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This book is the result of several years of research into the modeling and algorithm of problems in dynamic travel choice and related areas. Three types of discrete time dynamic travel choice models, along with numerical examples, are presented, i.e., deterministic, stochastic and fuzzy models. The notable features pertaining to these models are as follows: 1. The asymmetric property of the dynamic link travel time function is clearly verified, which leads to a variational inequality formulation. 2. The flow propagation constraint is implicitly defined in our model through the incidence relationship between the link inflow and route flow. 3. The inflow, exit flow, and number of vehicles on a link are identified as the three different states over time for the same vehicles under the flow propagation process. Therefore, only one link variable needs to be used in our dynamic travel choice models. This treatment can largely simplify the models' complexity, and possibly reduce the computation time. 4. The developed time-space network is consistent with scaling units both in temporal and spatial dimensions. 5. The proposed nested diagonalization method takes care of two types of link interactions, i.e., actual link travel times, and inflows other than that on the subject time-space link. 6. The equivalence analysis between a dynamic travel choice model and its corresponding equilibrium condition is performed by proving both the necessary and sufficient conditions under the presumption of equilibrated actual travel times.
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