Equilibrium models accounting for uncertainty and information provision in transportation networks
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Researchers in multiple areas have shown that characterizing and accounting for the uncertainty inherent in decision support models is critical for developing more efficient planning and operational strategies. This is particularly applicable for the transportation engineering domain as most strategic decisions involve a significant investment of money and resources across multiple stakeholders and has a considerable impact on the society. Moreover, most inputs to transportation models such as travel demand depend on a number of social, economic and political factors and cannot be predicted with certainty. Therefore, in recent times there has been an increasing emphasis being placed on identifying and quantifying this uncertainty and developing models which account for the same. This dissertation contributes to the growing body of literature in tackling uncertainty in transportation models by developing methodologies which address the uncertainty in input parameters in traffic assignment models. One of the primary sources of uncertainty in traffic assignment models is uncertainty in origin destination demand. This uncertainty can be classified into long term and short term demand uncertainty. Accounting for long term demand uncertainty is vital when traffic assignment models are used to make planning decisions like where to add capacity. This dissertation quantifies the impact of long term demand uncertainty by assigning multi-variate probability distributions to the demand. In order to arrive at accurate estimates of the expected future system performance, several statistical sampling techniques are then compared through extensive numerical testing to determine the most "efficient" sampling techniques for network assignment models. Two applications of assignment models, network design and network pricing are studied to illustrate the importance of considering long term demand uncertainty in transportation networks. Short term demand uncertainty such as the day-to-day variation in demand affect traffic assignment models when used to make operational decisions like tolling. This dissertation presents a novel new definition of equilibrium when the short term demand is assumed to follow a probability distribution. Various properties of the equilibrium such as existence, uniqueness and presence of a mathematical programming formulation are investigated. Apart from demand uncertainty, operating capacity in real world networks can also vary from day to day depending on various factors like weather conditions and incidents. With increasing deployment of Intelligent Transportation Systems, users get information about the impact of capacity or the state of the roads through various dissemination devices like dynamic message signs. This dissertation presents a new equilibrium formulation termed user equilibrium with recourse to model information provision and capacity uncertainty, where users learn the state or capacity of the link when they arrive at the upstream node of that link. Depending on the information received about the state of the upstream links, users make different route choice decisions. In this work, the capacity of the links in the network is assumed to follow a discrete probability distribution. A mathematical programming formulation of the user equilibrium with recourse model is presented along with solution algorithm. This model can be extended to analytically model network flows under information provision where the arcs have different cost functional form depending on the state of the arc. The corresponding system optimal with recourse model is also presented where the objective is minimize the total system cost. The network design problem where users are routed according to the user equilibrium with recourse principle is studied. The focus of this study is to show that planning decisions for networks users have access to information is significantly different from the no-information scenario.