the household members’ schedules as well as path flows at equilibrium. A primary assumption is that individuals associate a disutility to their travel patterns, which they try to minimize. First, a household disutility term is defined as a function of 1) total travel cost and 2) schedule inconsistencies. Then, the problem is formulated as a fixed-point equilibrium problem. Next, the user equilibrium conditions are defined, and a variational inequality (VI) formulation is presented, and it is shown that the solution to the VI problem meets the user equilibrium conditions. In order to investigate the solution properties of the problem formulation, the continuity and monotonicity of the involved functions is explored. Next, a solution algorithm is proposed, and the convergence characteristics of the proposed algorithm are demonstrated through numerical results obtained from application of the proposed algorithm to a large-scale real world network. Further, the author addresses the issue of trip chain equilibrium in a dynamic network equilibrium framework. For this purpose, the author proposes a reformulation of the trip-based demand gap function formulation for the VI formulation of the bi-criterion dynamic user equilibrium (BDUE) problem. Next, a solution algorithm is proposed for solving the BDUE problem with daily chain of activity-trips. Then, numerical results obtained from the applied algorithm to both small-scale and large-scale networks in a simulation setting are presented. The results suggest that recognizing the dependency of multiple trips in a chain and maintaining the departure time consistency of subsequent trips provide sharper drops in gap values; hence, convergence might be reached more quickly, as compared to when trips are considered independent of one another. In addition, the integrated model of schedule adjustment and dynamic traffic assignment is extended to incorporate the cancellation of activities. It is shown that incorporation of activity cancellation could improve the algorithmic convergence

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  • 02/13/2018
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