Valuation of uncertainty in travel time and arrival time - some findings from a choice experiment

We are developing a dynamic modeling framework in which we can evaluate the effects of different road pricing measures on individual choice behavior as well as on a network level. Important parts of this framework are different choice models which forecast the route, departure time and mode choice behavior of travelers under road pricing in the Netherlands. In this paper we discuss the setup of the experiment in detail and present our findings about dealing with uncertainty, travel time and schedule delays in the utility functions. To develop the desired choice models a stated choice experiment was conducted. In this experiment respondents were presented with four alternatives, which can be described as follows: Alternative A: paying for preferred travel conditions. Alternative B: adjust arrival time and pay less. Alternative C: adjust route and pay less. Alternative D: adjust mode to avoid paying charge. The four alternatives differ mainly in price, travel time, time of departure/arrival and mode and are based on the respondents’ current morning commute characteristics. The travel time in the experiment is based on the reported (by the respondent) free-flow travel time for the home-to-work trip, and the reported trip length. We calculate the level of travel time, by setting a certain part of the trip length to be in free-flow conditions and calculate a free-flow and congested part of travel time. Adding the free-flow travel time and the congested travel time makes the total minimum travel time for the trip. Minimum travel time, because to this travel time we add an uncertainty margin, creating the maximum travel time. The level of uncertainty we introduced between minimum and maximum travel time was based on the difference between the reported average and free-flow travel time. In simpler words then explained here, we told respondents that the actual travel time for this trip is unknown, but that between the minimum and maximum each travel time has an equal change of occurring. As a consequence of introducing uncertainty in travel time, the arrival time also receives the same margin. Using the data from the experiment we estimated choice models following the schedule delay framework from Vickrey (1969) and Small (1987), assigning penalties to shifts from the preferred time of departure/arrival to earlier or later times. In the models we used the minimum travel time and the expected travel time (average of minimum and maximum). Using the expected travel time incorporates already some of the uncertainty (half) in the attribute travel time, making the uncertainty attribute in the utility function not significant. The parameters values and values-of-time for using the minimum or expected travel time do not differ. Initially, we looked at schedule delays only from an arrival time perspective. Here we also distinguished between schedule delays based on the minimum arrival time and the expected arrival time (average of minimum and maximum). Again, when using expected schedule delays the uncertainty is included in the schedule delays and a separate uncertainty attribute in the utility function is not significant. There is another issue involved when looking at the preferred arrival time of the respondents; there are three cases to take into account: 1.If the minimum and maximum arrival times are both earlier than the preferred arrival time we are certain about a schedule delay early situation (based on minimum or expected schedule delays). 2.If the minimum and maximum arrival times are both later than the preferred arrival time we are certain about a schedule delay late situation (based on minimum or expected schedule delays). 3.The scheduling situation is undetermined when the preferred arrival time is between the minimum and maximum arrival time. In this case we use an expected schedule delay assuming a uniform distribution of arrival times between the minimum and maximum arrival time. Parameter values for both situations are very different and results from the minimum arrival time approach are more in line with expectations. There is a choice to take into account uncertainty in the utility function in either the expected travel time, expected schedule delays or as a separate attribute. In the paper we discuss the effects of different approaches. We extended our models to also include schedule delays based on preferred departure time. In the departure time scheduling components uncertainty is not included. Results show that the depart schedule delay late is significant and substantial, together with significant arrival schedule early and late. Further extension of the model includes taking into account the amount of flexibility in departure and arrival times for each respondent. The results will be included in this paper.

Using firm demographic microsimulation to evaluate land use and transport scenario evaluation - model calibration

Existing integrated land use transport interaction models simulate the level of employment in (aggregated) zones and lack the individual firm as a decision making unit. This research tries to improve the behavioural foundation of these models by applying a firm demographic modelling approach that first of all accounts for the individual firm as a decision making unit and secondly represents the urban system with high spatial detail. A firm demographic approach models transitions in the state of individual firms by simulating transitions and events such as the relocation decision, growth or shrinkage of firms or the death of a firm. Important advantage of such a decomposed approach is that it offers the opportunity to account for accessibility in each event in the desired way. The firm demographic model is linked to an urban transport model in order to obtain a dynamic simulation of mobility (and accessibility) developments. The paper describes the firm demographic model specifications as well as the interaction of the model with the urban transport model. The integrated simulation model can be used to analyse the effects of different spatial and transport planning scenarios on the location of economic activities and mobility.

Different Policy Objectives of the Road Pricing Problem – a Game Theory 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 travelers’ 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.

Multi-objective road pricing: a cooperative and competitive bilevel optimization approach

Costs associated with traffic externalities such as congestion, air pollution, noise, safety, etcetera are becoming unbearable. The Braess paradox shows that combating congestion by adding infrastructure may not improve traffic conditions, and geographical and/or financial constraints may not allow infrastructure expansion. Road pricing presents an alternative to combat traffic externalities. The traditional way of road pricing, namely congestion charging, may create negative benefits for society. In this effect, we develop a flexible pricing scheme internalizing costs arising from all externalities. Using a game theoretical approach, we extend the single authority road pricing scheme to a pricing scheme with multiple authorities/regions (with likely contradicting objectives)

Valuation of uncertainty in travel time and arrival time - some findings from a choice experiment

We are developing a dynamic modeling framework in which we can evaluate the effects of different road pricing measures on individual choice behavior as well as on a network level. Important parts of this framework are different choice models which forecast the route, departure time and mode choice behavior of travelers under road pricing in the Netherlands. In this paper we discuss the setup of the experiment in detail and present our findings about dealing with uncertainty, travel time and schedule delays in the utility functions. To develop the desired choice models a stated choice experiment was conducted. In this experiment respondents were presented with four alternatives, which can be described as follows: Alternative A: paying for preferred travel conditions. Alternative B: adjust arrival time and pay less. Alternative C: adjust route and pay less. Alternative D: adjust mode to avoid paying charge. The four alternatives differ mainly in price, travel time, time of departure/arrival and mode and are based on the respondents' current morning commute characteristics. The travel time in the experiment is based on the reported (by the respondent) free-flow travel time for the home-to-work trip, and the reported trip length. We calculate the level of travel time, by setting a certain part of the trip length to be in free-flow conditions and calculate a free-flow and congested part of travel time. Adding the free-flow travel time and the congested travel time makes the total minimum travel time for the trip. Minimum travel time, because to this travel time we add an uncertainty margin, creating the maximum travel time. The level of uncertainty we introduced between minimum and maximum travel time was based on the difference between the reported average and free-flow travel time. In simpler words then explained here, we told respondents that the actual travel time for this trip is unknown, but that between the minimum and maximum each travel time has an equal change of occurring. As a consequence of introducing uncertainty in travel time, the arrival time also receives the same margin. Using the data from the experiment we estimated choice models following the schedule delay framework from Vickrey (1969) and Small (1987), assigning penalties to shifts from the preferred time of departure/arrival to earlier or later times. In the models we used the minimum travel time and the expected travel time (average of minimum and maximum). Using the expected travel time incorporates already some of the uncertainty (half) in the attribute travel time, making the uncertainty attribute in the utility function not significant. The parameters values and values-of-time for using the minimum or expected travel time do not differ. Initially, we looked at schedule delays only from an arrival time perspective. Here we also distinguished between schedule delays based on the minimum arrival time and the expected arrival time (average of minimum and maximum). Again, when using expected schedule delays the uncertainty is included in the schedule delays and a separate uncertainty attribute in the utility function is not significant. There is another issue involved when looking at the preferred arrival time of the respondents; there are three cases to take into account: 1.If the minimum and maximum arrival times are both earlier than the preferred arrival time we are certain about a schedule delay early situation (based on minimum or expected schedule delays). 2.If the minimum and maximum arrival times are both later than the preferred arrival time we are certain about a schedule delay late situation (based on minimum or expected schedule delays). 3.The scheduling situation is undetermined when the preferred arrival time is between the minimum and maximum arrival time. In this case we use an expected schedule delay assuming a uniform distribution of arrival times between the minimum and maximum arrival time. Parameter values for both situations are very different and results from the minimum arrival time approach are more in line with expectations. There is a choice to take into account uncertainty in the utility function in either the expected travel time, expected schedule delays or as a separate attribute. In the paper we discuss the effects of different approaches. We extended our models to also include schedule delays based on preferred departure time. In the departure time scheduling components uncertainty is not included. Results show that the depart schedule delay late is significant and substantial, together with significant arrival schedule early and late. Further extension of the model includes taking into account the amount of flexibility in departure and arrival times for each respondent. The results will be included in this paper

Using firm demographic microsimulation to evaluate land use and transport scenario evaluation - model calibration

Existing integrated land use transport interaction models simulate the level of employment in (aggregated) zones and lack the individual firm as a decision making unit. This research tries to improve the behavioural foundation of these models by applying a firm demographic modelling approach that first of all accounts for the individual firm as a decision making unit and secondly represents the urban system with high spatial detail. A firm demographic approach models transitions in the state of individual firms by simulating transitions and events such as the relocation decision, growth or shrinkage of firms or the death of a firm. Important advantage of such a decomposed approach is that it offers the opportunity to account for accessibility in each event in the desired way. The firm demographic model is linked to an urban transport model in order to obtain a dynamic simulation of mobility (and accessibility) developments. The paper describes the firm demographic model specifications as well as the interaction of the model with the urban transport model. The integrated simulation model can be used to analyse the effects of different spatial and transport planning scenarios on the location of economic activities and mobility

The Design of Stated Choice Experiments: The State of Practice and Future Challenges

Since the work of Louviere and Woodworth (1983) and Louviere and Hensher (1983), stated choice (SC) methods have become the dominant data paradigm in the study of behavioural responses of individuals and households as well as other organizations, in fields as diverse as marketing, transport and environmental and health economics, to name but a few. In SC experiments, it is usual for sampled respondents to be asked to choose from amongst a number of labelled or unlabelled alternatives defined on a number of attribute dimensions, each in turn described by pre-specified levels drawn from some underlying experimental design. The choice task is then repeated a number of times, up to the total number of choice sets being offered over the experiment. Several experimental design strategies are available to the practitioner, however, within the transport literature, it appears that the most common form of experimental design used are orthogonal fractional factorial designs. In this paper we review the properties of such designs, and demonstrate that these properties are unlikely to be retained through to the estimation process. We also discuss an alternative design construction strategy, used to construct statistically optimal designs

Continuous-time general link transmission model with simplified fanning, Part II: Event-based algorithm for networks

In this paper a novel solution algorithm is proposed for solving general first order dynamic network loading (DNL) problems in general transport networks. This solution algorithm supports any smooth non-linear two regime concave fundamental diagram and adopts a simplified fanning scheme. It is termed eGLTM (event-based General Link Transmission Model) and is based on a continuous-time formulation of the kinematic wave model that adapts shockwave theory to simplify expansion fans. As the name suggests eGLTM is a generalisation of eLTM, which is a special case that solves the simplified first order model assuming a triangular fundamental diagram. We analyse the impact of modelling delay in the hypocritical branch of the fundamental diagram to assess the differences between the two models. In addition, we propose an additional stream of mixture events to propagate multi-commodity flow in event based macroscopic models, which makes both eLTM and eGLTM suitable for dynamic traffic assignment (DTA) applications. The proposed solution scheme can yield exact solutions as well as approximate solutions at a significantly lesser cost. The efficiency of the model is demonstrated in a number of case studies. Furthermore, different settings for our simplified fanning scheme are investigated as well as an extensive analysis on the effect of including route choice on the algorithms computational cost. Finally, a large scale case study is conducted to investigate the suitability of the model in a practical context and assess its efficiency compared to the simplified first order model