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This study focuses on developing and evaluating predictive models for bus travel times adaptable to any transit network, or to new roadway segments without prior travel time data. Most prior work relies on non-standardized features such as road traffic forecasts or closed-source datasets to test predictions on a single route or network. We leverage standardized and open-source data from GTFS and GTFS-RT feeds to gather four months of realtime bus position data from Seattle and Trondheim's transit networks. We then test and refine strategies for generalizing model predictions across both locations. To achieve this, we first develop a data pipeline to process and clean the raw data, then extract features from the standardized sources. We then evaluate the performance of several deep learning and heuristic models in predicting bus travel times between source and target bus networks. Holdout data is taken from selected routes in the source city to validate the internal generalization of the models. Data from the target city is used to evaluate the external generalization of the models. An ablation study explores the impact of different open data sources on model generalization (GPS, static timetables, OpenStreetMap and other realtime trips). We then extend the analysis to 33 international bus networks, placing the results in broader context and testing fine-tuning strategies for generalization. Results show that deep learning methods generalize well within the source network, with as little as 1% loss in MAPE on holdout routes. With minimal fine-tuning generalization is significantly improved on the target network. Model features built on static schedule data, realtime positions or OpenStreetMap embeddings improved generalization performance (up to 10% reduction in MAPE). This was more pronounced for networks with a greater initial quantity of training data. As a route-planning tool for roadways without prior data, geospatial data mining can provide reasonable bus travel time estimates. For cross-sectional bus network analysis, fine tuning on at least 100 trajectory samples for each target network is required to significantly outperform baseline heuristics. This necessitates a GTFS-RT or other standardized realtime data feed in the target city.

The nature of paratransit services makes for increased uncertainty in trip time, leading to reported unreliability and dissatisfaction by the users. While providing travel information has proved helpful in formal bus services and has been recommended for paratransit setup, little is reported about efforts at providing information to paratransit users. This study focused on one strand of possible travel information that can be provided – Travel Time. An artificial neural network (ANN)-based model was developed to predict paratransit travel times, geared towards providing information to improve user experiences. The developed model was tested on a real-world paratransit bus route (minibus taxi) in Kumasi. A travel time survey that employed a mobile phone application was used to collect data onboard the vehicles on the study route. Two ANN models were trained. The first used only historical datasets, while the second incorporated real-time information. The results show that the model in which real-time information was included performed better than that trained with only historical data. The developed models were compared with a historical average model and a regression-based model, and the results showed that the ANN models outperformed the others. The study showed that the nature of paratransit services and the limitations of continuous data collection, notwithstanding, travel times of paratransit trips can be predicted to a reasonable level of accuracy, as can be relied upon in providing information to the users.

Paratransit users have reportedly been unsatisfied with the quality of service that they receive. Efforts at replacing the service or formalizing operations to meet users’ mobility needs have faced challenges or outrightly resisted. Approaches such as providing travel information and deploying interventions along the roadway infrastructure where the government has authority have been suggested. Deploying any of these approaches will require insights from empirical data. The study considered a key measure of service quality to users and operators alike – travel time. It investigated factors affecting the travel time of paratransit at the route and segment levels. A travel time survey that employed a mobile app (Trands) onboard paratransit vehicle was used to collect travel time, stop, and other related information on a selected route. The backward stepwise regression technique was used to determine factors affecting paratransit travel were. Dwell time, signal delay, recurrent congestion index (RCI), non-trip stops, and deviation from route were significant variables at the route level. All the factors affecting segment travel were also part of those involving route travel time except the segment length. Interestingly, deviation from the route increased overall travel time, which is against its logic. Insights gained from the study were used in suggesting proposals that can reduce travel time and improve the service quality of paratransit.

The nature of paratransit services makes for increased uncertainty in trip time, leading to reported unreliability and dissatisfaction by the users. While providing travel information has proved helpful in formal bus services and has been recommended for paratransit setup, little is reported about efforts at providing information to paratransit users. This study focused on one strand of possible travel information that can be provided – Travel Time. An artificial neural network (ANN)-based model was developed to predict paratransit travel times, geared towards providing information to improve user experiences. The developed model was tested on a real-world paratransit bus route (minibus taxi) in Kumasi. A travel time survey that employed a mobile phone application was used to collect data onboard the vehicles on the study route. Two ANN models were trained. The first used only historical datasets, while the second incorporated real-time information. The results show that the model in which real-time information was included performed better than that trained with only historical data. The developed models were compared with a historical average model and a regression-based model, and the results showed that the ANN models outperformed the others. The study showed that the nature of paratransit services and the limitations of continuous data collection, notwithstanding, travel times of paratransit trips can be predicted to a reasonable level of accuracy, as can be relied upon in providing information to the users. [ABSTRACT FROM AUTHOR]

While much has been reported about bus travel times and their variability for formal bus services, little is known about travel time variation for paratransit, the dominant means of transportation in most low- and middle-income countries (LMICs). This study quantifies the components of paratransit travel time on a selected route in Kumasi, Ghana. It analyzes the variability of travel times within the day and from day to day. A mobile phone app was employed to conduct a travel time survey onboard paratransit vehicles on the study route. GPS and stop-related data were collected. Various travel time variability measures and heat map was used for within day and day-to-day variability analysis in both directions of the study section. About 16% of travel time in the study section was spent dwelling (boarding and alighting). The variation in travel times across the day was comparatively higher than those of formal bus services and fluctuated across the day with no distinct pattern within any given time period. Both early and late trips contributed to this variation across the day. Fridays had significantly different variability from other weekdays. [ABSTRACT FROM AUTHOR]

When predicting public transport routes in cities, important indicators should be considered: the duration of stay on the bus route, passenger flow on the bus route, points of attraction and the passenger’s average waiting time at stops. These indicators are the basis for planning the operation of city transport. In particular, predicting the duration of traffic by studying the average passenger’s waiting time at stops is an important planning tool for transport companies. Therefore, this study can improve the quality of scheduled services by reducing the gap between actual and scheduled travel time. This article discusses this relevance and, based on experimental evidence, points to the benefit of using studies of average passenger waiting times, especially considering population groups. In fact, most of the factors which affect public transport operation, as had been proven by previous studies, follow a definite mathematical methodology. The analysis was performed using the data from field studies of passenger flow at bus stops (Lviv, Ukraine). The study of passengers at stopping points makes it possible to improve the quality of public transport services (calculate travel duration between stops and the duration of stay at them more accurately). The duration of stay at selected objects depending on a number of passengers was studied. Also, there are given the results of a study of the waiting time of public transport passengers at bus stops are given. A comparison of the dependence of the bus waiting time on population groups was obtained. After receiving this information, system operators can design and adjust the data according to the estimated trip duration. Nevertheless, it is necessary to carry out research at different types of stops in different parts of cities to clarify these data and for a more detailed analysis.

The evaluation of performance of public transportation, such as bus lines for example, is a major issue for operators. To be able to integrate specific and local behaviors, microscopic simulations of the lines, modelling each buses on a daily basis, brings an actual added value in terms of precision and quality. A scientific deadlock then appears regarding the parameterization of the simulation model. In order to be able to gather relevant performance indicators on a potential evolution of the configuration of the line, validated and modifiable simulation models need to be developed. This study aims at proposing a model development methodology based on a multi-agent simulation framework and data inputs extracted by a hybrid approach combining machine learning (ML) trained on actual bus data to predict travel times and probabilistic distributions to accurately estimate travel time variability. It also aims to propose a two-step validation framework that exhibits the performance of the obtained model on a case study based on actual data. The results of the proposed approach are validated by a real case study of three bus lines, including a number of simulation scenarios, to study the impacts of bus recovery time and bus control strategies on bus punctuality. The results obtained show that proposed hybrid approach combining ML with probabilistic distributions outperforms probabilistic distributions on average. Overall, the results show a good fit with the actual Key Performance Indicator (KPI) used by bus operators.

ABSTRACTWhile much has been reported about bus travel times and their variability for formal bus services, little is known about travel time variation for paratransit, the dominant means of transportation in most low- and middle-income countries (LMICs). This study quantifies the components of paratransit travel time on a selected route in Kumasi, Ghana. It analyzes the variability of travel times within the day and from day to day. A mobile phone app was employed to conduct a travel time survey onboard paratransit vehicles on the study route. GPS and stop-related data were collected. Various travel time variability measures and heat map was used for within day and day-to-day variability analysis in both directions of the study section. About 16% of travel time in the study section was spent dwelling (boarding and alighting). The variation in travel times across the day was comparatively higher than those of formal bus services and fluctuated across the day with no distinct pattern within any given time period. Both early and late trips contributed to this variation across the day. Fridays had significantly different variability from other weekdays.

Accurate forecasting of bus travel time and its uncertainty is critical to service quality and operation of transit systems: it can help passengers make informed decisions on departure time, route choice, and even transport mode choice, and it also support transit operators on tasks such as crew/vehicle scheduling and timetabling. However, most existing approaches in bus travel time forecasting are based on deterministic models that provide only point estimation. To this end, we develop in this paper a Bayesian probabilistic model for forecasting bus travel time and estimated time of arrival (ETA). To characterize the strong dependencies/interactions between consecutive buses, we concatenate the link travel time vectors and the headway vector from a pair of two adjacent buses as a new augmented variable and model it with a mixture of constrained multivariate Gaussian distributions. This approach can naturally capture the interactions between adjacent buses (e.g., correlated speed and smooth variation of headway), handle missing values in data, and depict the multimodality in bus travel time distributions. Next, we assume different periods in a day share the same set of Gaussian components, and we use time-varying mixing coefficients to characterize the systematic temporal variations in bus operation. For model inference, we develop an efficient Markov chain Monte Carlo (MCMC) algorithm to obtain the posterior distributions of model parameters and make probabilistic forecasting. We test the proposed model using the data from two bus lines in Guangzhou, China. Results show that our approach significantly outperforms baseline models that overlook bus-to-bus interactions, in terms of both predictive means and distributions. Besides forecasting, the parameters of the proposed model contain rich information for understanding/improving the bus service, for example, analyzing link travel time and headway correlation using covariance matrices and understanding time-varying patterns of bus fleet operation from the mixing coefficients. Funding: This research is supported in part by the Fonds de Recherche du Quebec-Societe et Culture (FRQSC) under the NSFC-FRQSC Research Program on Smart Cities and Big Data, the Canadian Statistical Sciences Institute (CANSSI) Collaborative Research Teams grants, and the Natural Sciences and Engineering Research Council (NSERC) of Canada. X. Chen acknowledges funding support from the China Scholarship Council (CSC). Supplemental Material: The e-companion is available at https://doi.org/10.1287/trsc.2022.0214. [ABSTRACT FROM AUTHOR]

Abstract Improving bus travel time reliability can attract more commuters to use bus transit, and therefore reduces the share of cars and alleviates traffic congestion. This paper formulates a new bus travel time reliability metric that jointly considers two stochastic processes: the in-stop waiting process and in-vehicle travel time process, and the bus travel time reliability function is calculated by the convolution of independent events’ probabilities. The new reliability metric is defined as the probability when bus travel time is less than a certain threshold and can be used in both conditions with and without bus transfer. Next, Automatic Vehicle Location (AVL) data of the city of Harbin is used to demonstrate the applicability of the proposed method. Results show that factors such as weather, day of the week, departure time, travel distance, and the distance from the boarding stop to the bus departure station can significantly affect the travel time reliability. Then, a case with low bus departure frequency is analyzed to show the impact of travelers’ arrival distribution on their bus travel time reliability. Further, it is demonstrated that the travel time reliabilities of two bus transfer schemes of the same Origin–Destination (O–D) pair can have significantly different patterns. Understanding the bus travel time reliability pattern of the alternative bus routes can help passengers to choose a more reliable bus route under different conditions. The proposed bus travel time reliability metric is tested to be sensitive to the effect of different factors and can be applied in bus route recommendation, bus service evaluation, and optimization.

Travel time variability (TTV) is the key indicator used in assessing the service quality of bus transit system. This study explores the most appropriate model to describe the day-to-day TTV of bus section. By investigating a 7-month travel time data for 10 bus routes in Klang Valley, Malaysia, this study demonstrates that Burr distribution is the most promising model in describing bus TTV. Bus TTV is found to be sensitive to both temporal and spatial effect. This means that TTV service varies for weekdays and weekends (temporal). Also, it differs for the five operating environments (spatial) investigated in this study. The Burr regression analysis conducted in the second part of this study further confirmed that bus section length and traffic signal density are the major contributing factors to bus TTV. However, both factors have varying levels of impact under different spatiotemporal effect. For example, in the suburban and residential areas, these factors cause higher TTV on weekends but lesser during weekdays, while a vice versa impact is observed in the Central Business District. This distinguishes from earlier studies which purely assumed normality in the regression analysis while not emphasizing the importance of spatiotemporal factors on TTV. Thus, this study serves as an analysis tool that could be used in the planning of bus routes and schedules under varying bus operating environments and operation times.

The prediction of bus travel time with accuracy is a significant step toward improving the quality of public transportation. Drawing meaningful inferences from the data and using these to aid in prediction tasks is always an area of interest. Earlier studies predicted bus travel times by identifying significant regressors, which were identified based on chronological factors. However, travel time patterns may vary depending on time and location. A related question is whether the prediction accuracy can be improved with the choice of input variables. The present study analyzes this question systematically by presenting the input data in different ways to the prediction algorithm. The prediction accuracy increased when the dataset was grouped, and separate models were trained on them, the highest accurate case being the one where the data-derived clusters were considered. This demonstrates that understanding patterns and groups within the dataset helps in improving prediction accuracy. [ABSTRACT FROM AUTHOR]

Evaluating the performance of public transportation, such as bus lines for example, is a major issue for Public Transportation operators. To be able to integrate specific and local behaviors, microscopic line simulations, modeling each buses on a daily basis, provide actual added value in terms of precision and quality. Carrying out more realistic and accurate simulations requires the use of appropriate parameters. To achieve this, machine learning models trained on real-world data can be used to feed and parameterize simulation models. To address this scientific question, it is necessary to determine how to efficiently integrate machine learning and simulation models. This study aims to couple machine learning and microscopic simulation models using various strategies, evaluate their accuracy and performance and discuss the advantages and drawbacks of each. A case study involving three bus lines was conducted, with results validated against real-world data, showing a good fit for both online and offline strategies. With the best simulation time, good accuracy and adequate travel times and bus punctuality, an offline strategy seems to stand out from other coupling strategies. [ABSTRACT FROM AUTHOR]

In recent years, deep learning models proved their ability to solve complex problems in the areas such as computer vision and natural language processing, and are receiving a lot of attention within the community of transportation systems as well. Though these are known as data-driven approaches, it is not yet reported whether providing a huge amount of data is sufficient or whether extra domain knowledge added as features will improve their performance. It is reasonable to expect that the performance of deep learning models will be improved by incorporating field-specific knowledge into the problem. This paper tries to address this question by taking Convolutional Neural Networks (CNNs) as a sample deep learning technique and comparing its performance with and without adding extra information about the data as feature input, for the application of bus travel time prediction. To extract extra information, the data are pre-processed using visual and statistical analyses, and the obtained knowledge is incorporated with the deep learning method. For pre-processing heat maps and statistical analysis were conducted using k-means clustering and Davies-Bouldin (DB) score to identify the optimum number of input groups. Further, the accuracy levels were compared with the deep learning method that was built with just data alone as input. The proposed models were evaluated on two selected bus routes, 19B and M1, in the City of Chennai, India. Results show that the provision of domain-related information having a positive impact on the prediction accuracy of up to 3% in selected routes. Performance comparison with existing methods such as historical average, linear regression, ANN, LSTM, and Conv-LSTM was also carried out and it was observed that the proposed method performed better than other existing methods. [ABSTRACT FROM AUTHOR]

Improving bus travel time reliability can attract more commuters to use bus transit, and therefore reduces the share of cars and alleviates traffic congestion. This paper formulates a new bus travel time reliability metric that jointly considers two stochastic processes: the in-stop waiting process and in-vehicle travel time process, and the bus travel time reliability function is calculated by the convolution of independent events' probabilities. The new reliability metric is defined as the probability when bus travel time is less than a certain threshold and can be used in both conditions with and without bus transfer. Next, Automatic Vehicle Location (AVL) data of the city of Harbin is used to demonstrate the applicability of the proposed method. Results show that factors such as weather, day of the week, departure time, travel distance, and the distance from the boarding stop to the bus departure station can significantly affect the travel time reliability. Then, a case with low bus departure frequency is analyzed to show the impact of travelers' arrival distribution on their bus travel time reliability. Further, it is demonstrated that the travel time reliabilities of two bus transfer schemes of the same Origin–Destination (O–D) pair can have significantly different patterns. Understanding the bus travel time reliability pattern of the alternative bus routes can help passengers to choose a more reliable bus route under different conditions. The proposed bus travel time reliability metric is tested to be sensitive to the effect of different factors and can be applied in bus route recommendation, bus service evaluation, and optimization. [ABSTRACT FROM AUTHOR]

Bus travel time analysis plays a key role in transit operation planning, and methods are needed for investigating its variability and for forecasting need. Nowadays, telematics is opening up new opportunities, given that large datasets can be gathered through automated monitoring, and this topic can be studied in more depth with new experimental evidence. The paper proposes a time-series-based approach for travel time forecasting, and data from automated vehicle monitoring (AVM) of bus lines sharing the road lanes with other traffic in Rome (Italy) and Lviv (Ukraine) are used. The results show the goodness of such an approach for the analysis and reliable forecasts of bus travel times. The similarities and dissimilarities in terms of travel time patterns and city structure were also pointed out, showing the need to take them into account when developing forecasting methods.

Traffic congestion has become the new normal on urban roads, and the congested road conditions have a significant impact on routine bus system, increasing the uncertainty of travel time. In order to explore the relationship between traffic congestion and bus travel time reliability, five road congestion evaluation indexes, including intersection saturation, intersection queue length, road saturation, average travel speed and average number of stops, are selected to construct a comprehensive road congestion evaluation model based on fuzzy mathematical theory to evaluate the congestion degree of the actual roads. On this basis, the road congestion index is used to modify the classical BPR function model and intersection delay model, and the bus route travel time reliability model based on road congestion level is established by taking the trip as the combination of multiple road units. Using road survey data, the feasibility of the model is verified and the bus travel time reliability is calculated for different congestion levels. The results show that the congestion level is negatively correlated with bus route travel time reliability, satisfying the quadratic function relationship, of which the model results are consistent with the reality. [ABSTRACT FROM AUTHOR]

The prevailing model in the studies that estimate bus travel time is the linear regression which assumes the limit of the normal distribution for all observations. Besides, survival models can calculate that the probability of an event can change over time. Thus, examining event probabilities that change over time is ideal for risky basic models such as survival ones. Although these kinds of models are used less in the research of bus travel time, in this study Accelerated Failure Time (AFT) survival models and linear regression models are compared in the form of two modeling approaches, link-based, and section-based. As for modeling the Automated Vehicle Location (AVL), data of 32 buses in line number 313 in Tehran (from Sepah Sq. to Enqelab Sq.) is used, including the information for one week for May, August, and November 2015. According to the results, the accuracy of survival models is better than the linear regression model in both modeling approaches. Furthermore, the performance of the linear regression model is unfavorable for both observations of short (less than 100 seconds) and long (more than 900 seconds) travel time. In addition, the particular lane that has been built in the opposite direction in this route reduces the bus travel time by an average of about 15.7 percent.

Travel time is a variable that varies over both time and space. Hence, an ideal formulation should be able to capture its evolution over time and space. A mathematical representation capturing such variations was formulated from first principles, using the concept of conservation of vehicles. The availability of position and speed data obtained from GPS enabled buses provide motivation to rewrite the conservation equation in terms of speed alone. As the number of vehicles is discrete, the speed-based equation was discretized using Godunov scheme and used in the prediction scheme that was based on the Kalman filter. With a limited fleet size having an average headway of 30 min, availability of travel time data at small interval that satisfy the requirement of stability of numerical solution possess a big challenge. To address this issue, a continuous speed fill matrix spatially and temporally was developed with the help of historic data and used in this study. The performance of the proposed Advanced Time-Space Discterization (AdTSD) method was evaluated with real field data and compared with existing approaches. Results show that AdTSD approach was able to perform better than historical average approach with an advantage up to 11% and 5% compared to Base Time Space Discretization (BTSD) approach. Also, from the results it was observed that the maximum deviation in prediction was in the range of 2–3 min when it is predicted 10 km ahead and the error is close to zero when it is predicted a section ahead i.e. when the bus is close to a bus stop, indicating that the prediction accuracy achieved is suitable for real field implementation. [ABSTRACT FROM AUTHOR]

An important aspect of Intelligent Public Transportation Systems (IPTS) is providing accurate travel time information. Knowing arrival times of public vehicles in advance can reduce waiting times of passengers and attract more people to take public transport. Existing approaches have two main limitations in the field of bus travel time prediction. First, influenced by increasingly complex real-time traffic factors and sparsity of real-time data, bus travel times can be difficult to predict accurately in modern cities. Second, bus dwelling and transit times are predominantly affected by different factors and hence have different patterns, but little research focuses on how to divide dwelling and transit areas and to build independent models for them. Consequently, we propose a novel segment-based approach to predict bus travel times using a combination of real-time taxi and bus datasets, that can automatically divide bus routes into dwelling and transit segments. Two models are built to predict them separately by incorporating different impact traffic factors. We evaluate our approach using real-world trajectory datasets, collected in Xi'an, China during June 2017. Compared to existing methods, the experimental results reveal that our approach improves the accuracy of bus travel time prediction, especially under abnormal traffic conditions. [ABSTRACT FROM AUTHOR]

The evaluation of performance of public transportation, such as bus lines for example, is a major issue for operators. To be able to integrate specific and local behaviors, microscopic simulations of the lines, modelling each buses on a daily basis, brings an actual added value in terms of precision and quality. A scientific deadlock then appears regarding the parameterization of the simulation model. In order to be able to gather relevant performance indicators on a potential evolution of the configuration of the line, validated and modifiable simulation models need to be developed. This study aims at proposing a model development methodology based on a multi-agent simulation framework and data inputs extracted by a hybrid approach combining machine learning (ML) trained on actual bus data to predict travel times and probabilistic distributions to accurately estimate travel time variability. It also aims to propose a two-step validation framework that exhibits the performance of the obtained model on a case study based on actual data. The results of the proposed approach are validated by a real case study of three bus lines, including a number of simulation scenarios, to study the impacts of bus recovery time and bus control strategies on bus punctuality. The results obtained show that proposed hybrid approach combining ML with probabilistic distributions outperforms probabilistic distributions on average. Overall, the results show a good fit with the actual Key Performance Indicator (KPI) used by bus operators. [ABSTRACT FROM AUTHOR]

The design of bus stops significantly affects bus operation. The delay time caused by inappropriate bus stop design adversely influences the efficiency of the system. This paper aims to examine the influence of bus stops on bus operating time components through statistical analysis, using Singapore as a case study. Two common types of bus stops, bus bay and curb-side stop, were investigated during the field survey to obtain actual data of bus operation at stops. Sixteen stops were chosen in pairs to compare the differences in operating time at bus stops. Bus operating times, including acceleration time, dwell time, deceleration time, and delay time, were recorded, with five types of delay time categorized. A total of 2,653 valid data records were collected and processed. The results showed that buses have better operational performance at curb-side stops than at bus bays in terms of average passenger boarding and alighting time and acceleration time. These findings have operational and planning implications for transport authorities and operators with regard to evaluating the performance of bus operation and improving the design of bus stops. [ABSTRACT FROM AUTHOR]

Bus travel times are prone to high variability, especially in countries that lack lane discipline and have heterogeneous vehicle profiles. This leads to negative impacts such as bus bunching, increase in passenger waiting time and cost of operation. One way to minimize these issues is to accurately predict bus travel times. To address this, the present study used a modelbased approach by incorporating mean and variance in the formulation of the model. However, the accuracy of prediction did not improve significantly and hence a machine learning-based approach was considered. Support vector machines were used and prediction was done using ν-support vector regression with linear kernel function. The proposed scheme was implemented in Chennai using data collected from public transport buses fitted with global positioning system. The performance of the proposed method was analysed along the route, across subsections and at bus stops. Results show a clear improvement in performance under high variance conditions. [ABSTRACT FROM AUTHOR]

Bus travel-time prediction has drawn a lot of research interests in previous literature. This paper proposes a prediction model for bus travel time based on the support vector machine (SVM) regression method. A forgetting factor is introduced to assign the weight to the recent data resulting from the bus running time-based variable quantities. The Grubbs' test method is applied to remove outliers from the input data. The proposed model is assessed with the data of transit route number 23 in the city of Dalian, China. Results show that the SVM with the forgetting factor and the Grubbs' test method is a powerful tool for bus travel-time prediction. [ABSTRACT FROM AUTHOR]

Accurate bus travel time prediction in real-time is challenging, as numerous factors such as fluctuating travel demand, incidents, signals, bus stops, dwell times, and seasonal variations can affect travel time, a spatio-temporal variable. Literature that considered the spatio-temporal evolution of bus travel time adopting traffic flow theory-based models investigated one-equation models (also widely known as first-order model) predominantly while the two-equation models (commonly known as higher-order models) have not been sufficiently explored due to their complex structure, parameters to calibrate, hardship in obtaining the data, and difficulty in discretizing and solving. Motivated by this, the present study explores the suitability of higher order traffic flow models for the prediction of bus travel time. This study adopted a well-known two-equation model 'Aw-Rascle model' (Aw and Rascle, 2000), which addressed most of the limitations of the previous models, and discretized using a Finite volume method to preserve the conservational properties of Partial Differential Equations (PDE). As Global Positioning System (GPS) is a widespread data source for transit systems, the identified model was rewritten in terms of speed by adopting a suitable pressure function. The discretized model was represented in the state-state-space form and integrated with a filtering technique using appropriate inputs, to facilitate real-time implementation. The performance of the proposed methodology was evaluated and compared with a first order model (Lighthill Whittam Richards (LWR) model) based approach to understand the efficacy of the higher-order models in travel time prediction. The prediction accuracy in terms of Mean Absolute Percentage Error (MAPE) was around 14% for the proposed methodology with an absolute deviation of around +/-1.2 min, which was better than the existing LWR model-based prediction method. The developed real-time prediction methodology is a promising one to be integrated with Advanced Public Transportation Systems (APTS) applications. [Display omitted] • A higher order traffic flow model based prediction method was developed based on Aw-Rascle model. • The model was simplified by Zhang's pressure function and exponential speed-density relationship. • The model was modified in terms of velocity for the purpose of travel time prediction. • Solved using Godunov's scheme to develop a spatio-temporal prediction equation. • Particle filter, a nonlinear recursive prediction tool was adopted to facilitate real-time implementation. [ABSTRACT FROM AUTHOR]

Abstract: Neural networks have been employed in a multitude of transportation engineering applications because of their powerful capabilities to replicate patterns in field data. Predictions are always subject to uncertainty arising from two sources: model structure and training data. For each prediction point, the former can be quantified by a confidence interval, whereas total prediction uncertainty can be represented by constructing a prediction interval. While confidence intervals are well known in the transportation engineering context, very little attention has been paid to construction of prediction intervals for neural networks. The proposed methodology in this paper provides a foundation for constructing prediction intervals for neural networks and quantifying the extent that each source of uncertainty contributes to total prediction uncertainty. The application of the proposed methodology to predict bus travel time over four bus route sections in Melbourne, Australia, leads to quantitative decomposition of total prediction uncertainty into the component sources. Overall, the results demonstrate the capability of the proposed method to provide robust prediction intervals. [Copyright &y& Elsevier]