Advances in dynamic network modeling with spatial queue based traffic flow models
Dynamic network modeling has been extensively explored by the research community for the last three decades due to the advances of emerging technologies and the availability of large-scale time-dependent data. The dynamic models can outperform the static models in many research areas such as operational planning and real-time operational control. However, there still exist several gaps in the analytical dynamic network modeling, including a) dynamic network loading models which facilitate dynamic traffic assignment (DTA) without compromising traffic realism, b) dynamic user equilibrium and dynamic system optimal with desirable features such as simultaneous route and departure time choice, multiple OD networks, solution existence, and efficient algorithms, c) methods to compute the network inefficiency and the price of anarchy in the dynamic context, and d) new models for dynamic mechanism design with advanced traffic flow and dynamic user equilibrium. ^ The overall goal of this dissertation is to develop a series of analytical dynamic traffic assignment and dynamic mechanism design models to fill these gaps. The broaden impact of this dissertation is to provide a framework to predict traveler behavior, estimate traffic state, understand real-world and ideal network conditions, and suggest rational solutions to improve network performance. Specifically, in this dissertation: A dynamic network loading model is developed based on cell transmission model to captures realistic traffic conditions such as shockwave propagation, queue spill-back, FIFO, non-holding-back in multiple OD networks. It can be embedded directly in DTA formulations. A simultaneous route and departure time choice dynamic user equilibrium (DUE) problem for multiple OD networks is formulated as a complementarity system. The cost function is shown continuous and the solution existence is rigorously shown by advanced generalized variational inequality theory. An efficient projection algorithm is proposed to solve the DUE problems for medium-sized traffic networks. A dynamic system optimal (DSO) problem for multiple OD networks with route and departure time choice is formulated. A novel method to accurately compute path marginal cost is developed and the DSO problem is solved by the projection algorithm. The network inefficiency and price of anarchy are studied in dynamic networks to capture the trend of the relative difference between DUE and DSO solutions. For many traffic networks, we observe that the network inefficiency stabilizes after a certain demand level. A combined DUE and signal control problem is formulated as a Stackelberg game and is solved by the iterative optimization and assignment algorithm. Finally, a novel idea of path-based toll scheme is studied. We propose a heuristic algorithm to provide an incentive for travelers to avoid the congested paths and times, which improves the network performance.^
Satish V. Ukkusuri, Purdue University.