Dusica Joksimovic

Optimal Toll Design Problem in Dynamic Traffic Networks with Joint Route and Departure Time Choice

Road pricing is one of the market-based traffic control measures that can influence travel behavior to alleviate congestion on roads. This paper addresses the effects of uniform (constant, fixed) and time-varying (step) tolls on the travel behavior of users on the road network. The problem of determining optimal prices in a dynamic traffic network is considered by applying second-best tolling scenarios imposing tolls only to a subset of links on the network and considering elastic demand. The optimal toll design problem is formulated as a bilevel optimization problem with the road authority (on the upper level) setting the tolls and the travelers (on the lower level) who respond by changing their travel decisions (route and departure time choice). To formulate the optimal toll design problem, the so-called mathematical program with equilibrium constraints (MPEC) formulation was used, considering the dynamic nature of traffic flows on the one hand and dynamic pricing on the other. Until now, the MPEC formu...

Dynamic road pricing for optimizing network performance with heterogeneous users

In transport networks, travelers individually make route and departure time choice decisions that may not be optimal for the whole network. By introducing (time-dependent) tolls the network performance may be optimized. In the paper, the effects of time-dependent tolls on the network performance are analyzed using a dynamic traffic model. The network design problem is formulated as a bi-level optimization problem in which the upper level describes the network performance with chosen toll levels while the lower level describes the dynamic network model including user-specific route and departure time choice and the dynamic network loading. In case studies on a simple hypothetical network it is shown that network improvements can be obtained by introducing tolls. It is also shown that finding a global solution to the network design problem is complex as it is non-linear and non-convex.

Optimization of the Operation of Infrastructures

The need for improvement of the operation of infrastructures, which can be represented as complex socio-technical system, has created a demand on investigating optimization methods applicable in this area. This paper briefly presents main classes of optimization models and stresses the importance of hierarchical optimization. The example of the dynamic road pricing aimed at improving the road capacity illustrates how a bi-level optimization problem can be formulated. The upper level describes the overall road performance for the chosen toll levels and the lower level present the user-specific objective function with route and departure time selection

Different Policy Objectives of the Road-Pricing Problem: A Game-theoretic Approach

Using game theory we investigate a new approach to formulate and solve optimal tolls with a focus on different policy objectives of the road authority. The aim is to gain more insight into determining optimal tolls as well as into the behavior of users after tolls have been imposed on the network. The problem of determining optimal tolls is stated and defined using utility maximization theory, including elastic demand on the travelersÂ’ side and different objectives for the road authority. Game theory notions are adopted regarding different games and players, rules and outcomes of the games played between travelers on the one hand and the road authority on the other. Different game concepts (Cournot, Stackelberg and monopoly game) are mathematically formulated and the relationship between players, their payoff functions and rules of the games are defined for very simplistic cases. The games are solved for different scenarios and different objectives for the road authority, using the Nash equilibrium concept. Using the Stackelberg game concept as being most realistic for road pricing, a few experiments are presented illustrating the optimal toll design problem subject to different pricing policies considering different objectives of the road authority. Results show different outcomes both in terms of optimal tolls as well as in payoffs for travelers. There exist multiple optimal solutions and objective function may have a non- continuous shape. The main contribution is the two-level separation between of the users from the road authority in terms of their objectives and influences.

Optimal Toll Design Problem: A Dynamic Network Modelling Approach

This chapter focuses on time-varying optimal toll designs. The authors consider uniform and time-variable tolls during the peak, taking route choice and departure time choice responses of travelers into account. The authors demonstrate that policy objectives can be optimized by imposing tolls, and that different policy objectives can be optimized by imposing tolls, and that different policy objectives lead to different optimal tolling schemes and toll levels. Therefore, this chapter illustrates that the optimal design of road pricing depends on the policy objectives.