Historical Travel Time Research Articles

Bus Travel Time Prediction Based on the Similarity in Drivers’ Driving Styles

Providing accurate and real-time bus travel time information is crucial for both passengers and public transportation managers. However, in the traditional bus travel time prediction model, due to the lack of consideration of the influence of different bus drivers’ driving styles on the bus travel time, the prediction result is not ideal. In the traditional bus travel time prediction model, the historical travel data of all drivers in the entire bus line are usually used for training and prediction. Due to great differences in individual driving styles, the eigenvalues of drivers’ driving parameters are widely distributed. Therefore, the prediction accuracy of the model trained by this dataset is low. At the same time, the training time of the model is too long due to the large sample size, making it difficult to provide a timely prediction in practical applications. However, if only the historical dataset of a single driver is used for training and prediction, the amount of training data is too small, and it is also difficult to accurately predict travel time. To solve these problems, this paper proposes a method to predict bus travel times based on the similarity of drivers’ driving styles. Firstly, the historical travel time data of different drivers are clustered, and then the corresponding types of drivers’ historical data are used to predict the travel time, so as to improve the accuracy and speed of the travel time prediction. We evaluated our approach using a real-world bus trajectory dataset collected in Shenyang, China. The experimental results show that the accuracy of the proposed method is 13.4% higher than that of the traditional method.

An attention-based recurrent learning model for short-term travel time prediction.

With the advent of Big Data technology and the Internet of Things, Intelligent Transportation Systems (ITS) have become inevitable for future transportation networks. Travel time prediction (TTP) is an essential part of ITS and plays a pivotal role in congestion avoidance and route planning. The novel data sources such as smartphones and in-vehicle navigation applications allow traffic conditions in smart cities to be analyzed and forecast more reliably than ever. Such a massive amount of geospatial data provides a rich source of information for TTP. Gated Recurrent Unit (GRU) has been successfully applied to traffic prediction problems due to its ability to handle long-term traffic sequences. However, the existing GRU does not consider the relationship between various historical travel time positions in the sequences for traffic prediction. We propose an attention-based GRU model for short-term travel time prediction to cope with this problem enabling GRU to learn the relevant context in historical travel time sequences and update the weights of hidden states accordingly. We evaluated the proposed model using FCD data from Beijing. To demonstrate the generalization of our proposed model, we performed a robustness analysis by adding noise obeying Gaussian distribution. The experimental results on test data indicated that our proposed model performed better than the existing deep learning time-series models in terms of Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Coefficient of Determination (R2).

An augmented Lagrangian relaxation method for the mean-standard deviation based vehicle routing problem

With the ever-increasing trip demand and limited transportation resource, traffic congestions remain a tricky problem. Under traffic congestions, travel times are unstable and variable in a real-world network. When we conduct many time-sensitive vehicle routing optimizations such as vaccine transportation, it is essential to consider the travel time variability in these optimizations. However, most previous vehicle routing studies neglected the travel time variability and adopted the expected travel times or lengths of links. The historical travel times of multiple days allow us to access and describe the travel time variability. We can easily obtain the travel time means and standard deviations of links from these data. This study applies these two statistical indicators to vehicle routing optimization and concentrates on a mean-standard deviation based vehicle routing model. This model has a nonlinear and concave objective function that dramatically increases the problem complexity. We develop a novel augmented Lagrangian relaxation approach for this problem. A lower bound is constructed for this problem by applying the Lagrangian relaxation and decomposition technique twice. To break the inherent symmetry of this problem, we use the augmented Lagrangian relaxation method with block coordinate descent, linearization, and Lagrangian substitution techniques to achieve high-quality feasible solutions. Thus, the relative gap between the lower and upper bounds can be evaluated and reduced in the solving procedure. We implement the proposed method on the datasets modified from the standard benchmark instances. The average relative gaps of instances in sets A and P are 8.8% and 7.6%, respectively.

Path-oriented synchronized transit scheduling using time-dependent data

With the emergence of innovations associated with public transport (PT) services, such as Mobility-as-a-Service, demand responsive transit, and autonomous vehicles, the door-to-door PT journey is achievable via multiple transfers between and within different PT modes. As such, seamless transfers between different modes of public transportation become an increasingly important factor for the attractiveness of PT services. At the same time, recent developments in travel time prediction methodologies offer new, reliable data sources for the optimization of PT operations. This work, with the consideration of these two elements, develops a mixed integer linear programming model for the PT schedule synchronization problem. The novelty is threefold. First, a novel concept of path-oriented scheduling is proposed. The path transfer time is explicitly formulated and minimized to provide a seamless travel experience considering that the emerging multimodal mobility inevitably induces multiple transfers. Second, time-dependent travel time data is also utilized in the model, which allows us to harness new and more representative data sources for improving PT services. Third, in order to complement the increase in computational complexity as a result of the utilization of time-dependent travel time data, three novel valid inequalities (VIs) are derived. Numerical studies show that the use of time-dependent travel time data is beneficial in terms of reducing path transfer times, when compared to using the mean historical travel times. The numerical study also reveals a tradeoff between the maximum allowable path transfer time and trip time. Using simulation studies on three bus lines in Copenhagen, we demonstrate that the valid inequalities could reduce the computation time by 8.5% on average, where the maximum reduction of computation time could reach 54.0%. The proposed valid inequalities are benchmarked against two classes of valid inequalities in the literature. It is found that the proposed valid inequalities could outperform those in the literature. We also found that further improvement in computational performance can be attained by using a combination of the proposed valid inequalities.

Road network vulnerability analysis considering the probability and consequence of disruptive events: A spatiotemporal incident impact approach

This paper proposes a new data-driven impact area vulnerability analysis approach that considers both the probability of impact of incidents and their resulting effects on an impact area. Multi-year observed travel time and incident data are deployed to investigate the underlying traffic propagation dynamics. These datasets contain a wealth of information that reflects the occurrences of link closure/disruption by space and time and the network-wide impacts stemming from these disruptions. A novel approach is developed to identify the resulting spatial and temporal impacts of non-recurrent incidents. Rather than focusing solely on the travel time changes of the link subject to incident, this approach captures all aspects of the impacts of incidents by monitoring the dynamic propagation of congestion patterns in the set of links that are in the vicinity of the link subject to incident (i.e., impact area). These spatial and temporal dimensions of the impacts are subsequently used in a new vulnerability analysis. The performance of the developed approach was examined using historical travel time and incident data from the City of Calgary, Canada. The results indicate that the recorded temporal impact of incidents is not representative enough of the true impact of incidents because the dynamic spatial propagation of the effect of incidents on the impact area is overlooked. The proposed approach is capable of capturing the enduring spatiotemporal impact of incidents in a large-scale road network. The primary improvement of the developed vulnerability index is its ability to model multi-dimensional aspects of non-recurrent travel delays caused by non-current incidents in a road network.

Switching threshold of commuting Travelers’ route choice under different patterns of information

Travelers always exhibit bounded rationality due to limited perception. Based on the theory of bounded rationality, switching thresholds under different patterns of information are analyzed in this paper. An experiment platform including four scenarios, such as historical descriptive information, real-time descriptive information, historical travel time information and real-time travel time information is designed to obtain the participants’ travel preference and route choice behavior. The relationship among route switching behavior, perceived travel time difference and travelers’ preference is analyzed based on experiment’s results. The Probit regression method is utilized for calibrating the switching threshold under different patterns of information. The results prove the dissimilarity of switching thresholds in diverse patterns of information. The switching threshold under real-time information is lower than that under historical information. The estimated results of risk parameters prove that the traveler has a slight tendency to pursue risk. The method proposed in this paper can effectively quantify the degree of bounded rationality.

Evaluation of the Relationship Between Geographic Proximity and Treatment for People Referred to a Metropolitan Multidisciplinary Pain Clinic.

This study examined which patient characteristics are associated with traveling further to attend a metropolitan, publicly funded pain management service, and whether travel distance was associated with differences in treatment profile, duration, and percentage of appointments attended. Cross-sectional observational cohort study. Patients ≤70 years of age with a single referral between January 2014 and June 2018 who had not died within 12 months of their first appointment and who had a usual place of residence were included (N = 1,684; mean age = 47.2 years; 55.5% female). Travel distance was calculated with the HERE Routing API on the basis of historical travel times for each scheduled appointment. Median travel time was 27.5 minutes (Q1, Q3: 12.5, 46.2). Ordinal regression showed that women had 20% lower odds of traveling further, but people who were overweight or obese (odds ratio [OR] = 1.4-2.3), unemployed (OR = 1.27), or taking higher opioid dosages (OR = 1.79-2.82) had higher odds of traveling further. People traveling >60 minutes had fewer treatment minutes (median = 143 minutes) than people living within 15 minutes of the pain clinic (median = 440 minutes), and a smaller proportion of those traveling >60 minutes attended group programs vs. medical appointments only (n = 35, 17.0%) relative to those living within 15 minutes of their destination (n = 184, 32.6%). People living 16-30 minutes from the clinic missed the highest proportion of appointments. Although people traveling further for treatment may be seeking predominantly medical treatment, particularly opioid medications, the present findings highlight the need to further explore patient triage and program models of care to ensure that people living with persistent disabling pain can access the same level of care, regardless of where they live.

Day-to-day dynamics with advanced traveler information

This paper studies how the advanced traveler information affects the stability of the day-to-day flow evolution of a transportation system. Two scenarios are investigated regarding the types of information provided, where one type is the historical travel time and the other the forecasted travel time. Given the information, travelers are assumed to form their own perception/prediction on travel time and further choose the routes. The day-to-day dynamics under the two above-mentioned scenarios are formulated using both discrete-time and continuous-time models, and their respective local stability is analyzed. Findings from the discrete-time and continuous-time models are compared, which show that: (i) the discrete-time models behave in a more complex fashion than the continuous-time models, and (ii) the conclusions drawn from the discrete-time modeling and continuous-time modeling can be consistent, different or contradictory, which depends on the system parameters, network structure, the travel time functions and the route choice probability functions.

Dealing with latency effects in travel time prediction on motorways

Real-time traffic information is now a crucial part of operating a road network. The quality, accuracy and reliability of such information is critical to the road operators and users. Real-time travel time prediction methods using Automatic Number Plate Recognition cameras or Bluetooth/Wi-Fi readers that use matching algorithms to generate travel times in real-time can be vulnerable to an inherent latency issue. Measured travel times are based on vehicles that have already completed the journey and may not be representative for users about to commence that same journey. The aim of this research was to identify the latency in travel time prediction, quantify its effect, and develop a model to remove it. Datasets for the M50 motorway in Dublin, Ireland, were used to conduct the analysis. The results show that real-time travel times can be more accurately predicted when combined with historical travel time information. The approach was found to be valid and achievable and the developed tool can predict and inform both road operators and users during regular periods of congestion. The project also identified other data sources, such as real-time Automated Incident Detection (AID) loop data, incident and weather data, that can further enhance the predicted travel time calculation.

Empirical Study of Effect of Dynamic Travel Time Information on Driver Route Choice Behavior.

The objective of this paper is to study the effect of travel time information on day-to-day driver route choice behavior. A real-world experimental study is designed to have participants repeatedly choose between two alternative routes for five origin-destination pairs over multiple days after providing them with dynamically updated travel time information (average travel time and travel time variability). The results demonstrate that historical travel time information enhances behavioral rationality by 10% on average and reduces inertial tendencies to increase risk seeking in the gain domain. Furthermore, expected travel time information is demonstrated to be more effective than travel time variability information in enhancing rational behavior when drivers have limited experiences. After drivers gain sufficient knowledge of routes, however, the difference in behavior associated with the two information types becomes insignificant. The results also demonstrate that, when drivers lack experience, the faster less reliable route is more attractive than the slower more reliable route. However, with cumulative experiences, drivers become more willing to take the more reliable route given that they are reluctant to become risk seekers once experience is gained. Furthermore, the effect of information on driver behavior differs significantly by participant and trip, which is, to a large extent, dependent on personal traits and trip characteristics.

Prediction model for bus inter-stop travel time considering the impacts of signalized intersections

Since bus inter-stop travel times (BISTTs) are significant components of the route travel time, providing accurate BISTTs can effectively improve the route travel time prediction accuracy. In this paper we propose a novel prediction model for BISTTs, which takes five factors as input variables: stop distance, historical inter-stop travel times, number of intersections, intersection traffic volumes, and intersection signal timing schemes. The Lagrange Multiplier (LM) test is conducted to check autocorrelation in the model residuals. Cases of two bus routes in Harbin have been studied based on field data. Mean average errors for both bus routes are smaller than 8%, indicating the high prediction accuracy in predicting BISTTs. Sensitivity analysis is conducted and results show that excluding any one of those five factors would cause the failure of the model in the LM test, indicating that the presence of all factors is required to maintain the validity of this model.

The data-driven time-dependent traveling salesperson problem

In this paper, we study a single-vehicle routing problem with stochastic service times, stochastic time-dependent travel times, and soft time windows, where the travel times may be interdependent. The objective is to minimize the expected route duration plus penalties for late arrivals. The stochasticity is modeled using a set of scenarios based on historical data. This approach enables the spatial and temporal interdependencies in the road network to be captured. We introduce a specialized branch-and-bound algorithm and a successful adaptive large neighborhood search heuristic for the problem. In a numerical experiment based on real historical travel time data, we demonstrate the applicability of both methods to problem instances of up to 40 customers and 40 scenarios. These dimensions are safe upper bounds for instances originating from the field service operation domain. The resulting routes are tested on realistic scenarios that were not included in the problem input (the training set) to demonstrate the merits of using historical data. Compared with solutions that ignore the time dependency and/or stochasticity of the parameters, our solutions are consistently superior.

Travel-time Prediction Using K-nearest Neighbor Method with Distance Metric of Correlation Coefficient

Background: Real-time Travel Time (TT) information has become an essential component of daily life in modern society. With reliable TT information, road users can increase their productivity by choosing less congested routes or adjusting their trip schedules. Drivers normally prefer departure time-based TT, but most agencies in Korea still provide arrival time-based TT with probe data from Dedicated Short-Range Communications (DSRC) scanners due to a lack of robust prediction techniques. Recently, interest has focused on the conventional k-nearest neighbor (k-NN) method that uses the Euclidean distance for real-time TT prediction. However, conventional k-NN still shows some deficiencies under certain conditions. Methods: This article identifies the cases where conventional k-NN has shortcomings and proposes an improved k-NN method that employs a correlation coefficient as a measure of distance and applies a regression equation to compensate for the difference between current and historical TT. Results: The superiority of the suggested method over conventional k-NN was verified using DSRC probe data gathered on a signalized suburban arterial in Korea, resulting in a decrease in TT prediction error of 3.7 percent points on average. Performance during transition periods where TTs are falling immediately after rising exhibited statistically significant differences by paired t-tests at a significance level of 0.05, yielding p-values of 0.03 and 0.003 for two-day data. Conclusion: The method presented in this study can enhance the accuracy of real-time TT information and consequently improve the productivity of road users.

Bus Travel Time Prediction Model Based on Profile Similarity.

In road-based mass transit systems, travel time is a key factor in providing quality of service. This article proposes a method of predicting travel time for this type of transport system. This method estimates travel time by taking into account its historical behaviour, represented by historical profiles, and the current behaviour recorded on the public transport vehicle for which the prediction is to be made. The model uses the k-medoids clustering algorithm to obtain historical travel time profiles. A relevant feature of the model is that it does not require recent travel time data from other vehicles. For this reason, the proposed model may be used in intercity transport contexts in which service planning is carried out according to timetables. The proposed model has been tested with two real cases of intercity public transport routes and from the results obtained we may conclude that, in general, the average error of the predictions is around 13% compared to the observed travel time values.

Agent-Based Dynamic Traffic Assignment with Information Mixing

This study develops an approach for network assignment convergence using individualized agent-based routing and agent-specific link cost information as well as historical travel times. Each traveler is routed individually from their starting and ending network link at a specific departure time. The approach is gap-based in two ways. First, as in previous approaches, the re-assignment decision during the convergence process is based on the gap between the routed and experienced travel time from the previous iteration. Secondly, the historical time-dependent and prevailing traffic conditions are averaged into a single expected value for each agent using a weight calculated by a modified two-parameter Weibull survival function. This weight is individualized based on the relative gap of the traveler from the previous iteration, as well as the iteration number; a novel aspect of this work. The methodology is tested on a medium-scale network of Bloomington, IL. The algorithm converges after only two iterations, which is promising as computational time of a single iteration can be high for large-scale networks.

Travel time prediction for highway network based on the ensemble empirical mode decomposition and random vector functional link network

Travel time prediction supplies data support for the management and operation of the highway network. To deal with this problem, a model based on ensemble empirical mode decomposition and random vector functional link network is proposed in this paper. Ensemble empirical mode decomposition is firstly employed to decompose the complex travel time data series into several simple functions, which are then represented by the same number of random vector functional link networks. Finally, the outputs of all networks are combined by linear addition as the prediction results. A historical travel time data series (from 1 August 2016 to 1 November 2016) of two highways in China is investigated by the proposed models. For comparison, five individual prediction models and their respective ensemble variants are implemented for the same task. The results show that the proposed model outperforms all the other models in terms of symmetric mean absolute percentage error and normalized root mean square error. As for computational speed, the proposed model ranks the first among all the ensemble models. Moreover, the ensemble empirical mode decomposition is better than the empirical mode decomposition. The Friedman statistical test also confirms the results of the comparison. Experimental results reveal that the proposed model reaches the best overall performance and is a very promising model for complex travel time prediction.

Estimation of Urban Link Travel Time Distribution Using Markov Chains and Bayesian Approaches

Despite the wide application of Floating Car Data (FCD) in urban link travel time and congestion estimation, the sparsity of observations from a low penetration rate of GPS-equipped floating cars make it difficult to estimate travel time distribution (TTD), especially when the travel times may have multimodal distributions that are associated with the underlying traffic states. In this case, the study develops a Bayesian approach based on particle filter framework for link TTD estimation using real-time and historical travel time observations from FCD. First, link travel times are classified by different traffic states according to the levels of vehicle delays. Then, a state-transition function is represented as a Transition Probability Matrix of the Markov chain between upstream and current links with historical observations. Using the state-transition function, an importance distribution is constructed as the summation of historical link TTDs conditional on states weighted by the current link state probabilities. Further, a sampling strategy is developed to address the sparsity problem of observations by selecting the particles with larger weights in terms of the importance distribution and a Gaussian likelihood function. Finally, the current link TTD can be reconstructed by a generic Markov Chain Monte Carlo algorithm incorporating high weighted particles. The proposed approach is evaluated using real-world FCD. The results indicate that the proposed approach provides good accurate estimations, which are very close to the empirical distributions. In addition, the approach with different percentage of floating cars is tested. The results are encouraging, even when multimodal distributions and very few or no observations exist.

Stream travel time prediction using particle filtering approach

Travel-time information is an integral part of Advanced Traveler Information Systems and Advanced Traffic Management Systems. Real-time estimation of stream travel time will be helpful in making trip decisions such as route choice and departure time. The present study proposes a method to predict stream travel time using particle filtering approach which considers the predicted stream travel time as the sum of the median of historical travel times, random variations in travel time over time, and a model evolution error. The present model hypothesizes the median of historical travel times obtained from the collected data as a priori estimate and hence predicting the actual travel time will be equivalent to forecasting the variations in travel time according to the current measurements. In order to capture the random variations in travel time, a dynamic mathematical modeling approach with particle filtering technique is used. The results obtained from the implementation of the above method are compared with the measured travel time data and the prediction accuracy, quantified using the Mean Absolute Percentage Error and Mean Absolute Error was observed to be satisfactory. Performance of this method was compared to a basic speed-based approach, where travel time is obtained by time–distance relationship using space-mean speed, and the proposed method showed better performance.

Road Short-Term Travel Time Prediction Method Based on Flow Spatial Distribution and the Relations

There are many short-term road travel time forecasting studies based on time series, but indeed, road travel time not only relies on the historical travel time series, but also depends on the road and its adjacent sections history flow. However, few studies have considered that. This paper is based on the correlation of flow spatial distribution and the road travel time series, applying nearest neighbor and nonparametric regression method to build a forecasting model. In aspect of spatial nearest neighbor search, three different space distances are defined. In addition, two forecasting functions are introduced: one combines the forecasting value by mean weight and the other uses the reciprocal of nearest neighbors distance as combined weight. Three different distances are applied in nearest neighbor search, which apply to the two forecasting functions. For travel time series, the nearest neighbor and nonparametric regression are applied too. Then minimizing forecast error variance is utilized as an objective to establish the combination model. The empirical results show that the combination model can improve the forecast performance obviously. Besides, the experimental results of the evaluation for the computational complexity show that the proposed method can satisfy the real-time requirement.

Travel Time Prediction for Time-Table-Based Vehicles Traveling on Known Routes

This paper studies travel time prediction for time-table-based vehicles traveling on known routes using both the current and historical travel time information. In the authors experiment, the historical travel times stored in the database can be further dichotomized into uncongested (i.e., normal) and congested (i.e., abnormal) classes. With this fine-structured data of travel times, the method that embeds the empirical mode decomposition and grey theory (Chen and Wu, 2012) can be adopted to improve short-term travel time prediction. To demonstrate, using a real traffic data under abnormal traffic condition, this proposed method has been compared with the other four travel time prediction methods. The results show that the authros method is superior in terms of the mean absolute percentage error (MAPE) and hence more suitable to be applied in the real world.