Copula-Based Travel Time Distribution Estimation Considering Channelization Section Spillover

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

Travel time reliability (TTR) is widely used to evaluate transportation system performance. Adverse weather condition is an important factor for affecting TTR, which can cause traffic congestions and crashes. Considering the traffic characteristics under different traffic conditions, it is necessary to explore the impact of adverse weather on TTR under different conditions. This study conducted an empirical travel time analysis using traffic data and weather data collected on Yanan corridor in Shanghai. The travel time distributions were analysed under different roadway types, weather, and time of day. Four typical scenarios (i.e., peak hours and off-peak hours on elevated expressway, peak hours and off-peak hours on arterial road) were considered in the TTR analysis. Four measures were calculated to evaluate the impact of adverse weather on TTR. The results indicated that the lognormal distribution is preferred for describing the travel time data. Compared with off-peak hours, the impact of adverse weather is more significant for peak hours. The travel time variability, buffer time index, misery index, and frequency of congestion increased by an average of 29%, 19%, 22%, and 63%, respectively, under the adverse weather condition. The findings in this study are useful for transportation management agencies to design traffic control strategies when adverse weather occurs.

Understanding the nature of human movement is important in many fields, such as transportation management, urban planning, and epidemiology. In this study, we focus on travelers who are grouped by their travel modes in the Tokyo Metropolitan Area. Notably, for each group of travelers, the distribution of daily travel time follows a lognormal distribution. For any travel mode, the distributions of normalized travel time for different years (1968–2008) and distances to the city center converge to a curve, although the average travel time and share of travel modes vary. By employing the concept of utility, we developed a disaggregate model wherein an individual maximizes utility from traveling (=benefit - cost) by modifying daily travel time. This model theoretically explained the observed distributions of travel time. The model was further used to demonstrate travel mode choices. The model parameters were estimated using the distribution of travel time, travel mode share, and manageable assumptions. These results provided interesting interpretations of the perceptual utility of the daily travel time of a population. Moreover, the obtained curves of utility versus time are similar to the shapes of the overall benefits assumed in previous studies. Overall benefit is a concept that has been developed and examined since the 1980s, and our study provides a mathematical foundation for this idea.

Vehicle travel time on arterial roads is a crucial parameter for traffic management and traveler information systems. A travel time distribution is an effective way to represent the essential properties of this parameter. This paper proposes a modified Gaussian Mixture Model for representing travel time distributions on arterial roads with signalized intersections. The proposed model is applicable to travel time data from both fixed and mobile sensors. The performance of the model was evaluated using real travel time measurements from fixed sensors in the field and virtual mobile sensor data generated from those real-world measurements. The evaluation results show very good performance of the model in representing the traffic state on arterial roads. The model can be applied to historical datasets to estimate the amount of stop time and non-stop time for vehicles on arterial links during a specific time period, which is useful information for a variety of traffic applications, such as arterial travel time prediction and arterial traffic energy/emission estimation.

Riverbank filtration (RBF) is a surface water treatment technology that uses the aquifer adjacent to the river as a natural filter. A production well in the aquifer near the river draws water from both the aquifer and the river. As river water travels through the aquifer to the well, contaminants in the water undergo biologic and chemical reactions while traveling through the subsurface materials, leading to higher quality water at the well as compared with the river. A key parameter in siting the RBF well is the travel time of the contaminants from the river to the well, which must be sufficiently long to allow adequate time for biologic and chemical reactions to occur. Because the well induces flow into the aquifer from all along the river channel, multiple travel paths exist between the river and the well, each with a different contaminant travel time. The water produced at the well contains a collection of contaminant particles from these multiple travel paths and can be characterized by a distribution of travel times. The travel time of the contaminant depends on the groundwater velocity along the flow path, the sorption properties of the contaminant and the aquifer matrix, and the chemical reactions that occur during transport. In this work, we demonstrate the use of an adjoint-based modeling approach to characterize the distribution of travel times at the RBF well. In adjoint modeling, transport is modeled backward in space and time, from the point of view of the RBF well. The output of an adjoint simulation is the distribution of solute travel times at the RBF well at any time of interest. We consider different sorption models and sorption parameters, and we consider different chemical reactions and reaction rates. We simulate the travel time distributions using either MT3DMS or RT3D, depending on the type of chemical reaction, using a flow field generated using MODFLOW.

Travel time distribution studies are fundamental for supporting transportation system reliability studies, particularly for urban road networks. However, such studies are generally based on travel time data sets with limited sample sizes, which provide inconsistent findings. In this paper, a large amount of travel time data collected from the emerging radio frequency identification (RFID) technique are used to conduct empirical investigations and estimations of travel time distributions, and three major findings are determined. First, travel time data are shown to have a complex statistical structure: the travel time distribution is in general peaky, multi-modal, and skewed to the right, which cross validates findings shown in previous publications. Second, unimodal distribution models are shown to be unable to capture the complex statistical dynamics embedded in the travel time data; therefore, a multistate distribution model is more appropriate for modeling travel time distributions. In this respect, a three-component gaussian mixture model (GMM) is tested and results consistently outperform those of unimodal distribution models. Finally, the aggregation time interval is shown to have a trivial effect on the shape of travel time distributions: the travel time distribution is stable under different aggregation time intervals. Future work is recommended to investigate further travel time variabilities and travel time distribution estimations.

A novel generative adversarial network for estimation of trip travel time distribution with trajectory data

In an urban road network, travel times are not uniquely determined by the traffic states due to stochastic properties of traffic flow, stochastic arrivals and departures at intersections and traffic signal control. As a result, for a given traffic state, a range of travel times (delays) is found. This can be represented by a distribution of travel times (delays). Calibrating a model for the travel time only for the expectation value gives a large ‘noise’ such that the model will have little value for the prediction purpose. In this paper, the delay distribution function as derived from the analytical model under different circumstances is introduced. The overflow queue distribution which is the parameter in the delay distribution function is estimated based on traffic measurements, e.g., the measured delays, flows and cycle time. The Least Squares (LS) and Maximum Likelihood (ML) Estimation are used to perform the parameter estimation in the delay distribution. The Genetic Algorithm (GA) is applied to find the optimal solution for the objective functions in terms of minimizing square error and maximizing the likelihood function. Based on the estimated model parameters, the delay distribution is reconstructed. The estimated delay distribution is compared with that obtained from VISSIM simulation. Results show that both ML and LS estimation methods perform well in the undersaturated condition. While in the oversaturated condition, the ML method performs considerably better than the LS method.

It is widely accepted that travelers value both the reliability of travel time and its mean or expected value. Strategies for traffic signal control typically seek to optimize average travel times, although reliability is in general not explicitly taken into account. In this paper, we propose a new framework for evaluating the consequences of signal-control tactics on both reliability and expected values of travel time, based on an analytic model of travel time distribution. A genetic-algorithm-based approach is then employed to identify optimal multicriteria signal control strategies, including sensitivity analysis, to the relative weighting between reliability and expected value. We expose the properties of the proposed framework via an empirical case study of four alternative optimization approaches (the signal setting optimized with the traditional Webster's method, TRANSYT model, and the newly proposed model) under various traffic conditions. Results indicate that the newly proposed framework outperforms the alternative signal control strategies in terms of both travel-time variability and expected travel time.

Valuing travel time variability: Characteristics of the travel time distribution on an urban road

The 6th edition of the Highway Capacity Manual (HCM-6) includes the concept of travel time reliability (TTR), which attempts to determine the distribution of average trip travel times over an extended period. TTR is an inherent part of travelers’ route choice decisions and is used by traffic managers to better quantify operations rather than simply using average travel times. The focus of this paper is on the HCM-6 urban street TTR methodology contained in Chapter 17. The approach uses historical data (e.g., weather and volume fluctuations) and simple empirical data (e.g., 1-day volume count) to provide the user with average travel time and reliability predictions for a traffic facility over an extended period (e.g., a year). To the best of the authors’ knowledge, there is no existing literature on validating the HCM-6 methodology with empirical data. The goals of this paper were to validate the HCM-6 urban street reliability methodology by comparing the empirical Bluetooth (BT) travel time distributions with the estimated HCM-6 distribution, and to propose potential HCM-6 augmentation strategies. Archived BT data from a 0.5-mi urban arterial in Lincoln, Nebraska was used for comparison. It was found that there were statistically significant differences, but minimal practical differences, between the mean of the predicted HCM-6 travel time distribution and the mean of the empirical distribution. However, the HCM-6 distribution had a lower variance than the empirical distribution. Not surprisingly, the HCM-6 model underestimated the TTR metrics (buffer index and the planning time index) by approximately 62% and 9%, respectively.

Semi-exclusive right-of-way trams were considered in this research. Compared with subways, the travel time of trams fluctuates greatly due to manual driving and control by traffic signal at intersections. In this work, schedule optimisation was combined with signal timing optimisation of intersections along a tramline to improve the robustness of tram operation (i.e. the ability to resist relatively small-scale delays). On the basis of the normal needed travel time, an appropriate slack time is added to the timetable to absorb delays during tram operation. Based on historical tram trajectory data, the tram's travel time distribution at each running section/station was obtained. The PM-Band passive signal priority model was used to construct an integer programming problem to solve the slack time of timetable and signal timing at intersections. Finally, a tram robustness evaluation simulation model was established based on historical data and the robustness of the timetable was tested by adding random interference time in the tram travel process. The result shows that, compared with the traditional method, the modified timetable has great advantages in indicators such as average punctuality rate, standard deviation of the whole travel time and average delay time.

Here we present a theoretical interpretation of high‐frequency, high‐quality tracer time series from the Hafren catchment at Plynlimon in mid‐Wales. We make use of the formulation of transport by travel time distributions to model chloride transport originating from atmospheric deposition and compute catchment‐scale travel time distributions. The relevance of the approach lies in the explanatory power of the chosen tools, particularly to highlight hydrologic processes otherwise clouded by the integrated nature of the measured outflux signal. The analysis reveals the key role of residual storages that are poorly visible in the hydrological response, but are shown to strongly affect water quality dynamics. A significant accuracy in reproducing data is shown by our calibrated model. A detailed representation of catchment‐scale travel time distributions has been derived, including the time evolution of the overall dispersion processes (which can be expressed in terms of time‐varying storage sampling functions). Mean computed travel times span a broad range of values (from 80 to 800 days) depending on the catchment state. Results also suggest that, in the average, discharge waters are younger than storage water. The model proves able to capture high‐frequency fluctuations in the measured chloride concentrations, which are broadly explained by the sharp transition between groundwaters and faster flows originating from topsoil layers.

Analyzing travel time distribution based on different travel time reliability patterns using probe vehicle data

Route travel time information is essential for better travel planning, traffic guidance and congestion avoidance. An available way of representing such information is the estimation of travel time distribution (TTD). However, most methods both in literature and practice prefer to estimate route mean travel times rather than TTDs, especially with less consideration about the spatiotemporal correlations between adjacent links. This study develops a framework of estimating urban route TTD based on Markov chain approach and pair-copula construction with emphasis on capturing the dependence in time and space. The proposed method is validated with Radio Frequency Identification Data collected from an urban arterial in Nanjing, China. The results indicate that the proposed method can dynamically capture the positively correlated, negatively correlated, and uncorrelated relationships between adjacent link travel times. Moreover, the performance of the proposed method produces the least deviation from the route empirical distributions, compared to the considered competing methods.