Accuracy of the Gothenburg congestion charges forecast

This paper explores the accuracy of the transport model forecast of the Gothenburg congestion charges, implemented in 2013. The design of the charging system implies that the path disutility cannot be computed as a sum of link attributes. The route choice model is therefore implemented as a hierarchical algorithm, applying a continuous value of travel time (VTT) distribution. The VTT distribution was estimated from stated choice (SC) data. However, based on experience of impact forecasting with a similar model and of impact outcome of congestion charges in Stockholm, the estimated VTT distribution had to be stretched to the right. We find that the forecast traffic reductions across the cordon and travel time gains were close to those observed in the peak. However, the reduction in traffic across the cordon was underpredicted off-peak. The necessity to make the adjustment indicates that the VTT inferred from SC data does not reveal the travellers’ preferences, or that there are factors determining route choice other than those included in the model: travel distance, travel time and congestion charge.     

Predicting travel time reliability using mobile phone GPS data

Estimates of road speeds have become commonplace and central to route planning, but few systems in production provide information about the reliability of the prediction. Probabilistic forecasts of travel time capture reliability and can be used for risk-averse routing, for reporting travel time reliability to a user, or as a component of fleet vehicle decision-support systems. Many of these uses (such as those for mapping services like Bing or Google Maps) require predictions for routes in the road network, at arbitrary times; the highest-volume source of data for this purpose is GPS data from mobile phones. We introduce a method (TRIP) to predict the probability distribution of travel time on an arbitrary route in a road network at an arbitrary time, using GPS data from mobile phones or other probe vehicles. TRIP captures weekly cycles in congestion levels, gives informed predictions for parts of the road network with little data, and is computationally efficient, even for very large road networks and datasets. We apply TRIP to predict travel time on the road network of the Seattle metropolitan region, based on large volumes of GPS data from Windows phones. TRIP provides improved interval predictions (forecast ranges for travel time) relative to Microsoft’s engine for travel time prediction as used in Bing Maps. It also provides deterministic predictions that are as accurate as Bing Maps predictions, despite using fewer explanatory variables, and differing from the observed travel times by only 10.1% on average over 35,190 test trips. To our knowledge TRIP is the first method to provide accurate predictions of travel time reliability for complete, large-scale road networks.     

Modeling stochastic perception error in the mean-excess traffic equilibrium model

In this paper, we extend the α-reliable mean-excess traffic equilibrium (METE) model of Chen and Zhou (Transportation Research Part B 44(4), 2010, 493-513) by explicitly modeling the stochastic perception errors within the travelers’ route choice decision processes. In the METE model, each traveler not only considers a travel time budget for ensuring on-time arrival at a confidence level α, but also accounts for the impact of encountering worse travel times in the (1 − α) quantile of the distribution tail. Furthermore, due to the imperfect knowledge of the travel time variability particularly in congested networks without advanced traveler information systems, the travelers’ route choice decisions are based on the perceived travel time distribution rather than the actual travel time distribution. In order to compute the perceived mean-excess travel time, an approximation method based on moment analysis is developed. It involves using the conditional moment generation function to derive the perceived link travel time, the Cornish-Fisher Asymptotic Expansion to estimate the perceived travel time budget, and the Acerbi and Tasche Approximation to estimate the perceived mean-excess travel time. The proposed stochastic mean-excess traffic equilibrium (SMETE) model is formulated as a variational inequality (VI) problem, and solved by a route-based solution algorithm with the use of the modified alternating direction method. Numerical examples are also provided to illustrate the application of the proposed SMETE model and solution method.     

Effect of speed limits in degradable transport networks

This paper studies how link-specific speed limits influence the performance of degradable transport networks, in which the capacity of each link is a degradable random variable. The distribution and cumulative distribution of link travel time have been presented with the effect of speed limits taken into account. The mean and variance of link and route travel time are formulated. Three link states have been classified, and their physical meanings have been discussed. The relationship between critical capacity, travel time and speed limit has been elaborated. We have proposed a Speed Limit- and Reliability-based User Equilibrium (SLRUE), adopting travel time budget as the principle of travelers’ route choice. A heuristic method employing the method of successive averages is developed to solve the SLRUE in degradable networks. Through numerical studies, we find that for some networks both the mean and standard deviation of the total travel time could be reduced simultaneously by imposing some speed limits. The speed limit design problem has been studied, and it is found that imposing speed limits cannot always reduce the total travel time budget of a network.     

Probe data-driven travel time forecasting for urban expressways by matching similar spatiotemporal traffic patterns

Travel time is an effective measure of roadway traffic conditions. The provision of accurate travel time information enables travelers to make smart decisions about departure time, route choice and congestion avoidance. Based on a vast amount of probe vehicle data, this study proposes a simple but efficient pattern-matching method for travel time forecasting. Unlike previous approaches that directly employ travel time as the input variable, the proposed approach resorts to matching large-scale spatiotemporal traffic patterns for multi-step travel time forecasting. Specifically, the Gray-Level Co-occurrence Matrix (GLCM) is first employed to extract spatiotemporal traffic features. The Normalized Squared Differences (NSD) between the GLCMs of current and historical datasets serve as a basis for distance measurements of similar traffic patterns. Then, a screening process with a time constraint window is implemented for the selection of the best-matched candidates. Finally, future travel times are forecasted as a negative exponential weighted combination of each candidate’s experienced travel time for a given departure. The proposed approach is tested on Ring 2, which is a 32km urban expressway in Beijing, China. The intermediate procedures of the methodology are visualized by providing an in-depth quantitative analysis on the speed pattern matching and examples of matched speed contour plots. The prediction results confirm the desirable performance of the proposed approach and its robustness and effectiveness in various traffic conditions.     

On the cost of misperceived travel time variability

Because individuals may misperceive travel time distributions, using the implied reduced form of the scheduling model might fall short of capturing all costs of travel time variability. We reformulate a general scheduling model employing rank-dependent utility theory and derive two special cases as econometric specifications to study these uncaptured costs. It is found that reduced-form expected cost functions still have a mean–variance form when misperception is considered, but the value of travel time variability is higher. We estimate these two models with stated-preference data and calculate the empirical cost of misperception. We find that: (i) travelers are mostly pessimistic and thus tend to choose departure times too early to achieve a minimum cost, (ii) scheduling preferences elicited using a stated-choice method can be relatively biased if probability weighting is not considered, and (iii) the extra cost of misperceiving the travel time distribution might be nontrivial when time is valued differently over the time of day and is substantial for some people.     

Understanding Travel Time Expenditures Around the World: Exploring the Notion of a Travel Time Frontier

Travel behavior researchers have been intrigued by the amount of time that people allocate to travel in a day, i.e., the daily travel time expenditure, commonly referred to as a “travel time budget”. Explorations into the notion of a travel time budget have once again resurfaced in the context of activity-based and time use research in travel behavior modeling. This paper revisits the issue by developing the notion of a travel time frontier (TTF) that is distinct from the actual travel time expenditure or budget of an individual. The TTF is defined in this paper as an intrinsic maximum amount of time that people are willing to allocate for travel. It is treated as an unobserved frontier that influences the actual travel time expenditure measured in travel surveys. Using travel survey datasets from around the world (i.e., US, Switzerland and India), this paper sheds new light on daily travel time expenditures by modeling the unobserved TTF and comparing these frontiers across international contexts. The stochastic frontier modeling methodology is employed to model the unobserved TTF as a production frontier. Separate models are estimated for commuter and non-commuter samples to recognize the differing constraints between these market segments. Comparisons across the international contexts show considerable differences in average unobserved TTF values.     

A travel time reliability model of urban expressways with varying levels of service

Urban expressways usually experience several levels of service (LOS) because of the stop-and-go traffic flow caused by congestion. Moreover, multiple shock waves generate at different LOS interfaces. The dynamic of shock waves strongly influences the travel time reliability (TTR) of urban expressways. This study proposes a path TTR model that considers the dynamic of shock waves by using probability-based method to characterize the TTR of urban expressways with shock waves. Two model parameters are estimated, namely distribution of travel time (TT) per unit distance and travel distances in different LOS segments. Generalized extreme value distribution and generalized Pareto distribution are derived as distributions of TT per unit distance for six different LOS. Distribution parameters are estimated by using historical floating car data. Travel distances in different LOS segments are calculated based on shock wave theory. The range of TT along the path, which can help drivers arrange their trips, can be obtained from the TTR model. Finally, comparison is made among the proposed TTR model, generalized Pareto contrast model, which does not consider different LOS or existence of shock waves, and normal contrast model, which assumes TT per unit distance as normal distribution without considering shock wave. Results show that the proposed model achieves higher prediction accuracy and reduces the prediction range of TT. The conclusions can be further extended to TT prediction and assessment of measures to improve reliability of TT in a network.     

Identifying optimal data aggregation interval sizes for link and corridor travel time estimation and forecasting

With the recent increase in the deployment of ITS technologies in urban areas throughout the world, traffic management centers have the ability to obtain and archive large amounts of data on the traffic system. These data can be used to estimate current conditions and predict future conditions on the roadway network. A general solution methodology for identifying the optimal aggregation interval sizes for four scenarios is proposed in this article: (1) link travel time estimation, (2) corridor/route travel time estimation, (3) link travel time forecasting, and (4) corridor/route travel time forecasting. The methodology explicitly considers traffic dynamics and frequency of observations. A formulation based on mean square error (MSE) is developed for each of the scenarios and interpreted from a traffic flow perspective. The methodology for estimating the optimal aggregation size is based on (1) the tradeoff between the estimated mean square error of prediction and the variance of the predictor, (2) the differences between estimation and forecasting, and (3) the direct consideration of the correlation between link travel time for corridor/route estimation and forecasting. The proposed methods are demonstrated using travel time data from Houston, Texas, that were collected as part of the automatic vehicle identification (AVI) system of the Houston Transtar system. It was found that the optimal aggregation size is a function of the application and traffic condition.

On including travel time reliability of road traffic in appraisal

In many countries, decision-making on proposals for national or regional infrastructure projects in passenger and freight transport includes carrying out a cost–benefit analysis for these projects. Reductions in travel times are usually a key benefit. However, if a project also reduces the variability of travel time, travellers, freight operators and shippers will enjoy additional benefits, the ‘reliability benefits’. Until now, these benefits are usually not included in the cost–benefit analysis. To include reliability of travel or transport time in the cost–benefit analysis of infrastructure projects not only monetary values of reliability, but also reliability forecasting models are needed. As a result of an extensive feasibility study carried out for the German Federal Ministry of Transport, Building and Urban Development this paper aims to provide a literature overview and outcomes of an expert panel on how best to calculate and monetise reliability benefits, synthesised into recommendations for implementing travel time reliability into existing transport models in the short, medium, and long term. The paper focuses on road transport, which has also been the topic for most of the available literature on modelling and valuing transport time reliability.     

A copula-based approach for estimating the travel time reliability of urban arterial

Estimating the travel time reliability (TTR) of urban arterial is critical for real-time and reliable route guidance and provides theoretical bases and technical support for sophisticated traffic management and control. The state-of-art procedures for arterial TTR estimation usually assume that path travel time follows a certain distribution, with less consideration about segment correlations. However, the conventional approach is usually unrealistic because an important feature of urban arterial is the dependent structure of travel times on continuous segments. In this study, a copula-based approach that incorporates the stochastic characteristics of segments travel time is proposed to model arterial travel time distribution (TTD), which serves as a basis for TTR quantification. First, segments correlation is empirically analyzed and different types of copula models are examined. Then, fitting marginal distributions for segment TTD is conducted by parametric and non-parametric regression analysis, respectively. Based on the estimated parameters of the models, the best-fitting copula is determined in terms of the goodness-of-fit tests. Last, the model is examined at two study sites with AVI data and NGSIM trajectory data, respectively. The results of path TTD estimation demonstrate the advantage of the proposed copula-based approach, compared with the convolution model without capturing segments correlation and the empirical distribution fitting methods. Furthermore, when considering the segments correlation effect, it was found that the estimated path TTR is more accurate than that by the convolution model.     

A finite mixture model of vehicle-to-vehicle and day-to-day variability of traffic network travel times

This study proposes an approach to modeling the effects of daily roadway conditions on travel time variability using a finite mixture model based on the Gamma–Gamma (GG) distribution. The GG distribution is a compound distribution derived from the product of two Gamma random variates, which represent vehicle-to-vehicle and day-to-day variability, respectively. It provides a systematic way of investigating different variability dimensions reflected in travel time data. To identify the underlying distribution of each type of variability, this study first decomposes a mixture of Gamma–Gamma models into two separate Gamma mixture modeling problems and estimates the respective parameters using the Expectation–Maximization (EM) algorithm. The proposed methodology is demonstrated using simulated vehicle trajectories produced under daily scenarios constructed from historical weather and accident data. The parameter estimation results suggest that day-to-day variability exhibits clear heterogeneity under different weather conditions: clear versus rainy or snowy days, whereas the same weather conditions have little impact on vehicle-to-vehicle variability. Next, a two-component Gamma–Gamma mixture model is specified. The results of the distribution fitting show that the mixture model provides better fits to travel delay observations than the standard (one-component) Gamma–Gamma model. The proposed method, the application of the compound Gamma distribution combined with a mixture modeling approach, provides a powerful and flexible tool to capture not only different types of variability—vehicle-to-vehicle and day-to-day variability—but also the unobserved heterogeneity within these variability types, thereby allowing the modeling of the underlying distributions of individual travel delays across different days with varying roadway disruption levels in a more effective and systematic way.     

Making time count: Traveler activity engagement on urban transit

In practice, travel time is assigned a cost and treated as a disutility to be minimized. There is a growing body of research supporting the hypothesis that travel time has some value of its own, and the proliferation of information and communication technology (ICT) may be contributing to that value. Travelers’ attitudes are confounded with their mode choice, and as telecommunications mediate travel behavior, analysts must recognize the interaction between time use and customer satisfaction for appropriate travel demand management. To that end, this paper presents results from jointly estimated models of travelers’ latent satisfaction and on-board activity engagement using Chicago transit rider data gathered in April 2010. The simple questionnaire and small sample corroborate the findings of past research indicating travel attitudes and activity engagement have potential to influence travelers’ value of time, and many transit riders consider transit a better use of time and/or money than driving. The findings affirm the need for a more holistic understanding of value of time for travel demand management and infrastructure valuation. As time use has an influence on users’ valuation of the transit mode, offering opportunities to conduct certain leisure activities could improve the perceived value of travel time.     

Multi-step prediction of experienced travel times using agent-based modeling

This paper develops an agent-based modeling approach to predict multi-step ahead experienced travel times using real-time and historical spatiotemporal traffic data. At the microscopic level, each agent represents an expert in a decision-making system. Each expert predicts the travel time for each time interval according to experiences from a historical dataset. A set of agent interactions is developed to preserve agents that correspond to traffic patterns similar to the real-time measurements and replace invalid agents or agents associated with negligible weights with new agents. Consequently, the aggregation of each agent’s recommendation (predicted travel time with associated weight) provides a macroscopic level of output, namely the predicted travel time distribution. Probe vehicle data from a 95-mile freeway stretch along I-64 and I-264 are used to test different predictors. The results show that the agent-based modeling approach produces the least prediction error compared to other state-of-the-practice and state-of-the-art methods (instantaneous travel time, historical average and k-nearest neighbor), and maintains less than a 9% prediction error for trip departures up to 60 min into the future for a two-hour trip. Moreover, the confidence boundaries of the predicted travel times demonstrate that the proposed approach also provides high accuracy in predicting travel time confidence intervals. Finally, the proposed approach does not require offline training thus making it easily transferable to other locations and the fast algorithm computation allows the proposed approach to be implemented in real-time applications in Traffic Management Centers.     

A genetic algorithm-based method for improving quality of travel time prediction intervals

The transportation literature is rich in the application of neural networks for travel time prediction. The uncertainty prevailing in operation of transportation systems, however, highly degrades prediction performance of neural networks. Prediction intervals for neural network outcomes can properly represent the uncertainty associated with the predictions. This paper studies an application of the delta technique for the construction of prediction intervals for bus and freeway travel times. The quality of these intervals strongly depends on the neural network structure and a training hyperparameter. A genetic algorithm–based method is developed that automates the neural network model selection and adjustment of the hyperparameter. Model selection and parameter adjustment is carried out through minimization of a prediction interval-based cost function, which depends on the width and coverage probability of constructed prediction intervals. Experiments conducted using the bus and freeway travel time datasets demonstrate the suitability of the proposed method for improving the quality of constructed prediction intervals in terms of their length and coverage probability.     

The effect of travel time variability on route choice decision: a generalized linear mixed model based analysis

The effect of travel time variability (TTV) on route choice behavior is explored in this study. A stated preference survey is conducted to collect behavioral data on Shanghai drivers’ choice between a slow but stable route and a fast but unreliable route. Travel time and TTV are respectively measured by mean and standard deviation of random travel time. The generalized linear mixed model (GLMM) is applied to quantify trade-offs between travel time and TTV. The GLMM based route choice model effectively accounts for correlations among repeated observations from the same respondent, and captures heterogeneity in drivers’ values of TTV. Model estimation results show that, female drivers and drivers with rich driving experience are less likely to choose a route with high TTV; smaller expected travel time of a route increase the probability of its being chosen; all drivers have intrinsic preference for a route with smaller expected travel time, but the degree of preference may vary within the population; TTV on average has negative effects on route choice decision, but a small portion of drivers are risk-prone to choose a fast but unreliable route despite high TTV.     

Crowding in public transport systems: Effects on users,operation and implications for the estimation of demand

The effects of high passenger density at bus stops, at rail stations, inside buses and trains are diverse. This paper examines the multiple dimensions of passenger crowding related to public transport demand, supply and operations, including effects on operating speed, waiting time, travel time reliability, passengers’ wellbeing, valuation of waiting and in-vehicle time savings, route and bus choice, and optimal levels of frequency, vehicle size and fare. Secondly, crowding externalities are estimated for rail and bus services in Sydney, in order to show the impact of crowding on the estimated value of in-vehicle time savings and demand prediction. Using Multinomial Logit (MNL) and Error Components (EC) models, we show that alternative assumptions concerning the threshold load factor that triggers a crowding externality effect do have an influence on the value of travel time (VTTS) for low occupancy levels (all passengers sitting); however, for high occupancy levels, alternative crowding models estimate similar VTTS. Importantly, if demand for a public transport service is estimated without explicit consideration of crowding as a source of disutility for passengers, demand will be overestimated if the service is designed to have a number of standees beyond a threshold, as analytically shown using a MNL choice model. More research is needed to explore if these findings hold with more complex choice models and in other contexts.     

Catching the tail: Empirical identification of the distribution of the value of travel time

Recent methodological advances in discrete choice analysis in combination with certain stated choice experiments have allowed researchers to check empirically the identification of the distribution of latent variables such as the value of travel time (VTT). Lack of identification is likely to be common and the consequences are severe. E.g., the Danish value of time study found the 15% right tail of the VTT distribution to be unidentified, making it impossible to estimate the mean VTT without resorting to strong assumptions with equally strong impact on the resulting estimate. This paper analyses data generated from a similar choice experiment undertaken in Sweden during 2007-2008 in which the range of trade-off values between time and money was significantly increased relative to the Danish experiment. The results show that this change allowed empirical identification of effectively the entire VTT distribution. In addition to informing the design of future choice experiments, the results are also of interest as a validity test of the stated choice methodology. Failure in identifying the right tail of the VTT would have made it difficult to maintain that respondents’ behaviour is consistent with utility maximisation in the sense intended by the experimenter.     

Decomposing travel times measured by probe-based traffic monitoring systems to individual road segments

In probe-based traffic monitoring systems, traffic conditions can be inferred based on the position data of a set of periodically polled probe vehicles. In such systems, the two consecutive polled positions do not necessarily correspond to the end points of individual links. Obtaining estimates of travel time at the individual link level requires the total traversal time (which is equal to the polling interval duration) be decomposed. This paper presents an algorithm for solving the problem of decomposing the traversal time to times taken to traverse individual road segments on the route. The proposed algorithm assumes minimal information about the network, namely network topography (i.e. links and nodes) and the free flow speed of each link. Unlike existing deterministic methods, the proposed solution algorithm defines a likelihood function that is maximized to solve for the most likely travel time for each road segment on the traversed route. The proposed scheme is evaluated using simulated data and compared to a benchmark deterministic method. The evaluation results suggest that the proposed method outperforms the bench mark method and on average improves the accuracy of the estimated link travel times by up to 90%.     

Link travel time inference using entry/exit information of trips on a network

This paper studies link travel time estimation using entry/exit time stamps of trips on a steady-state transportation network. We propose two inference methods based on the likelihood principle, assuming each link associates with a random travel time. The first method considers independent and Gaussian distributed link travel times, using the additive property that trip time has a closed-form distribution as the summation of link travel times. We particularly analyze the mean estimates when the variances of trip time estimates are known with a high degree of precision and examine the uniqueness of solutions. Two cases are discussed in detail: one with known paths of all trips and the other with unknown paths of some trips. We apply the Gaussian mixture model and the Expectation–Maximization (EM) algorithm to deal with the latter. The second method splits trip time proportionally among links traversed to deal with more general link travel time distributions such as log-normal. This approach builds upon an expected log-likelihood function which naturally leads to an iterative procedure analogous to the EM algorithm for solutions. Simulation tests on a simple nine-link network and on the Sioux Falls network respectively indicate that the two methods both perform well. The second method (i.e., trip splitting approximation) generally runs faster but with larger errors of estimated standard deviations of link travel times.