|Ph.D Student||Gofer Eylam|
|Subject||Inducing Control to Network Congestion Games|
|Department||Department of Civil and Environmental Engineering||Supervisors||Professor David Mahalel|
|Mr. Joseph Prashker (Deceased)|
|Full Thesis text|
Two fundamental problems rise in the management of large scale transportation networks. The first is how to predict, to some extent, the flow patterns in the network, given its properties. The second problem is the management problem of such a network, in order to optimize its performances. Solutions for the first problem are traditionally formulated to be consistent with Wardrop's 1st principle, the main assumption of which is that all travelers have perfect information. However, this assumption fails to describe users' variability that exists in real-life networks.
In our study, we propose the mixed path-choices approach to overcome the limitations of the traditional Wardrop equilibrium model. This probabilistic approach stems from both the mixed-strategy approach of classic game theory and contemporary approaches of algorithmic game theory. Similarly to Wardrop’s approach, it is expected that the system under mixed path-choices assumptions, will converge to a (Nash) equilibrium operating point - to a mixed user equilibrium (MSUE) operating point.
The existence of the MSUE and its mathematical properties are analyzed on the first part of the dissertation. Our discussion on the MSUE in this part is based on the results of studies in the field of game theory, and specifically on studies that focus on congestion games. In the second part of the dissertation we discuss one of the most accepted methods of traffic control - marginal cost pricing, and we analyze its applicability under the assumptions of MSUE. From the analysis we were able to formulate the relationship between the MSUE problem and the mixed path-choices global optimum problem. This led us to the formulation of the MSUE as a convex minimization problem in a similar fashion as the Beckmann transformation. Using mixed path-choices enables us to treat the network flows and travel times as random variables. In the third part of the dissertation we discuss the distribution of the paths' and links' flows and the distribution of their travel times. In the last part of the dissertation we discuss traffic control policies that are based on signalized intersections under the framework of MSUE. In this part we formulate the optimal traffic control under mixed path-choices framework problem as a bi-level optimization problem, and we analyze the conditions for a solution existence.