Travel Time Distribution Research Articles

Travel Time Probability Prediction Based on Constrained LSTM Quantile Regression

Travel time reliability assessment has been widely used in recent years to evaluate the performance of transportation networks and measure the operation level of transportation systems. Weather, as one of the important factors influencing travel time reliability, affects the relationship between the supply and requirement of urban road networks. Considering the traffic characteristics under different traffic conditions, a study on the influence of weather on travel time reliability under different conditions is proposed to predict the probability of travelers completing their trips within the expected time under different weather conditions. Based on the urban road network data and cab trajectory data of Harbin city, this paper correlates the floating vehicle location with the road network information through a hidden Markov model to reduce the influence of vehicle trajectory errors on the calculation results of path travel time. To analyze the entire distribution of extreme travel time and its impact on the reliability of travel time under various traffic situations, it captures the tail features of the travel time distribution based on extreme value theory. Then, to increase the predictability of each quantile, it combines a deep-learning LSTM model and a quantile regression model to create a probabilistic travel time prediction model utilizing combined layers. The proposed model is compared with the linear quantile regression and neural network quantile regression models, and the model is evaluated in terms of point prediction results and probabilistic prediction results, respectively, to ensure the accuracy of predictions from the model. As a result, the prediction accuracy of the model in this paper is greatly improved, and the degree of violating quantile constraints is greatly reduced.

Short-term bus travel time prediction for transfer synchronization with intelligent uncertainty handling

This paper presents two novel approaches for uncertainty estimation adapted and extended for the multi-link bus travel time problem. The uncertainty is modeled directly as part of recurrent artificial neural networks, but using two fundamentally different approaches: one based on Deep Quantile Regression and the other on Bayesian neural network. Both approaches use a recurrent neural network to predict multiple time steps into the future, but handle the time-dependent uncertainty estimation differently. We present a novel sampling technique in order to aggregate quantile estimates for link level travel time to yield the multi-link travel time distribution needed for a vehicle to travel from its current position to a specific downstream stop point or transfer site.To motivate the relevance of uncertainty-aware models in the domain, we focus on the connection protection application as a case study: An expert system to determine whether a bus driver should hold and wait for a connecting service, thus ensuring the connection, or break the connection and reduce its own delay. Our results show that the proposed quantile sampling method performs overall best for the 80%, 90% and 95% prediction intervals, both for a 15 min time horizon into the future (t+1), but also for the 30 and 45 min time horizon (t+2 and t+3), with a constant, but very small underestimation of the uncertainty interval (1–4 pp.). However, we also show, that the Bayesian model still can outperform the DQR for specific cases. Lastly, we demonstrate how a simple decision support system can take advantage of our uncertainty-aware travel time models to prioritize the difference in travel time uncertainty for bus holding at strategic points, thus reducing the introduced delay for the connection protection application.

Travel Time Distribution Estimation by Learning Representations Over Temporal Attributed Graphs

Travel time estimation is a crucial task in practical transportation applications, while providing the reliability of estimation is important in many working scenarios. Most existing studies do not consider the dynamics of traffic status for different road segments in real time, thus yielding unsatisfactory results. To address the problem, we propose to formulate the traffic network as a temporal attributed graph and perform node representation learning on it. The learned representation is capable of jointly exploiting the dynamic traffic conditions and the topology of the road network, which is then fed into a route-based spatio-temporal dependence learning module to estimate the travel time. By incorporating a distribution loss function, our proposed model is able to predict the distribution of travel time. In the meantime, we design an auxiliary local task of predicting the congestion status of each road segment, which further enhances the generalization performance of the representation learning. Extensive experiments on real-world large-scale datasets demonstrated the superiority of our method compared with the state-of-the-arts.

Combining noisy well data and expert knowledge in a Bayesian calibration of a flow model under uncertainties: an application to solute transport in the Ticino basin

Groundwater flow modeling is commonly used to calculate groundwater heads, estimate groundwater flow paths and travel times, and provide insights into solute transport processes within an aquifer. However, the values of input parameters that drive groundwater flow models are often highly uncertain due to subsurface heterogeneity and geologic complexity in combination with lack of measurements/unreliable measurements. This uncertainty affects the accuracy and reliability of model outputs. Therefore, parameters’ uncertainty must be quantified before adopting the model as an engineering tool. In this study, we model the uncertain parameters as random variables and use a Bayesian inversion approach to obtain a posterior, data-informed, probability density function (pdf) for them: in particular, the likelihood function we consider takes into account both well measurements and our prior knowledge about the extent of the springs in the domain under study. To keep the modelistic and computational complexities under control, we assume Gaussianity of the posterior pdf of the parameters. To corroborate this assumption, we run an identifiability analysis of the model: we apply the inversion procedure to several sets of synthetic data polluted by increasing levels of noise, and we determine at which levels of noise we can effectively recover the “true value” of the parameters. We then move to real well data (coming from the Ticino River basin, in northern Italy, and spanning a month in summer 2014), and use the posterior pdf of the parameters as a starting point to perform an uncertainty quantification analysis on groundwater travel-time distributions.

Research on Relative Threshold of Abnormal Travel in Subway Based on Bilateral Curve Fitting

Abnormal passenger behavior in rail transit has become a top priority, as it affects operational safety. Passenger travel time is the main basis for identifying abnormal behavior while considering the flexibility of travel time. Currently, the main method is to use absolute threshold discrimination based on the distribution of travel time. However, there is a problem of missing abnormal passenger behavior due to the large difference in travel time between the Origin-Destinations (ODs). Therefore, this paper proposes a method of setting corresponding thresholds for each OD. By analyzing the percentile curves of the overall and individual OD pairs, it was found that the turning point of the curve had a significant feature, and the difference between the two sides of the curve was obvious. This paper proposes a bilateral fitting method, and the results show that this method can calculate the relative threshold for different OD pairs. The significant advantages of this method are its low cost and wide coverage.

Simulation of vehicle traffic at exit from the adjacent territory to main streets

Abstract. Problem. The transport systems of Ukrainian cities have a fairly high number of problem areas with difficult conditions for traffic, one such example being exits to main streets from adjacent territories. The probability of transport problems at such facilities is difficult to predict even at the design stage, which ultimately has negative consequences that affect the quality of transport services for road users within these facilities. These shortcomings are already being addressed by traffic management specialists who have transport modeling skills and have the appropriate software packages at their disposal. Goal. The main purpose of the article is to estimate vehicle delays at the adjacent territory exit to main streets using PTV VISSIM. Methodology. Development of a simulation model of the object selected for the study; assessment of traffic delays for the existing traffic management option; development of measures to improve traffic management at the selected object of experimental research and evaluation of their effectiveness. Results. The result of the simulation model is the animation of traffic in the form of a real-time graphic and the subsequent output of transport and technical parameters: travel time distribution, traffic delays, queue length, idle time, emissions, fuel consumption, which can be differentiated by user group. Originality. The results of the simulation of the proposed variant of transport service for traffic participants at the adjacent territory exit to main streets indicate its very high efficiency and the possibility of implementation even under conditions of a significant increase in the intensity of flows. Practical value. Using the traffic simulation model of adjacent territory exit to main streets developed in PTV VISSIM, which is based on the results of field observations of vehicle traffic, allows us to draw reasonable conclusions about improving the quality of transport service at the object selected for the study.

Feeder Bus Timetabling Optimization for High-Speed Railway Station with Uneven Departure Interval

This paper proposes a bus timetable with uneven departure interval, which is mainly used to optimize the bus timetable at high-speed railway stations. The railway comprehensive transportation hub is an important node for the connection between the internal and external transportation of the city. Efficient transfer efficiency can not only improve the travel satisfaction of passengers, but also enable public transport enterprises to retain passenger flow in the competition with rail enterprises. Therefore, this paper analyzes the travel time distribution law of railway passenger transfer to public transport, constructs a timetable optimization model that adapts to the passenger flow law, and uses genetic algorithm to solve it. The optimization results show that, without changing the departure frequency, the waiting time of passengers in peak hours using the uneven departure interval mode is reduced by 29.6%, and the waiting time in average peak hours is reduced by 16.2%. If the departure frequency is changed, the waiting time of passengers in the uneven departure interval mode will also be shorter than that in the equal time departure mode.

Development of a Machine-Learning-Based Novel Framework for Travel Time Distribution Determination Using Probe Vehicle Data

Investigating travel time variability is critical for pre-trip planning, reliable route selection, traffic management, and the development of control strategies to mitigate traffic congestion problems cost-effectively. Hence, a large number of studies are available in the literature which determine the most suitable distribution to fit the travel time data, but these studies recommend different distributions for the travel time data, and there is a disagreement on the best distribution option for fitting to the travel time data. The present study proposes a novel framework to determine the best distribution to represent the travel time data obtained from probe vehicles by using the modern machine learning technique. This study employs vast travel time data collected by fitting GPS tracking units on the probe vehicles and offers a comprehensive investigation of travel time distribution in different scenarios generated due to spatiotemporal variation of the travel time. The study also considers the effect of weather and uses the three most commonly used non-parametric goodness-of-fit tests (namely, Kolmogorov–Smirnov test, Anderson–Darling test, and chi-squared test) to fit and rank a comprehensive set of around 60 unimodal statistical distributions. The framework proposed in the study can determine the travel time distribution with 91% accuracy. Additionally, the distribution determined by the framework has an acceptance rate of 98.4%, which is better than the acceptance rates of the distributions recommended in existing studies. Because of its robustness and applicability in many different traffic situations, the proposed framework can also be used in developing countries with heterogeneous disordered traffic conditions to evaluate the road network’s performance in terms of travel time reliability.

Sociodemographic and Geographic Variation in Access to Neuro-Ophthalmologists in the United States.

Neuro-ophthalmologists have expertise in rare and complex disorders, but the ability of patients to access neuro-ophthalmic care has not been examined at a nationwide level. Using the 2020 directory of all 502 members of the North American Neuro-Ophthalmology Society as a reference, we found the practice locations of 461 confirmed practicing members and converted each street address to latitude and longitude coordinates. We calculated the travel distance and time from each census tract to the nearest practice location and calculated population-weighted averages by state, region, and other prespecified factors. Choropleth maps were used to visualize the distribution of travel distances and times across the United States. California had the most practicing neuro-ophthalmologists out of any state (50), whereas 4 states (DE, MT, SD, and WY) had none. Washington, DC and MA had the most neuro-ophthalmologists per capita. The average travel distance and time to the nearest neuro-ophthalmologists were found to be 40.90 miles and 46.50 minutes, respectively, although a large portion of western plains and mountain regions had travel times of over 120 minutes. Patients in rural areas had longer travel times than those in urban areas, and Native American patients had the longest travel times of any racial or ethnic group. The travel time to see a neuro-ophthalmologist varies widely by state, region, and rurality, with Native American patients and rural patients being disproportionately affected. By identifying the areas with the greatest travel burdens, future policies can work to alleviate these potential barriers to care.

Modified two-fluid model of traffic flow

ABSTRACT Researchers widely use the two-fluid model (TFM) to evaluate the performance of urban networks. However, the TFM is deterministic and does not capture the stochastic relation between speed and density. The present study develops a modified two-fluid model (MTFM). The variance function or the distribution of speed or travel time for a given density is incorporated using a percentile-based indicator, travel time uncertainty (TTU). The percentile-based indicators for the speed distribution are more robust than the variance or other moment-based indicators. The effect of TTU is incorporated using two parameters, and . The applicability of the proposed MTFM is demonstrated using empirical data collected at the corridor and network levels. The TFM and MTFM were calibrated by formulating a nonlinear optimization problem. Based on the investigation using the corridor and network-level data, it was concluded that the MTFM showed better performance than the existing model. .

Assessing the effect of construction-induced consolidation on groundwater travel time distribution under unconfined conditions

Assessing the effect of construction-induced consolidation on groundwater travel time distribution under unconfined conditions

Travel-time prediction using neural-network-based mixture models

Accurate estimation of travel times is an important step in smart transportation and smart building systems. Poor estimation of travel times results in both frustrated users and wasted resources. Current methods that estimate travel times usually only return point estimates, losing important distributional information necessary for accurate decision-making. We propose using neural network-based mixture distributions to predict a user's travel times given their origin and destination coordinates. We show that our method correctly estimates the travel time distribution, maximizes utility in a downstream elevator scheduling task, and is easy to retrain—making it a versatile and an inexpensive-to-maintain module when deployed in smart crowd management systems.

Using Empirical Travel Time Distributions for Calibration of a Model of Pedestrian Dynamics

Using Empirical Travel Time Distributions for Calibration of a Model of Pedestrian Dynamics

Multiprocessing for the Particle Tracking Model MODPATH.

Particle tracking has several important applications for solute transport studies in aquifer systems. Travel time distribution at observation points, particle coordinates in time and streamlines are some practical results providing information of expected transport patterns and interaction with boundary conditions. However, flow model complexity and simultaneous displacement of multiple particle groups leads to rapid increase of computational requirements. MODPATH is a particle tracking engine for MODFLOW models and source code displays potential for parallel processing of particles. This article addresses the implementation of this feature with the OpenMP library. Two synthetic aquifer applications are employed for performance tests on a desktop computer with increasing number of particles. Speed up analysis shows that dynamic thread scheduling is preferable for highly heterogeneous flows, providing processing adaptivity to the presence of slow particles. In simulations writing particles position in time, thread exclusive output files lead to higher speed up factors. Results show that above a threshold number of particles, simulation runtimes become independent of flow model grid complexity and are controlled by the large number of particles, then parallel processing reduces simulation runtimes for the particle tracking model MODPATH. Article impact statement: Parallel particles processing for MODPATH using the OpenMP library.

Probability distributions analysis of travel time variability for the public transit system

Travel time variability (TTV) plays a significant role in analysing the reliability of public transit system. The research works carried out on travel time variability under Indian traffic conditions are very few and these studies did not analyse the performance of travel time distribution in detail, considering different temporal and spatial aggregations. In this study, travel time variability is analysed using travel time distributions considering different temporal and spatial aggregations. The Automatic Vehicle Location (AVL) data of four transit routes of Mysore City, Karnataka, India are used to evaluate travel time distributions with respect to temporal aggregations (peak period, off-peak period, 60 minutes, 30 minutes and 15 minutes) and spatial aggregations (route level and segment level). The performance of travel time distributions is analysed using the Anderson-Darling (AD) test. The segments with signalised intersections and different land-use types are analysed to evaluate the distribution fit for various conditions. The results of both route and segment level analysis report highest accuracy and robustness values for Generalised Extreme Value (GEV) distribution. The distribution is proved to be superior in describing travel time variability of public transit.

Navigation With Time Limits in Transportation Networks: A Fourth Moment Approach

This paper investigates the stochastic on-time arrival (SOTA) problem in transportation networks. We propose a fourth moment approach (FMA), which calculates the tight lower bound of a given routing policy’s on-time-arrival probability, through estimating the first four moments of the policy’s travel time. Then, we employ the generalized policy iteration (GPI) scheme to gradually improve the policy towards the optimal one. Different from state-of-the-art algorithms for the SOTA problem, which require the full travel time distribution and usually incur high computational cost due to the convolution integration operation, FMA only requires the moments of travel-time statistics, which are easily estimated from the statistics perspective. Moreover, the algorithm’s computational complexity analysis indicates the relatively light computational load requirement of FMA. Experimental results in a range of transportation networks show FMA’s superior performance over state of the arts.

Performance evaluation of spatial lumped model and spatial distributed travel time model using event based rainfall for hydrological simulation

Performance evaluation of spatial lumped model and spatial distributed travel time model using event based rainfall for hydrological simulation

Molecular diffusion and pore-scale mechanical dispersion controls on time-variant travel time distribution in hillslope aquifers

The travel time distribution (TTD) is a lumped representation of the age composition of water leaving the system. Under nonstationary rainfall injection conditions, the TTD varies with transient groundwater flow, leading to a time-variant TTD. It reflects water and solute exports responding to rainfall. The time-variant TTD, time-variant residence time distribution (RTD) and storage selection function (SAS function) provide fundamental insights into transport and mixing processes in groundwater flow system. This study investigates the control of local-scale mixing (i.e., molecular diffusion and pore-scale mechanical dispersion) on time-variant TTD, RTD and SAS function. A solute transport model is constructed to simulate the time-variant TTD, RTD and SAS function under the influence of local-scale mixing; and a particle tracking model is applied to simulated time-variant TTD, RTD and SAS function without the influence of local-scale mixing. Generally, the TTD and cumulative TTD are found to be more sensitive to local-scale mixing than RTD and cumulative RTD due to the ‘volume effect’. The local-scale mixing smoothens the sharp fluctuations of backward TTD and SAS function. The differences of cumulative breakthrough curves and cumulative backward TTDs between two models deviate to negative value except the tails of the two functions, and this verifies the random velocity theory. The differences of cumulative RTDs between the two models indicate the hydrodynamic dispersion can result in more young water leaving the system and more old water remaining in the storage. Meanwhile, two rainfall time series, one with seasonality and one without seasonality, are applied in the two models separately; it is found that the hydrodynamic dispersion shapes the 2-dimensional backward TTD by increasing its continuity along the 45° direction. Finally, the spatial distribution of mean groundwater age is used to illustrate the local-scale mixing in the aquifer and further explain the controls of local-scale mixing on time-variant TTD, RTD and SAS function mechanistically.

Modelling electrical conductivity variation using a travel time distribution approach in the Duck River catchment, Australia

AbstractSolute dynamics depend strongly on hydrologic flow paths and transit times within catchments. In this paper, we use a travel time tracking method to simulate stream salinity (as measured by electrical conductivity) in the Duck River catchment, NW Tasmania, Australia. The study couples storage selection function transit time modelling with two alternate approaches to model electrical conductivity (EC). The first approach assumes the catchment has a cyclic salt balance (i.e., rainfall source, stream flow sink) that is in dynamic equilibrium and evapoconcentration of salt is the only process changing concentration. The second approach assumes that the salinity of water in catchment storages is a function of water age in those stores, without explicitly simulating salt mass balance processes. The paper compares these alternate approaches in terms of EC simulation performance, simulated stream water age distributions, and simulated storage age distributions. A split sample calibration‐validation analysis was conducted using the 2008 and 2009 water years. Both EC simulation approaches reproduced stream EC variations very well under both calibration and validation. The simulations using the age‐related EC simulation approach produced less biased results and, consequently, higher model coefficient of efficiency for validation periods. This approach also produced more consistent model parameter estimates between periods. There were systematic differences in the resultant age distributions between models, particularly for the solute balance‐based simulations where parameters (catchment storage size) changed more between the two calibration periods. The effect of time varying versus static storage selection functions were compared, with clear evidence that time varying storage selection functions with parameters linked to catchment conditions (flow) are essential for adequate simulation of EC dynamics during flow events.

Optimization of multi-type sensor locations for simultaneous estimation of origin-destination demands and link travel times with covariance effects

This paper investigates the multi-type traffic sensor location problem for simultaneous estimation of origin-destination (OD) demands and link travel times while also considering the two sources of spatial covariance effects on a road network with uncertainties. The first source is the statistical correlation of the vehicular traffic demands for different OD pairs in a typical hourly period (e.g., morning peak hour) on a daily scale, as the travel demand patterns vary daily, weekly, and seasonally over the year. The second source is the stochastic nature of the link travel times on different road links during the peak hour period and their correlation with adjacent links in congested conditions. By considering these aspects, a novel model is formulated to optimize the number and locations of multi-type traffic sensors for simultaneous estimation of stochastic OD demands and link travel times during the same peak-hour period over a year. This estimation is supported by the data recorded by multi-type traffic sensors such as point sensors and automatic vehicle identification sensors, which yield the link speed/flow and path travel time information, respectively. Based on the integrated observations from multi-type traffic sensors, a novel Kullback–Leibler divergence-based model is developed to accommodate different probability distributions of OD demands and link travel times in different traffic conditions. Moreover, an improved firefly algorithm is developed to solve the multi-type sensor location problem. Specifically, the search strategy of this algorithm is enhanced by considering the mean and covariance of the OD demands and link travel times. Numerical examples of synthetic and real-world road networks are used to illustrate the applications and merits of the developed multi-type sensor location model for simultaneously estimating the OD demands and link travel times while also considering covariance effects.