【Title】Distributionally Robust Traffic Equilibrium Models
【Speaker】Dr.Ugur Arikan, Singapore University of Technology and Design (SUTD)
【Host】Dr. Hai Jiang
【Time】13:30-14:30, March 8th (Thursday) , 2018
【Location】 Room N412, Shunde Building
【Abstract】Traffic equilibrium models are fundamental to the analysis of transportation systems. The stochastic user equilibrium (SUE) model which relaxes the perfect information assumption of the deterministic user equilibrium is one such model. We develop a new user equilibrium model that uses the marginal distribution model as the underlying route choice model. In this choice model, the marginal distributions of the path utilities are specified but the joint distribution is not. By focusing on the joint distribution that maximizes expected utility, we show that the proposed equilibrium exists and is unique under mild assumptions on the marginal distributions. We develop an equivalent convex optimization formulation. For specific choices of marginal distributions, the model recreates the optimization formulation of logit SUE and weibit SUE. Another class of SUE models is derived under the assumption of a Markovian choice behavior for the users. However, due to additional computational complexity of the dynamic choice model, the application of this model has been thus far mainly restricted to the multinomial logit model where the link error terms are assumed to be i.i.d Gumbel random variables. In practice, however the complete distribution of the random utilities is rarely known to a system planner. We propose a distributionally robust optimization perspective on the Markovian traffic equilibrium (MTE) model and analyze the properties of a corresponding choice model under the assumption that the marginal distributions of the link utilities are known but the joint distribution is unknown. By using a distributionally robust approach from the system planner's view, we propose a convex optimization formulation to compute the equilibrium traffic flows that generalizes the popular entropy formulation of the Markovian multinomial logit model. Importantly, our formulation is completely link based and relaxes the assumption of independence and identical distributions in the link utilities. Our numerical experiments indicate that the distributionally robust approach provides modeling flexibility and computational tractability for system planners interested in calculating traffic equilibrium flows. Proposed SUE/MTE models are flexible since they can capture perception variance scaling at the route/link level and allow for modeling different user preferences by allowing for skewed distributions and heavy tailed distributions. The models can also be generalized to incorporate bounded support distributions and discrete distributions which allows to distinguish between used and unused routes/links.
【Short Bio】Dr.Ugur Arikan is a postdoctoral researcher in the Singapore University of Technology and Design (SUTD). Prior to joining SUTD, he obtained his BS, MSc and PhD degrees in Industrial Engineering from the Middle East Technical University, Turkey. His main research interests include optimization, algorithms & heuristics and discrete choice models. His recent work focused on the area of transportation. In urban transportation, he works on the interplay of choice, robustness and optimization; and re-thinking the last-mile system with emerging modes. In air transportation, he works on integrated aircraft-crew-passenger scheduling; and on large network-based optimization models and heuristic approaches to provide real time recovery decisions, with a special emphasis on passenger convenience.
 
All interested are welcome!