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.     

Estimating bike-share trips using station level data

Bicycle sharing systems (BSS) have increased in number rapidly since 2007. The potential benefits of BSS, mainly sustainability, health and equity, have encouraged their adoption through support and promotion by mayors in Europe and North America alike. In most cases municipal governments desire their BSS to be successful and, with few exceptions, state them as being so. New technological improvements have dramatically simplified the use and enforcement of bicycle return, resulting in the widespread adoption of BSS. Unfortunately little evaluation of the effectiveness of differently distributed and managed BSS has taken place. Comparing BSS systems quantitatively is challenging due to the limited data made available. The metrics of success presented by municipalities are often too general or incomparable to others making relative evaluations of BSS success arduous. This paper presents multiple methodologies allowing the estimation of the number of daily trips, the most significant measure of BSS usage, based on data that is commonly available, the number of bicycles available at a station over time. Results provide model coefficients as well as trip count estimates for select cities. Of four spatial and temporal aggregate models the day level aggregation is found to be most effective for estimation. In addition to trip estimation this work provides a rigorous formalization of station level data and the ability to distinguish spatio-temporal rebalancing quantities as well as new characteristics of BSS station use.     

Predicting travel time reliability using mobile phone GPS data

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

Transit network design based on travel time reliability

This paper presents a transit network optimization method, in which travel time reliability on road is considered. A robust optimization model, taking into account the stochastic travel time, is formulated to satisfy the demand of passengers and provide reliable transit service. The optimization model aims to maximize the efficiency of passenger trips in the optimized transit network. Tabu search algorithm is defined and implemented to solve the problem. Then, transit network optimization method proposed in this paper is tested with two numerical examples: a simple route and a medium-size network. The results show the proposed method can effectively improve the reliability of a transit network and reduce the travel time of passengers in general.     

On the value of highway travel time information systems

After the widespread deployment of Advanced Traveler Information Systems, there exists an increasing concern about their profitability. The costs of such systems are clear, but the quantification of the benefits still generates debate. This paper analyzes the value of highway travel time information systems. This is achieved by modeling the departure time selection and route choice with and without the guidance of an information system. The behavioral model supporting these choices is grounded on the expected utility theory, where drivers try to maximize the expected value of their perceived utility. The value of information is derived from the reduction of the unreliability costs as a consequence of the wiser decisions made with information. This includes the reduction of travel times, scheduling costs and stress. This modeling approach allows assessing the effects of the precision of the information system in the value of the information.Different scenarios are simulated in a generic but realistic context, using empirical data measured on a highway corridor accessing the city of Barcelona, Spain. Results show that travel time information only has a significant value in three situations: (1) when there is an important scheduled activity at the destination (e.g. morning commute trips), (2) in case of total uncertainty about the conditions of the trip (e.g. sporadic trips), and (3) when more than one route is possible. Information systems with very high precision do not produce better results. However, an acceptable level of precision is completely required, as information systems with very poor precision may even be detrimental. The paper also highlights the difference between the user value and the social value of the information. The value of the information may not benefit only the user. For instance, massive dissemination of travel time information contributes to the reduction of day-to-day travel time variance. This favors all drivers, even those without information. In these situations travel time information has the property that its social benefits exceed private benefits (i.e. information has positive externalities). Of course, drivers are only willing to cover costs equal or smaller than their private benefits, which in turn may justify subsidies for information provision.     

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.     

A bi-objective user equilibrium model of travel time reliability in a road network

Travel time, travel time reliability and monetary cost have been empirically identified as the most important criteria influencing route choice behaviour. We concentrate on travel time and travel time reliability and review two prominent user equilibrium models incorporating these two factors. We discuss some shortcomings of these models and propose alternative bi-objective user equilibrium models that overcome the shortcomings. Finally, based on the observation that both models use standard deviation of travel time within their measure of travel time reliability, we propose a general travel time reliability bi-objective user equilibrium model. We prove that this model encompasses those discussed previously and hence forms a general framework for the study of reliability related user equilibrium. We demonstrate and validate our concepts on a small three-link example.     

An analysis of the factors influencing differences in survey-reported and GPS-recorded trips

Recent advances in global positioning systems (GPS) technology have resulted in a transition in household travel survey methods to test the use of GPS units to record travel details, followed by the application of an algorithm to both identify trips and impute trip purpose, typically supplemented with some level of respondent confirmation via prompted-recall surveys. As the research community evaluates this new approach to potentially replace the traditional survey-reported collection method, it is important to consider how well the GPS-recorded and algorithm-imputed details capture trip details and whether the traditional survey-reported collection method may be preferred with regards to some types of travel. This paper considers two measures of travel intensity (survey-reported and GPS-recorded) for two trip purposes (work and non-work) as dependent variables in a joint ordered response model. The empirical analysis uses a sample from the full-study of the 2009 Indianapolis regional household travel survey. Individuals in this sample provided diary details about their travel survey day as well as carried wearable GPS units for the same 24-h period. The empirical results provide important insights regarding differences in measures of travel intensities related to the two different data collection modes (diary and GPS). The results suggest that more research is needed in the development of workplace identification algorithms, that GPS should continue to be used alongside rather than in lieu of the traditional diary approach, and that assignment of individuals to the GPS or diary survey approach should consider demographics and other characteristics.     

Estimating travel time functions for urban roads: options and issues

Travel time functions specify the relationship between the travel time on a road and the volume of traffic on the road. Until recently, the parameters of travel time functions were rarely estimated in practice; however, a compelling case can be made for the empirical examination of these functions. This paper reviews, and qualitatively evaluates, a range of options for developing a set of travel time functions. A hierarchy of travel time functions is defined based on four levels of network detail: area, corridor, route and link. This hierarchy is illustrated by considering the development of travel time functions for Adelaide. Alternative sources of data for estimating travel time functions are identified.

In general, the costs and benefits increase as the travel time functions are estimated at finer levels of network detail. The costs of developing travel time functions include data acquisition costs and analysis costs. The benefits include the potential for reducing prediction errors, the degree of application flexibility and the policy sensitivity of the travel time functions.     

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.

Dynamic travel time prediction using data clustering and genetic programming

The current state-of-practice for predicting travel times assumes that the speeds along the various roadway segments remain constant over the duration of the trip. This approach produces large prediction errors, especially when the segment speeds vary temporally. In this paper, we develop a data clustering and genetic programming approach for modeling and predicting the expected, lower, and upper bounds of dynamic travel times along freeways. The models obtained from the genetic programming approach are algebraic expressions that provide insights into the spatiotemporal interactions. The use of an algebraic equation also means that the approach is computationally efficient and suitable for real-time applications. Our algorithm is tested on a 37-mile freeway section encompassing several bottlenecks. The prediction error is demonstrated to be significantly lower than that produced by the instantaneous algorithm and the historical average averaged over seven weekdays (p-value <0.0001). Specifically, the proposed algorithm achieves more than a 25% and 76% reduction in the prediction error over the instantaneous and historical average, respectively on congested days. When bagging is used in addition to the genetic programming, the results show that the mean width of the travel time interval is less than 5 min for the 60–80 min trip.     

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.     

On including travel time reliability of road traffic in appraisal

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

Review of optimal sensor location models for travel time estimation

The problem of optimally locating fixed sensors on a traffic network infrastructure has been object of growing interest in the past few years. Sensor location decisions models differ from each other according to the type of sensors that are to be located and the objective that one would like to optimize. This paper surveys the existing contributions in the literature related to the problem of locating fixed sensors on the network to estimate travel times. The review consists of two parts: the first part reviews the methodological approaches for the optimal location of counting sensors on a freeway for travel time estimation; the second part focuses on the results related to the optimal location of Automatic Vehicle Identification (AVI) readers on the links of a network to get travel time information.     

Additive measures of travel time variability

This paper derives a measure of travel time variability for travellers equipped with scheduling preferences defined in terms of time-varying utility rates, and who choose departure time optimally. The corresponding value of travel time variability is a constant that depends only on preference parameters. The measure is unique in being additive with respect to independent parts of a trip. It has the variance of travel time as a special case. Extension is provided to the case of travellers who use a scheduled service with fixed headway.     

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

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

Aggregation and travel time calculation over large scale traffic networks: An empiric study on the Grenoble City

In this paper we consider aggregation technique to reduce the complexity of large-scale traffic network. In particular, we consider the city of Grenoble and show that, by clustering adjacent sections based on a similarity of speed condition, it is possible to cut down the complexity of the network without loosing crucial and intrinsic information. To this end, we consider travel time computation as a metric of comparison between the original graph and the reduced one: for each cluster we define four attributes (average speed, primary and secondary length and heading) and show that, in case of an aggregation rate of 95%, these attributes are sufficient in order to maintain the travel time error below the 25%.     

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

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

A 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.     

Hierarchical travel demand estimation using multiple data sources: A forward and backward propagation algorithmic framework on a layered computational graph

Aiming to develop a theoretically consistent framework to estimate travel demand using multiple data sources, this paper first proposes a multi-layered Hierarchical Flow Network (HFN) representation to structurally model different levels of travel demand variables including trip generation, origin/destination matrices, path/link flows, and individual behavior parameters. Different data channels from household travel surveys, smartphone type devices, global position systems, and sensors can be mapped to different layers of the proposed network structure. We introduce Big data-driven Transportation Computational Graph (BTCG), alternatively Beijing Transportation Computational Graph, as the underlying mathematical modeling tool to perform automatic differentiation on layers of composition functions. A feedforward passing on the HFN sequentially implements 3 steps of the traditional 4-step process: trip generation, spatial distribution estimation, and path flow-based traffic assignment, respectively. BTCG can aggregate different layers of partial first-order gradients and use the back-propagation of “loss errors” to update estimated demand variables. A comparative analysis indicates that the proposed methods can effectively integrate different data sources and offer a consistent representation of demand. The proposed methodology is also evaluated under a demonstration network in a Beijing subnetwork.