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.     

Assessment of factors associated with travel time reliability and prediction: an empirical analysis using probabilistic reasoning approach

Significant efforts have been made in modeling a travel time distribution and establishing measures of travel time reliability (TTR). However, the literature on evaluating the factors affecting TTR is not well established. Accordingly, this paper presents an empirical analysis to determine potential factors that are associated with TTR. This study mainly applies the Bayesian Networks model to assess the probabilistic association between road geometry, traffic data, and TTR. The results from this model reveal that land use characteristics, intersection factors, and posted speed limits are directly associated with TTR. Evaluating the strength of the association between TTR and the directly related variables, the log odds ratio analysis indicates that the land use factor has the highest impact (0.83) followed by the intersection factor (0.57). The findings from this study can provide valuable resources to planners and traffic operators in their decision-making to improve TTR with quantitative evidence.     

Reprint of: Modelling the impact of traffic incidents on travel time reliability

Traffic incidents are recognised as one of the key sources of non-recurrent congestion that often leads to reduction in travel time reliability (TTR), a key metric of roadway performance. A method is proposed here to quantify the impacts of traffic incidents on TTR on freeways. The method uses historical data to establish recurrent speed profiles and identifies non-recurrent congestion based on their negative impacts on speeds. The locations and times of incidents are used to identify incidents among non-recurrent congestion events. Buffer time is employed to measure TTR. Extra buffer time is defined as the extra delay caused by traffic incidents. This reliability measure indicates how much extra travel time is required by travellers to arrive at their destination on time with 95% certainty in the case of an incident, over and above the travel time that would have been required under recurrent conditions. An extra buffer time index (EBTI) is defined as the ratio of extra buffer time to recurrent travel time, with zero being the best case (no delay). A Tobit model is used to identify and quantify factors that affect EBTI using a selected freeway segment in the Southeast Queensland, Australia network. Both fixed and random parameter Tobit specifications are tested. The estimation results reveal that models with random parameters offer a superior statistical fit for all types of incidents, suggesting the presence of unobserved heterogeneity across segments. What factors influence EBTI depends on the type of incident. In addition, changes in TTR as a result of traffic incidents are related to the characteristics of the incidents (multiple vehicles involved, incident duration, major incidents, etc.) and traffic characteristics.     

International experience with speed limits during and prior to the energy crisis of 1973–4

This paper presents an artificial neural network (ANN) based method for estimating route travel times between individual locations in an urban traffic network. Fast and accurate estimation of route travel times is required by the vehicle routing and scheduling process involved in many fleet vehicle operation systems such as dial‐a‐ride paratransit, school bus, and private delivery services. The methodology developed in this paper assumes that route travel times are time‐dependent and stochastic and their means and standard deviations need to be estimated. Three feed‐forward neural networks are developed to model the travel time behaviour during different time periods of the day‐the AM peak, the PM peak, and the off‐peak. These models are subsequently trained and tested using data simulated on the road network for the City of Edmonton, Alberta. A comparison of the ANN model with a traditional distance‐based model and a shortest path algorithm is then presented. The practical implication of the ANN method is subsequently demonstrated within a dial‐a‐ride paratransit vehicle routing and scheduling problem. The computational results show that the ANN‐based route travel time estimation model is appropriate, with respect to accuracy and speed, for use in real applications.     

Estimating freeway route travel time distributions with consideration to time‐of‐day,inclement weather,and traffic incidents

This paper develops an efficient probabilistic model for estimating route travel time variability, incorporating factors of time‐of‐day, inclement weather, and traffic incidents. Estimating the route travel time distribution from historical link travel time data is challenging owing to the interactions among upstream and downstream links. Upon creating conditional probability function for each link travel time, we applied Monte Carlo simulation to estimate the total travel time from origin to destination. A numerical example of three alternative routes in the City of Buffalo shows several implications. The study found that weather conditions, except for snow, incur minor impact on off‐peak and weekend travel time, whereas peak travel times suffer great variations under different weather conditions. On top of that, inclement weather exacerbates route travel time reliability, even when mean travel time increases moderately. The computation time of the proposed model is linearly correlated to the number of links in a route. Therefore, this model can be used to obtain all the origin to destination travel time distributions in an urban region. Further, this study also validates the well‐known near‐linear relation between the standard deviation of travel time per unit distance and the corresponding mean value under different weather conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

Travel time estimation for urban road networks using low frequency probe vehicle data

The paper presents a statistical model for urban road network travel time estimation using vehicle trajectories obtained from low frequency GPS probes as observations, where the vehicles typically cover multiple network links between reports. The network model separates trip travel times into link travel times and intersection delays and allows correlation between travel times on different network links based on a spatial moving average (SMA) structure. The observation model presents a way to estimate the parameters of the network model, including the correlation structure, through low frequency sampling of vehicle traces. Link-specific effects are combined with link attributes (speed limit, functional class, etc.) and trip conditions (day of week, season, weather, etc.) as explanatory variables. The approach captures the underlying factors behind spatial and temporal variations in speeds, which is useful for traffic management, planning and forecasting. The model is estimated using maximum likelihood. The model is applied in a case study for the network of Stockholm, Sweden. Link attributes and trip conditions (including recent snowfall) have significant effects on travel times and there is significant positive correlation between segments. The case study highlights the potential of using sparse probe vehicle data for monitoring the performance of the urban transport system.     

Travel time estimation from sparse floating car data with consistent path inference: A fixed point approach

Estimation of urban network link travel times from sparse floating car data (FCD) usually needs pre-processing, mainly map-matching and path inference for finding the most likely vehicle paths that are consistent with reported locations. Path inference requires a priori assumptions about link travel times; using unrealistic initial link travel times can bias the travel time estimation and subsequent identification of shortest paths. Thus, the combination of path inference and travel time estimation is a joint problem. This paper investigates the sensitivity of estimated travel times, and proposes a fixed point formulation of the simultaneous path inference and travel time estimation problem. The methodology is applied in a case study to estimate travel times from taxi FCD in Stockholm, Sweden. The results show that standard fixed point iterations converge quickly to a solution where input and output travel times are consistent. The solution is robust under different initial travel times assumptions and data sizes. Validation against actual path travel time measurements from the Google API and an instrumented vehicle deployed for this purpose shows that the fixed point algorithm improves shortest path finding. The results highlight the importance of the joint solution of the path inference and travel time estimation problem, in particular for accurate path finding and route optimization.     

Designing heterogeneous sensor networks for estimating and predicting path travel time dynamics: An information-theoretic modeling approach

With a particular emphasis on the end-to-end travel time prediction problem, this paper proposes an information-theoretic sensor location model that aims to minimize total travel time uncertainties from a set of point, point-to-point and probe sensors in a traffic network. Based on a Kalman filtering structure, the proposed measurement and uncertainty quantification models explicitly take into account several important sources of errors in the travel time estimation/prediction process, such as the uncertainty associated with prior travel time estimates, measurement errors and sampling errors. By considering only critical paths and limited time intervals, this paper selects a path travel time uncertainty criterion to construct a joint sensor location and travel time estimation/prediction framework with a unified modeling of both recurring and non-recurring traffic conditions. An analytical determinant maximization model and heuristic beam-search algorithm are used to find an effective lower bound and solve the combinatorial sensor selection problem. A number of illustrative examples and one case study are used to demonstrate the effectiveness of the proposed methodology.     

Forecasting journey time distribution with consideration to abnormal traffic conditions

Travel time is an important index for managers to evaluate the performance of transportation systems and an intuitive measure for travelers to choose routes and departure times. An important part of the literature focuses on predicting instantaneous travel time under recurrent traffic conditions to disseminate traffic information. However, accurate travel time prediction is important for assessing the effects of abnormal traffic conditions and helping travelers make reliable travel decisions under such conditions. This study proposes an online travel time prediction model with emphasis on capturing the effects of anomalies. The model divides a path into short links. A Functional Principal Component Analysis (FPCA) framework is adopted to forecast link travel times based on historical data and real-time measurements. Furthermore, a probabilistic nested delay operator is used to calculate path travel time distributions. To ensure that the algorithm is fast enough for online applications, parallel computation architecture is introduced to overcome the computational burden of the FPCA. Finally, a rolling horizon structure is applied to online travel time prediction. Empirical results for Guangzhou Airport Expressway indicate that the proposed method can capture an abrupt change in traffic state and provide a promising and reliable travel time prediction at both the link and path levels. In the case where the original FPCA is modified for parallelization, accuracy and computational effort are evaluated and compared with those of the sequential algorithm. The proposed algorithm is found to require only a piece rather than a large set of traffic incident records.     

Application of the support vector machine and heuristic k-shortest path algorithm to determine the most eco-friendly path with a travel time constraint

This study aims to determine an eco-friendly path that results in minimum CO₂ emissions while satisfying a specified budget for travel time. First, an aggregated CO₂ emission model for light-duty cars is developed in a link-based level using a support vector machine. Second, a heuristic k-shortest path algorithm is proposed to solve the constrained shortest path problem. Finally, the CO₂ emission model and the proposed eco-routing model are validated in a real-world network. Specifically, the benefit of the trade-off between CO₂ emission reduction and the travel time budget is discussed by carrying out sensitivity analysis on a network-wide scale. A greater spare time budget may enable the eco-routing to search for the most eco-friendly path with higher probability. Compared to the original routes selected by travelers, the eco-friendly routes can save an average of 11% of CO₂ emissions for the trip OD pairs with a straight distance between 6 km and 9 km when the travel time budget is set to 10% above the least travel time. The CO₂ emission can also be reduced to some degree for other OD pairs by using eco-routing. Furthermore, the impact of market penetration of eco-routing users is quantified on the potential benefit for the environment and travel-time saving.     

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.     

Incorporating uncertainty into short-term travel time predictions

To improve the quality of travel time information provided to motorists, there is a need to move away from point forecasts of travel time. Specifically, techniques are needed which predict the range of travel times which motorists may experience. This paper focuses on travel time prediction on motorways and evaluates three models for predicting the travel time range in real time as well as up to 1 h ahead. The first model, termed lane by lane tracing, relies on speed data from each lane to replicate the trajectories of relatively slow and relatively fast vehicles on the basis of speed differences across the lanes. The second model is based on the relationship between mean travel time (estimated using a neural network model) and driver-to-driver travel time variability. The results provide insight into the relative merits of the proposed techniques and confirm that they provide a basis for reliable travel time range prediction in the short-term prediction context (up to 1 h ahead).     

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.     

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.

Probe vehicle data sampled by time or space: Consistent travel time allocation and estimation

A characteristic of low frequency probe vehicle data is that vehicles traverse multiple network components (e.g., links) between consecutive position samplings, creating challenges for (i) the allocation of the measured travel time to the traversed components, and (ii) the consistent estimation of component travel time distribution parameters. This paper shows that the solution to these problems depends on whether sampling is based on time (e.g., one report every minute) or space (e.g., one every 500 m). For the special case of segments with uniform space-mean speeds, explicit formulae are derived under both sampling principles for the likelihood of the measurements and the allocation of travel time. It is shown that time-based sampling is biased towards measurements where a disproportionally long time is spent on the last segment. Numerical experiments show that an incorrect likelihood formulation can lead to significantly biased parameter estimates depending on the shapes of the travel time distributions. The analysis reveals that the sampling protocol needs to be considered in travel time estimation using probe vehicle data.     

Modelling the relationship between travel behaviours and social disadvantage

The purpose of this paper is to model the travel behaviour of socially disadvantaged population segments in the United Kingdom (UK) using the data from the UK National Travel Survey 2002–2010. This was achieved by introducing additional socioeconomic variables into a standard national-level trip end model (TEM) and using purpose-based analysis of the travel behaviours of certain key socially disadvantaged groups. Specifically the paper aims to explore how far the economic and social disadvantages of these individuals can be used to explain the inequalities in their travel behaviours.The models demonstrated important differences in travel behaviours according to household income, presence of children in the household, possession of a driver’s licence and belonging to a vulnerable population group, such as being disabled, non-white or having single parent household status. In the case of household income, there was a non-linear relationship with trip frequency and a linear one with distance travelled. The recent economic austerity measures that have been introduced in the UK and many other European countries have led to major cutbacks in public subsidies for socially necessary transport services, making results such as these increasingly important for transport policy decision-making. The results indicate that the inclusion of additional socioeconomic variables is useful for identifying significant differences in the trip patterns and distances travelled by low-income.     

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.     

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.     

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.     

A distribution-fitting-free approach to calculating travel time reliability ratio

Empirical studies have revealed that travel time variability (TTV) can significantly affect travelers’ behaviors and planners’ cost-benefit assessment of transportation projects. It is therefore important to systematically quantify the value of TTV (VTTV) and its impact. Recently, Fosgerau’s valuation method makes this quantification possible by converting the value of travel time (VTT) and the VTTV into monetary unit. Travel time reliability ratio (TTRR), defined as a ratio of the VTTV to the VTT, is a key parameter in Fosgerau’s valuation method. Calculating TTRR involves an integral of the inverse cumulative distribution function (CDF) of the standardized travel time distribution (STTD), i.e., the mean lateness factor. Using a well-fitted STTD is a straightforward way to calculate TTRR. However, it will encounter the following challenges: (1) determination of a well-fitted STTD; (2) non-existence of an algebraic expression for the CDF and its inverse CDF; and (3) lack of a closed-form expression to efficiently calculate TTRR. To circumvent the above issues, this paper proposes a distribution-fitting-free analytical approach based on the Cornish-Fisher expansion as an alternative way to calculate TTRR without the need to fit the whole CDF. The validity domain is rigorously derived for guaranteeing the accuracy of the proposed method. Realistic travel time datasets that cover 17 links are used to systematically explore the feature and accuracy of the proposed method in estimating TTRR. The comparative results demonstrate that the proposed method can efficiently and effectively estimate TTRR. When travel time datasets satisfy the validity domain, the proposed method outperforms the distribution fitting method in estimating TTRR.