Modeling heterogeneous risk-taking behavior in route choice: A stochastic dominance approach

This paper proposes a unified approach to modeling heterogonous risk-taking behavior in route choice based on the theory of stochastic dominance (SD). Specifically, the first-, second-, and third-order stochastic dominance (FSD, SSD, TSD) are respectively linked to insatiability, risk-aversion and ruin-aversion within the framework of utility maximization. The paths that may be selected by travelers of different risk-taking preferences can be obtained from the corresponding SD-admissible paths, which can be generated using general dynamic programming. This paper also analyzes the relationship between the SD-based approach and other route choice models that consider risk-taking behavior. These route choice models employ a variety of reliability indexes, which often make the problem of finding optimal paths intractable. We show that the optimal paths with respect to these reliability indexes often belong to one of the three SD-admissible path sets. This finding offers not only an interpretation of risk-taking behavior consistent with the SD theory for these route choice models, but also a unified and computationally viable solution approach through SD-admissible path sets, which are usually small and can be generated without having to enumerate all paths. A generic label-correcting algorithm is proposed to generate FSD-, SSD-, and TSD-admissible paths, and numerical experiments are conducted to test the algorithm and to verify the analytical results.     

Sampling of alternatives for route choice modeling

This paper presents a new paradigm for choice set generation in the context of route choice model estimation. We assume that the choice sets contain all paths connecting each origin–destination pair. Although this is behaviorally questionable, we make this assumption in order to avoid bias in the econometric model. These sets are in general impossible to generate explicitly. Therefore, we propose an importance sampling approach to generate subsets of paths suitable for model estimation. Using only a subset of alternatives requires the path utilities to be corrected according to the sampling protocol in order to obtain unbiased parameter estimates. We derive such a sampling correction for the proposed algorithm.Estimating models based on samples of alternatives is straightforward for some types of models, in particular the multinomial logit (MNL) model. In order to apply MNL for route choice, the utilities should also be corrected to account for the correlation using, for instance, a path size (PS) formulation. We argue that the PS attribute should be computed based on the full choice set. Again, this is not feasible in general, and we propose a new version of the PS attribute derived from the sampling protocol, called Expanded PS.Numerical results based on synthetic data show that models including a sampling correction are remarkably better than the ones that do not. Moreover, the Expanded PS shows good results and outperforms models with the original PS formulation.     

Route choice of cyclists in Zurich

This paper presents the first route choice model for bicyclists estimated from a large sample of GPS observations and overcomes the limitations inherent in the generally employed stated preference approach. It employs an improved mode detection algorithm for GPS post-processing to determine trips made by bicycle, which are map matched to an enriched street network. The alternatives are generated as a random sample from an exhaustive, but constrained search. Accounting for the similarity between the alternatives with the path-size factor the MNL estimates show that the elasticity with regards to trip length is nearly four times larger than that with respect to the share of bike paths. The elasticity with respect to the product of length and maximum gradient of the route is small. No other variable describing the routes had an impact. The heterogeneity of the cyclists is captured through interaction terms formulated on their average behaviour.     

Bike route choice modeling using GPS data without choice sets of paths

Concerned by the nuisances of motorized travel on urban life, policy makers are faced with the challenge of making cycling a more attractive alternative for everyday transportation. Route choice models can help achieve this objective by gaining insights into the trade-offs cyclists make when choosing their routes and by allowing the effect of infrastructure improvements to be analyzed. We estimate a link-based bike route choice model from a sample of GPS observations in the city of Eugene on a network comprising over 40,000 links. The so-called recursive logit (RL) model (Fosgerau et al., 2013) does not require to sample any choice set of paths. We show the advantages of this approach in the context of prediction by focusing on two applications of the model: link flows and accessibility measures. Compared to the path-based approach which requires to generate choice sets, the RL model proves to make significant gains in computational time and to avoid paradoxical accessibility measure results discussed in previous works, e.g. Nassir et al. (2014).     

A model and algorithm for multicriteria route-mode choice

Using an idea proposed independently by Quandt and Schneider, the paper declares mode choice to be a special instance of route choice. It describes a (non-logit) model which includes in its route-choice mechanism the decision variables traditionally associated with mode choice. With the assumption that each traveller selects the route which minimizes his own personal linear choice function, it is clear that the routes with a nonzero chance of being picked are only those not dominated by any other path (e.g. are not both costlier and longer than any other path). The precise probability of a route being chosen is just the integral over the appropriate portion of the probability density of the coefficients of the choice function. The integration limits are implied by the amount of each disutility on each of the undominated routes. An algorithm is given which is quite efficient in finding these paths in a large and complex multimodal network.     

Modelling route choice behaviour in a tolled road network with a time surplus maximisation bi-objective user equilibrium model

In this paper, we propose a novel approach to model route choice behaviour in a tolled road network with a bi-objective approach, assuming that all users have two objectives: (1) minimise travel time; and (2) minimise toll cost. We assume further that users have different preferences in the sense that for any given path with a specific toll, there is a limit on the time that an individual would be willing to spend. Different users can have different preferences represented by this indifference curve between toll and time. Time surplus is defined as the maximum time minus the actual time. Given a set of paths, the one with the highest (or least negative) time surplus will be the preferred path for the individual. This will result in a bi-objective equilibrium solution satisfying the time surplus maximisation bi-objective user equilibrium (TSmaxBUE) condition. That is, for each O–D pair, all individuals are travelling on the path with the highest time surplus value among all the efficient paths between this O–D pair.We show that the TSmaxBUE condition is a proper generalisation of user equilibrium with generalised cost function, and that it is equivalent to bi-objective user equilibrium. We also present a multi-user class version of the TSmaxBUE condition and demonstrate our concepts with illustrative examples.     

On dynamics of traffic queues in a road network with route choice based on real time traffic information

Introducing real time traffic information into transportation network makes it necessary to consider development of queues and traffic flows as a dynamic process. This paper initiates a theoretical study of conditions under which this process is stable. A model is presented that describes within-one-day development of queues when drivers affected by real-time traffic information choose their paths en route. The model is reduced to a system of differential equations with delay. Equilibrium points of the system correspond to constant queue lengths. Stability of the system is investigated using characteristic values of the linearised minimal face flow. A traffic network example illustrating the method is provided.     

The relationship between non-motorized mode choice and the local physical environment

By estimating multinomial choice models, this paper examines the relationship between travel mode choice and attributes of the local physical environment such as topography, sidewalk availability, residential density, and the presence of walking and cycling paths. Data for student and staff commuters to the University of North Carolina in Chapel Hill are used to illustrate the relationship between mode choice and the objectively measured environmental attributes, while accounting for typical modal characteristics such as travel time, access time, and out-of-pocket cost. Results suggest that jointly the four attributes of the local physical environment make significant marginal contributions to explaining travel mode choice. In particular, the estimates reveal that local topography and sidewalk availability are significantly associated with the attractiveness of non-motorized modes. Point elasticities are provided and recommendations given regarding the importance of incorporating non-motorized modes into local transportation planning and in the study of how the built environment influences travel behavior.     

A two-stage stochastic optimization model for the transfer activity choice in metro networks

This research focuses on finding the best transfer schemes in metro networks. Using sample-based time-invariant link travel times to capture the uncertainty of a realistic network, a two-stage stochastic integer programming model with the minimized expected travel time and penalty value incurred by transfer activities is formulated. The first stage aims to find a sequence of potential transfer nodes (stations) that can compose a feasible path from origins to destinations in the transfer activity network, and the second stage provides the least time paths passing by the generated transfer stations in the first stage for evaluating the given transfer schemes and then outputs the best routing information. To solve our proposed model, an efficient hybrid algorithm, in which the label correcting algorithm is embedded into a branch and bound searching framework, is presented to find the optimal solutions of the considered problem. Finally, the numerical experiments are implemented in different scales of metro networks. The computational results demonstrate the effectiveness and performance of the proposed approaches even for the large-scale Beijing metro network.     

Fast-charging station choice behavior among battery electric vehicle users

This study explores how battery electric vehicle users choose where to fast-charge their vehicles from a set of charging stations, as well as the distance by which they are generally willing to detour for fast-charging. The focus is on fast-charging events during trips that include just one fast-charge between origin and destination in Kanagawa Prefecture, Japan. Mixed logit models with and without a threshold effect for detour distance are applied to panel data extracted from a two-year field trial on battery electric vehicle usage in Japan. Findings from the mixed logit model with threshold show that private users are generally willing to detour up to about 1750 m on working days and 750 m on non-working days, while the distance is 500 m for commercial users on both working and non-working days. Users in general prefer to charge at stations requiring a shorter detour and use chargers located at gas stations, and are significantly affected by the remaining charge. Commercial users prefer to charge at stations encountered earlier along their paths, while only private users traveling on working days show such preference and they turn to prefer the stations encountered later when choosing a station in peak hours. Only private users traveling on working days show a strong preference for free charging. Commercial users tend to pay for charging at a station within 500 m detour distance. The fast charging station choice behavior is heterogeneous among users. These findings provide a basis for early planning of a public fast charging infrastructure.     

Complementarity formulations for the cell transmission model based dynamic user equilibrium with departure time choice, elastic demand and user heterogeneity

In this paper we formulate the dynamic user equilibrium problem with an embedded cell transmission model on a network with a single OD pair, multiple parallel paths, multiple user classes with elastic demand. The formulation is based on ideas from complementarity theory. The travel time is estimated based on two methods which have different transportation applications: (1) maximum travel time and (2) average travel time. These travel time functions result in linear and non-linear complementarity formulations respectively. Solution existence and the properties of the formulations are rigorously analyzed. Extensive computational experiments are conducted to demonstrate the benefits of the proposed formulations on various test networks.     

Stochastic user equilibrium with equilibrated choice sets: Part I – Model formulations under alternative distributions and restrictions

The aim of this paper is to remove the known limitations of Deterministic and Stochastic User Equilibrium (DUE and SUE), namely that only routes with the minimum cost are used in DUE, and that all permitted routes are used in SUE regardless of their costs. We achieve this by combining the advantages of the two principles, namely the definition of unused routes in DUE and of mis-perception in SUE, such that the resulting choice sets of used routes are equilibrated. Two model families are formulated to address this issue: the first is a general version of SUE permitting bounded and discrete error distributions; the second is a Restricted SUE model with an additional constraint that must be satisfied for unused paths. The overall advantage of these model families consists in their ability to combine the unused routes with the use of random utility models for used routes, without the need to pre-specify the choice set. We present model specifications within these families, show illustrative examples, evaluate their relative merits, and identify key directions for further research.     

Where do cyclists ride? A route choice model developed with revealed preference GPS data

To better understand bicyclists’ preferences for facility types, GPS units were used to observe the behavior of 164 cyclists in Portland, Oregon, USA for several days each. Trip purpose and several other trip-level variables recorded by the cyclists, and the resulting trips were coded to a highly detailed bicycle network. The authors used the 1449 non-exercise, utilitarian trips to estimate a bicycle route choice model. The model used a choice set generation algorithm based on multiple permutations of path attributes and was formulated to account for overlapping route alternatives. The findings suggest that cyclists are sensitive to the effects of distance, turn frequency, slope, intersection control (e.g. presence or absence of traffic signals), and traffic volumes. In addition, cyclists appear to place relatively high value on off-street bike paths, enhanced neighborhood bikeways with traffic calming features (aka “bicycle boulevards”), and bridge facilities. Bike lanes more or less exactly offset the negative effects of adjacent traffic, but were no more or less attractive than a basic low traffic volume street. Finally, route preferences differ between commute and other utilitarian trips; cyclists were more sensitive to distance and less sensitive to other infrastructure characteristics for commute trips.     

Counting the different efficient paths for transportation networks and its applications

This paper deals with an interesting problem about how to efficiently compute the number of different efficient paths between an origin‐destination pair for a transportation network because these efficient paths are the possible paths used by drivers to some extent. Based on a novel triangle operation derived, it first presents a polynomial‐time combinatorial algorithm that can obtain the number of different simple paths between any two nodes for an acyclic network as well as the total travel cost of these paths. This paper proceeds to develop a combinatorial algorithm with polynomial‐time complexity for both counting the different efficient paths between an origin‐destination pair and calculating the total travel cost of these paths. As for applications, this paper shows that the preceding two algorithms can yield the lower and upper bounds for the number of different simple paths between an origin‐destination pair, while it has already be recognized that a polynomial‐time algorithm getting such a number does not exist for a general network. Furthermore, the latter algorithm can be applied for developing a heuristic method for the traffic counting location problem arising from the origin‐destination matrix estimation problems.     

Metropolis–Hastings sampling of paths

We consider the previously unsolved problem of sampling paths according to a given distribution from a general network. The problem is difficult because of the combinatorial number of alternatives, which prohibits a complete enumeration of all paths and hence also forbids to compute the normalizing constant of the sampling distribution. The problem is important because the ability to sample from a known distribution introduces mathematical rigor into many applications, including the estimation of choice models with sampling of alternatives that can be formalized as paths in a decision network (most obviously route choice), probabilistic map matching, dynamic traffic assignment, and route guidance.     

A day-to-day dynamical model for the evolution of path flows under disequilibrium of traffic networks with fixed demand

Transportation networks are often subjected to perturbed conditions leading to traffic disequilibrium. Under such conditions, the traffic evolution is typically modeled as a dynamical system that captures the aggregated effect of paths-shifts by drivers over time. This paper proposes a day-to-day (DTD) dynamical model that bridges two important gaps in the literature. First, existing DTD models generally consider current path flows and costs, but do not factor the sensitivity of path costs to flow. The proposed DTD model simultaneously captures all three factors in modeling the flow shift by drivers. As a driver can potentially perceive the sensitivity of path costs with the congestion level based on past experience, incorporating this factor can enhance real-world consistency. In addition, it smoothens the time trajectory of path flows, a desirable property for practice where the iterative solution procedure is typically terminated at an arbitrary point due to computational time constraints. Second, the study provides a criterion to classify paths for an origin–destination pair into two subsets under traffic disequilibrium: expensive paths and attractive paths. This facilitates flow shifts from the set of expensive paths to the set of attractive paths, enabling a higher degree of freedom in modeling flow shift compared to that of shifting flows only to the shortest path, which is behaviorally restrictive. In addition, consistent with the real-world driver behavior, it also helps to preclude flow shifts among expensive paths. Improved behavioral consistency can lead to more meaningful path/link time-dependent flow profiles for developing effective dynamic traffic management strategies for practice. The proposed DTD model is formulated as the dynamical system by drawing insights from micro-economic theory. The stability of the model and existence of its stationary point are theoretically proven. Results from computational experiments validate its modeling properties and illustrate its benefits relative to existing DTD dynamical models.     

Identifying a behaviourally relevant choice set from stated choice data

Stated choice experiments are designed optimally in a statistical sense but not necessarily in a behavioural choice making sense. Statistical designs, and consequently model estimation, assume that the set of alternatives offered in the experiment are processed by respondents with a specific processing strategy. Much has been studied about attribute processing using discrete choice methods in travel choice studies, but this paper focuses more broadly on processing of alternatives in the choice set offered in the experiment. This paper is motivated by the primary idea that the distribution of predicted choice probabilities associated with a set of alternatives defining a given choice set might provide strong evidence on the strategies that agents appear to use when choosing a preferred alternative. In an empirical setting of a choice set of size three, four model specifications are considered including a model for the selection of the best alternative in the full choice set and three variants of a best–worst regime. Using state choice data on road pricing reform, the empirical analysis examines which model specification delivers the most accurate prediction of the chosen alternative. The results suggest which alternatives really matter in choice making and hence the alternatives that might be included in a choice set for model specification.     

An improved Dial's algorithm for logit-based traffic assignment within a directed acyclic network

Abstract

Dial's algorithm is one of the most effective and popular procedures for a logit-type stochastic traffic assignment, as it does not require path enumeration over a network. However, a fundamental problem associated with the algorithm is its simple definition of ‘efficient paths’, which sometimes produces unrealistic flow patterns. In this paper, an improved algorithm based on the route extension coefficient is proposed in order to circumvent this problem, in which ‘efficient paths’ simultaneously consider link travel cost and minimum travel cost. Path enumeration is still not required and a similar computing efficiency with the original algorithm is guaranteed. A limitation of the algorithm is that it can only be applied to a directed acyclic network because a topological sorting algorithm is used to decide the order of the sequential calculation. A numerical example based on the Beijing subway network illustrates the effectiveness of the proposed algorithm. It is found that it is able to exclude most unrealistic paths, but include all reasonable paths when compared with path enumeration and the original Dial's algorithm.     

Algorithms to find shortest and alternative paths in free flow and congested traffic regimes

Location-based systems can be very helpful to mobile users if they are able to suggest shortest paths to destination taking into account the actual traffic conditions. This would allow to inform the drivers not only about the current shortest paths to destination but also about alternative, timely computed paths to avoid being trapped in the traffic jams signaled by cyber-physical-social systems. To this aim, the paper proposes a set of algorithms that solve very fast the All Pair Shortest Paths problem in both the free flow and congested traffic regimes, for road networks of medium-large size, thus enabling location-based systems to deal with emergencies and critical traffic conditions in city and metropolitan areas, whose transport networks typically range from some hundreds to many thousands of nodes, respectively. The paths to avoid being trapped in the traffic jams are computed by using a simulation of the shockwave propagation, instead of historical data. A parallel version of the algorithms is also proposed to solve the All Pair Shortest Paths problem for metropolitan areas with very large road networks. A time performance analysis of the proposed algorithms for transport networks of various size is carried out.     

Multidimensional choice model transferability

Transferability studies have focused on the component models of the conventional four-step urban travel forecasting model system. This study extends previous analyses by examining the transferability of models describing multidimensional travel and related choices. In particular, we examine the hypothesis that joint and sequential choice models are equally transferable against the alternative hypotheses that either of the model types is more transferable. Measures of goodness of fit and transfer effectiveness are formulated for sequential choice models to provide a consistent comparison between the joint and sequential models. An empirical analysis is undertaken in the context of joint (multinomial logit) and sequential (nested logit) models of automobile ownership and mode choice to work. This study finds little difference between the transferability of these joint and sequential models. However, this conclusion appears to be dependent on the similarity of the estimation results for the joint and sequential models in this case. These results suggest a need for additional testing in other empirical contexts to identify the relative transferability of joint versus sequential models when the estimation results are distinct.