Dynamic Optimal Toll Design Problem ? Travel Behavioral Analysis Including Departure Time Choice and Heterogeneous Users
Dusica Joksimovic, Technical University of Delft, NL
In this paper we consider a network design problem in which the aim is to analyze the travel behavior of heterogeneous road users. By introducing different tolling schemes the network performance may be optimized.
In this paper the dynamic optimal 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 behavior of travelers including user-specific route and departure time choice. Considering the optimal toll design problem, the aim of the road authority is to optimize system performance (e.g. to minimize the total travel time) by choosing the optimal tolls for a subset of links, within realistic constraints and subject to the dynamic traffic assignment. The aim of travelers is to maximize their own travel utility function.
We assume that travelers will decide which route and which departure time to take using utility maximization theory. After that tolls are imposed, the travelers will reconsider their route and departure time choice decisions. Not all travelers will behave on the same way. Depending on their characteristics (e.g. value of time) some travelers can afford to pay toll and travel without congestions while the others not.
Modeling of travel behavior in optimal toll design problem
Generalized travel cost function is modeled by a linear combination and extended to capture (not only route travel time) but also value of time of travelers, route toll costs, and penalties for scheduling delays. Value of time is the only class specific parameter in the generalized travel cost function. We focus on travelers with e.g. different purposes like business trips (high value of time) and leisure trips (low value of time). Based on experienced generalized travel costs, each traveler is assumed to simultaneously choose the route and departure time that he or she perceives to have the least travel costs (yielding a stochastic user equilibrium (SUE) assignment). The joint probability of choosing a specific route and departure time are given by multinomial logit (MNL) model. The relationship between the route flows and the travel times is given by the dynamic network loading component. The lower level of the optimal toll design problem (departure time and route choice component) is formulated using a variational inequality approach.
For the formulation of the whole optimal toll design problem (road pricing and behavioral part) a Mathematical Program with Equilibrium Constraints is used. Further, grid search and genetic algorithm (GA) as a more sophisticated optimization method are used to solve this rather complex problem and determine time-dependent tolls on a dynamic traffic network.
In case studies on a simple hypothetical network the travel behavior under different tolling schemes is analyzed. For that purpose first the case with zero tolls is introduced and compared with cases including tolls.
It is shown that the travelers shift towards non-congested and untolled route and time periods. Furthermore, it can be observed that there are many more travelers with high value of time on tolled route than travelers with a low value of time. This is to be expected, as travelers with a high value of time care less about toll costs and more about a short trip time.
For illustration, route costs and route flows for optimal toll levels when minimizing total travel time are presented on Figure 1.
Figure 1. Route costs and route flows
In this paper we analyze travel behavior of heterogeneous travelers due to tolls. Second-best scenarios are considered in this paper, assuming that only a subset of links can be tolled. We formulate the optimal toll design problem as a network design problem in which optimal time-varying tolls need to be determined, taking route and departure time changes of travelers as a response to the prices into account. The contributions of the paper can be listed as follows:
a) heterogeneous users are considered and analyzed;
b) not only route choice but also departure time choice is modeled;
c) dynamic instead of static traffic flows and road pricing strategies are considered;
The aim of the research is to investigate the feasibility of the dynamic model framework proposed in this paper and to investigate effects of tolls on the travel behavior of road users.
Joksimovic D, M.C.J Bliemer and P.H.L. Bovy (2005). Optimal toll design Problem in dynamic traffic networks- with joint route and departure time choice.
Association for European Transport