Travel Time Distribution Research Articles

Structural and hydrodynamic controls on fluid travel time distributions across fracture networks

Fracture networks are preferential flow paths playing a critical role in a wide range of environmental and industrial problems. Their complex multiscale structure leads to broad distributions of fluid travel times, affecting many biogeochemical processes. Yet, the relationship between the fracture network structures, their hydrodynamic properties, and the resulting anomalous transport dynamics remains unclear. We use a large database of fracture network models to investigate the factors controlling fluid velocity and travel-time distributions across a wide range of networks, from synthetic to field-calibrated models, with aperture variability at both fracture and network scales. Analysis reveals that transport statistics have generic properties across investigated networks, including notably heavy-tailed travel time distributions. Networks of increasing complexity and heterogeneity lead to broader velocity distributions and more channeled velocity fields, where flow concentrates in a narrow channel web in the three-dimensional (3D) fracture structure. While heterogeneity in point-velocity statistics increases travel-time variability, channeling tends to reduce it. This counterintuitive phenomenon challenges current theories, which assume that long travel time power law exponents are determined solely by point-velocity statistics. By analyzing velocity and travel time statistics for different flow structures, we develop a coupled Continuous Time Random Walk framework capturing the unexpected control of the velocity field's spatial structure on anomalous transport in fracture networks. This leads to a unique class of random walk models capturing the respective roles of velocity heterogeneity and spatial structure on transport in networks. These findings open a prospective for characterizing, modeling, and predicting transport dynamics in complex networks, with potential applications to geological, biological, and engineered networks.

Dynamic Optimization of Exclusive Bus Lane Location Considering Reliability: A Case Study of Beijing

For metropolises like Beijing, heavy congestions cause transit passengers’ unreliable travel time, including in vehicle time and waiting time. Comparing with other managerial measures, designing a lane for bus use only is an effective method to improve travel reliability, for it can eliminate the influence on bus-driving conditions. This paper proposes a reliable and practical method to determine exclusive bus lanes (EBL). A reliability-based optimization model is established, in which the tradeoff among bus and private car passengers’ travel time, reliability, and EBL construction cost are considered. Based on the actual network, a user equilibrium demand assignment model is applied to estimate the dynamic bus flow distribution. Since the model is nonlinear, a two-step method is proposed where tangent lines are introduced to constitute an envelope curve to linearize the model. This work conducts the statistical modeling and fitting analysis with actual bus trajectory data, collected on EBL in Beijing during peak hours. Passenger travel time distributions are fitted to estimate the statistical passenger travel time; Lognormal distribution and Gaussian distribution are the best fit. The optimization results indicate that the passenger travel time reliability can be improved by 5.5% by the optimized EBL location scheme. This study will provide a theoretical basis and methodological support for improving the service level of the public transportation system in large cities through the scientific planning of exclusive bus lanes.

Estimation of vessel link-level travel time distribution: A directed network-driven approach

Accurate vessel travel time estimation is essential for operational efficiency and route optimization. Despite the prevalent use of the automatic identification system (AIS) in garnering multifaceted real-time data, ambiguities and inaccuracies in travel time predictions persist. It leads to planning uncertainties, inefficient resource allocations, and heightened operational costs in maritime logistics. To addresses these issues, this paper proposed a nuanced method to enhance the precision and reliability of vessel travel time estimations. Firstly, a directed maritime network is constructed by extracting essential information from AIS-based historical vessel trajectories. This lays the foundation for the subsequent analytical processes. Secondly, the non-parametric kernel density estimation (KDE) is applied to this constructed network, enabling the estimation of vessel travel time distributions across various network links. The non-parametric KDE is used in combination with AIS data, which improves the specificity and accuracy of the travel time estimations at the link level. Finally, this paper employs cellular automata (CA) simulations to validate the accuracy of the KDE-based estimations. Comparison between the simulation results and real-world data reveals a high degree of accuracy in the proposed method, confirming its applicability and effectiveness in estimating vessel travel times.

Agent-based digital traffic model generation for regions facing data scarcity using aggregated cellphone data: a case study for Brussels

ABSTRACT The adoption of agent-based models (ABMs) in transport research has highlighted their potential in digitally simulating travel behaviour from a bottom-up perspective. However, generating ABMs remains a complex multi-step process, often suffering from the lack of model representation or reliance on proprietary data, thereby limiting ABMs' transferability, especially in regions facing data scarcity. This research presents a systematic ABM generation algorithm for Brussels, Belgium, that generates high-quality ABMs more representative of real-life travel patterns, including incorporating external travel demand and allowing multiple destinations for the same activity types in activity chaining. Additionally, our algorithm's input data only contains social-spatial data and aggregated cellphone matrices. Due to the ubiquitous nature of such data worldwide, our algorithm demonstrates significant transferability to other regions for ABM generation while preserving individual privacy. We demonstrate the input data and the proposed algorithm step by step. The ABM generated using MATSim is validated against real-world data regarding mode share, distance share, travel time distribution and traffic counts. Overall, this research would serve as valuable guidance for ABM modellers in data collection and specific modelling setups, lowering the entry barrier of ABM research towards more efficient, representative and reproducible ABMs.

Electrical conductivity fluctuations as a tracer to determine time-dependent transport characteristics in hyporheic sediments

Assessing solute transport in riverbed sediments is important for quantifying the effective reactivity of hyporheic sediments and the magnitude of exchange flows between rivers and their river beds. A typical approach of estimating transport in riverbed sediments is by measuring natural tracers such as fluctuations of temperature or electrical conductivity (EC) and fitting models to them that assume time-independent travel time distributions, implying steady-state flow. Here, we use a transport parameterization that is based on the advection–dispersion equation (ADE) with coefficients that continuously vary in time. The ADE is solved numerically and its solution is fitted to measured EC time series using Bayesian parameter inference. A continuous function of model parameters is constructed by smoothly interpolating between point values with different temporal resolution, and Tikhonov regularization is used to avoid spurious parameter fluctuations. The approach is tested using EC time series synchronously measured in river water and hyporheic porewater of two urban rivers in Germany and one urban river in South Australia. For all datasets the goodness of fit was improved by introducing a time-dependent EC offset. Estimated porewater velocities were highly transient in three out of the four datasets with values increasing by up to a factor of six over the course of a day. Flux transients were likely related to both variations of hydraulic gradients along and spatial shifting of flow paths. Comparison to stationary, non-parametric deconvolution indicated that transient flow may induce multimodality in stationary travel time distributions. Given the high temporal dynamics of transport in the streambed sediments of the three investigated urban rivers, we envision that the presented model is also a valuable tool to improve the assessment of reactive transport in riverbed sediments.

Potential Amplifiers of Hydrological Drought: A Deep Dive into the Seasonal Variations of New, Young, and Old Water Fractions in the Stream Discharge of a Pre-Alpine Catchment

This study examines runoff generation processes by focusing on new, young, and old water fractions in the stream discharge within the Swiss pre-Alpine Alp catchment and its smaller tributaries, Erlenbach and Vogelbach. Young water represents a contribution from the three most recent rainfall-runoff events. This research utilises a four-year time series of daily stable water isotope data from stream water and precipitation to investigate seasonal variations. An extended two-component hydrograph separation method is applied to analyse the catchment water and tracer mass balance across both the event and pre-event time axes. The calculated new, young and old water components in stream discharge help estimate time-varying backward travel time distributions. Factors such as air temperature, snow depth, and evapotranspiration data are considered to understand isotope fractionation because of phase changes. The results suggest that discharge generated in autumn and winter may have longer backward travel times compared with spring or summer discharge. Additionally, forest cover influences water fractions older than 40 days. The study identifies a nivo-pluvial runoff regime, with new water fractions peaking in August (Erlenbach, Vogelbach) and January (Alp). Young water fractions reach their highest levels at the start of winter and during snowmelt, while old water fractions peak towards the end of snowmelt and in mid-autumn. The Alp catchment and its tributaries exhibit higher new and young water components than old water following a month of low precipitation and high evapotranspiration in July. These findings are significant in light of the projected drier summers in Central Europe.

Nitrate trend reversal in Dutch dual-permeability chalk springs, evaluated by tritium-based groundwater travel time distributions

Historical use of fertilizer and manure on farmlands is known to have a lasting impact on ecosystems and water resources, but few studies assess the legacy of nitrate pollution on groundwater and surface water after farming applications were reduced. We studied the response of nitrate in spring water to a reduction of nitrogen fertilizer applications in agriculture realized since the mid-1980s. We assessed the travel time distribution of groundwater based on a time series of tritium measurements for 90 springs and small brooks that drain a dual porosity chalk aquifer. The travel time distributions were constrained using the tritium data in combination with time series of nitrate concentrations, applying a shape-free travel time distribution model. A clear trend reversal of nitrate concentrations was observed and simulated for springs with a large fraction of young water (< 30 years old) whereas the nitrate response in springs with relatively older water was attenuated and delayed. We conclude that obtaining a time series of tritium data helps to constrain age distributions of water that is discharged from dual permeability aquifers. The fraction of water aged <30 years was a meaningful parameter to distinguish between different types of springs. Nitrate trends in springs that drain large fractions of young water (> 0.6) show higher peak concentrations, shorter lag-time between leaching and outflow peaks and steeper declines after trend reversal, relative to trends in springs which are dominantly fed by older groundwater. The study thus shows that the nitrate legacy of groundwater systems is strongly determined by the range of their travel time distributions, and trend reversal in receiving springs and surface waters may appear within 10 to 15 years after measures to reduce nitrate losses from farming.

Estimating travel time in the Helsinki region utilising sequential Bayesian inference

This paper explores application of Bayesian inference (BI) to dynamic travel time estimation in the Helsinki region. Accurate travel time prediction is crucial in a wide range of fields, including departure time and routing. Limited real-time data challenge modelling accuracy. To address this, this paper utilises BI, particularly sequential Bayesian inference (SBI) for evolving observed values. Incorporating 2018 real-time data and 2015 information as prior knowledge, travel time distribution will be updated. Validation yields a 4.0% mean absolute error between the updated 2018 distribution and actual travel time. Also, using the 2015 posterior distribution as prior by way of SBI yields a 4.6% mean absolute error. Results highlight that SBI is an effective tool for updating distributions. This paper underscores potential of BI in addressing data scarcity and enhancing accuracy of transportation models. By supplying precise travel time estimates, this approach benefits congestion relief and travel planning. With evolving travel time data, BI promises to advance transportation modelling.

Uncertainty modeling and propagation for groundwater flow: a comparative study of surrogates

We compare sparse grid stochastic collocation and Gaussian process emulation as surrogates for the parameter-to-observation map of a groundwater flow problem related to the Waste Isolation Pilot Plant in Carlsbad, NM. The goal is the computation of the probability distribution of a contaminant particle travel time resulting from uncertain knowledge about the transmissivity field. The latter is modelled as a lognormal random field which is fitted by restricted maximum likelihood estimation and universal kriging to observational data as well as geological information including site-specific trend regression functions obtained from technical documentation. The resulting random transmissivity field leads to a random groundwater flow and particle transport problem which is solved realization-wise using a mixed finite element discretization. Computational surrogates, once constructed, allow sampling the quantities of interest in the uncertainty analysis at substantially reduced computational cost. Special emphasis is placed on explaining the differences between the two surrogates in terms of computational realization and interpretation of the results. Numerical experiments are given for illustration.

The k-th order mean-deviation model for route choice under uncertainty

This study introduces the k-th order mean-deviation model for optimizing route choice within large, stochastic, and time-variant networks. This model addresses the limitations of the traditional mean-standard deviation approach by better handling extreme outcomes in travel times. It features an objective function called the “travel time budget”, which combines the average path travel time with a safety margin. This margin is defined by a trade-off coefficient and a selected deviation measure (total or semi) of the travel time. The model is divided into three variations: 1) The mean-total deviation (MTD) model for symmetric travel time distributions, 2) The mean-upper-semi-deviation (MUSD) model for asymmetric distributions prioritizing upper semi-deviations, suitable for risk-averse travelers, and 3) The mean-lower-semi-deviation (MLSD) model for asymmetric distributions focusing on lower semi-deviations, preferred by risk-prone individuals. We explore these models’ alignment with the stochastic dominance (SD) rule and develop a solution methodology based on SD principles. Numerical experiments in two real-world transportation networks demonstrate the models’ effectiveness and show how the choice of deviation affects route selection decisions.

RoGeR v3.0.5 – a process-based hydrological toolbox model in Python

Abstract. Although water availability and water quality are equally important for effective water resources management at various spatial and temporal scales, to date, a combined representation of soil water balance components and water quality components in Python is not available. The new RoGeR toolbox contains models that can be used for not only the quantification of hydrological processes, fluxes and stores, but also solute transport processes based on StorAge selection (SAS). This study presents the code structure and functionalities of RoGeR developed as a scientific model toolbox following defined open-source software guidelines. RoGeR uses five different computational backends covering just-in-time compilation, parallelism and graphical processing units (GPUs) that might be used for optimizing computational performance. We show that graphical processing unit computing has the greatest potential to improve computation time and energy usage, especially for large modelling experiments. A simple modelling experiment highlights the capabilities of the new RoGeR model toolbox. We simulated the soil water balance, stable water isotope (18O) transport, and corresponding travel time distributions of the Eberbaechle catchment, Germany, for a 3-year period. Due to the current limitations of a variety of process components, further development of RoGeR as a scientific software is needed. Future modifications are easily possible due to the open software architecture of RoGeR.

Mechanisms of Suprapermafrost Groundwater Recharge Streamflow in Alpine Permafrost Regions: Insights From Young Water Fraction Analysis

AbstractThis study investigates the temporal processes of suprapermafrost groundwater (SPG)‐supplied streamflow in alpine permafrost regions, aiming to fill the gap in understanding this process from a water‐age perspective. Precipitation, streamflow, and SPG samples were collected from the Three‐Rivers Headwaters Region (TRHR). We defined the physical meaning of Fyw (the young water fraction) of the SPG and calculated it for the first time. The results showed that in the TRHR, the SPG mean travel time (MTT) was 159 days, and approximately 46.4% of SPG was younger than 77 days, whereas the streamflow MTT was 342 days, and approximately 12.2% of the streamflow was younger than 97 days. The correlation analysis revealed that various climatic factors played dominant roles in the recharge time variations of the SPG‐supplied streamflow within the TRHR. The SPG recharge rate did not significantly affect the streamflow Fyw; however, the thickness of the active layer ultimately controlled the SPG transit time distribution. Regression analysis further demonstrated the nonlinear impact of precipitation, average temperature, and average freezing days on SPG Fyw, which is closely related to seasonal freeze–thaw heat conduction and groundwater heat advection in the active layer. During the initial ablation period, the streamflow was primarily recharged by young SPG, resulting in a short‐tail travel time distribution. Our findings provide valuable insights into runoff generation and concentration processes in permafrost regions and have important implications for water resource management.

Reliable lifelong planning A*: Technique for re-optimizing reliable shortest paths when travel time distribution updating

Re-optimization technique is an efficient approach for solving the shortest path problem in dynamic deterministic networks, where link travel times are updated in real-time. However, existing re-optimization techniques, built on the assumption that link travel times are deterministic, cannot be used to solve reliable shortest path problems in real road networks with noticeable levels of travel time uncertainties. This study proposes a novel re-optimization technique, named reliable lifelong planning A* (RLPA*), for re-optimizing reliable shortest path finding results in dynamic stochastic networks, where link travel time distributions are updated in real-time. The proposed RLPA* technique can efficiently determine the optimal solution in dynamic stochastic networks by reusing path search results produced in the previous time instance. The proposed RLPA* technique is further utilized to solve the K reliable shortest paths problem, which is regarded as a series of reliable shortest path searches in a dynamic stochastic network. To validate the proposed algorithms, a comprehensive case study using real traffic data is conducted. The case study results demonstrated that the proposed algorithms significantly outperform the corresponding state-of-the-art algorithms on all testing networks.

Net escape velocity, transfer probability, and travel time distributions within a cross-ventilated room model sheltered by urban-like block array

Natural ventilation offers significant advantages, especially in terms of energy conservation. However, most published articles have focused on the ventilation flow rate to determine the average contaminant concentration, while few have examined local ventilation distributions. Therefore, isothermal steady-state Reynolds-averaged Navier–Stokes simulations were conducted to analyze the airflow and scalar concentration fields of a cross-ventilation model sheltered by buildings. Based on these fields, we generated the spatial distributions of ventilation indices, namely, the net escape velocity (NEV), point-to-point indices transfer probability (TP), and travel time (TT), to discuss the dispersion of scalars emitted from local points in a room with natural ventilation. The NEV, which indicates the direction of the scalar discharge from each cell, exhibited a distribution distinct from the advection velocity because of concentration gradient effect. Higher TPs were observed when evaluated from a contaminant source to a target point following the NEV streamlines. Meanwhile, lower TTs were observed when evaluated in a point near the source and also from a contaminant source to a target point following the NEV streamlines. Although TP and TT are independent ventilation indices, a negative correlation between them was observed. Instead of the ventilation flow rate, the detailed structure of scalar dispersion can now be described by simultaneously analyzing the ventilation efficiency indices, which provide information on the general contaminant transport direction, and the probability and duration of transfer from a source to a target point. This potentially helps in the design of ventilation system especially in room lay-out to avoid cross-contamination.

Mesoscopic model of cycling trip energy expenditure based on operating modes

Cyclist physical exertion is largely ignored in quantitative travel analysis, partly due to a lack of appropriate tools. Microscopic models of second-by-second energy expenditure based on equations of motion are data intensive and cannot be applied to hypothetical routes (such as needed for route choice modelling). Macroscopic models of aggregate energy expenditure based on a fixed assumed energy intensity are insensitive to traveller, trip, and contextual factors that are relevant for behavioural research and policy analysis (such as bicycle type or trip purpose). Building on concepts from motor vehicle emissions analysis, this paper proposes a mesoscopic approach to model cycling trip energy expenditure based on the distribution of travel time across discrete states of motion (“operating modes”) for different classes of traveller and trip (“model segments”). We aim to answer two key questions for model implementation: 1) which variables most effectively classify trips into model segments and 2) what operating mode definition most consistently characterizes cycling energy expenditure within model segments? We also evaluate the precision of the mesoscopic model relative to cycling energy estimates from microscopic and macroscopic models. Applied to a dataset of naturalistic cycling trips in Vancouver, Canada, the proposed mesoscopic model with six model segments based on 3 segmenting variables (rider gender, electric-assist bicycle, and high or low speed tier) explains up to 28 % of the variance in trip-level energy estimates from the microscopic model (within around 35 W of the microscopic estimates, on average). Further research to develop cycling trip energy models for general application is discussed.

Stochastic queue profile estimation using license plate recognition data

Queue profile has garnered significant attention for its precise description of queue formation and dissipation at signalized intersections. License Plate Recognition (LPR) systems, recording full-sample lane-based departure times of individual vehicles, offer an ideal data source for queue profile estimation. Thus, this paper presents a stochastic queue profile estimation method utilizing LPR data. It adopts the classic Input-Output model as a baseline to reconstruct arrival and departure curves using departure information from LPR detectors at successive intersections. A pseudo departure curve is then derived from the distribution of free-flow travel time. The stochastic queue profile is further reconstructed by analyzing the relationship among these curves, accounting for potential lane changes and overtaking behavior. The proposed method is validated through empirical and simulation cases. The empirical case achieves accurate queue length estimation with a Mean Absolute Error (MAE) of 5.38 m, while the simulation case yields precise stochastic queue profiles with an MAE of 5.95 m and an average deviation of 2.40 m for queue length. Sensitivity analysis demonstrates the method's robustness across parameters like demand-to-capacity ratio, miss detection ratio, and overtaking ratio. This work holds promise for real-time signal control optimization and vehicular trajectory reconstruction.

Uncertainty and sensitivity analysis of a travel‐time distribution‐based stream water electrical conductivity model

AbstractIn this paper, we analyse the uncertainty and parameter sensitivity of a conceptual water quality model, based on a travel time distribution (TTD) approach, simulating electrical conductivity (EC) in the Duck River, Northwest Tasmania, Australia for a 2‐year period. Dynamic TTDs of stream water were estimated using the StorAge Selection (SAS) approach, which was coupled with two alternate methods to model stream water EC: (1) a solute‐balance approach and (2) a water age‐based approach. Uncertainty analysis using the Differential Evaluation Adoptive Metropolis (DREAM) algorithm showed that: 1. parameter uncertainty was a small contribution to the overall uncertainty; 2. most uncertainty was related to input data uncertainty and model structure; 3. slightly lower total error was obtained in the water age‐based model than the solute‐balance model; 4. using time‐variant SAS functions reduced the model uncertainty markedly, which likely reflects the effect of dynamic hydrological conditions over the year affecting the relative importance of different flow pathways over time. Model parameter sensitivity analysis using the Variogram Analysis of Response Surfaces (VARS‐TOOL) framework found that parameters directly related to the EC concentration were most sensitive. In the solute‐balance model, the rainfall concentration Crain and in the age‐based model, the parameter controlling the rate of change of EC with age (λ) were the most sensitive parameter. Model parameters controlling the age mixes of both evapotranspiration and streamflow water fluxes (i.e., the SAS function parameters) were influential for the solute‐balance model. Little change in parameter sensitivity over time was found for the age‐based concentration relationship; however, the parameter sensitivity was quite dynamic over time for the solute‐balance approach. The overarching outcomes provide water quality modellers, engineers and managers greater insight into catchment functioning and its dependence on hydrological conditions.

Characterising travel behaviour patterns of transport hub station area users using mobile phone data

Understanding the travel behaviour of transport hub users is vital for improving transport services. Although previous research has explored passenger behaviour in and around transport hubs, there is a lack of comprehensive studies on travel patterns within hub station areas. To this end, this study harnessed mobile phone data to analyse the travel behaviour within a hub station area, using Beijing South Railway Station as a representative case. A series of recognition criteria was set up based on spatio-temporal information to categorize users within the station area. We categorised station area users into transport hub users (THU) and non-transport-hub users (NTHU) and examined their distinct travel patterns. The results reveal distinct travel patterns for THU and NTHU. NTHU are predominantly concentrated in and around the station area. THU, however, display longer trip distances and more widely distributed endpoints. In terms of travel time distribution, NTHU show evident morning and evening peak phenomena, while the travel time distribution of THU fluctuates throughout the day. The study also employed association rule analysis to illustrate strong connections between the station area, Beijing's core, central areas, and even urban fringe areas. The results reveal that the station area is most closely connected to the core and central areas of Beijing, from where many users are attracted to the station area. In addition, some urban fringe areas also have strong connections with the station area. These findings inform urban transport planning and personalised travel services.

Lognormal distribution of daily travel time and a utility model for its emergence

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.

Stochastic ambulance dispatching and routing in mass casualty incident under road vulnerability

This paper investigates the stochastic ambulance dispatching and routing (SADR) problem with multiple casualty collection points in the mass casualty incidents (MCI) under uncertainty of road vulnerability and traffic congestion caused by an earthquake. A two-stage stochastic mixed-integer nonlinear programming model is formulated to derive a reliable and high-quality ambulance scheduling, dispatching and routing solution for maximizing expected number of survivors of all casualties. An integrated simulation optimization approach combining a data-driven travel time scenario generation algorithm, sample average approximation, and a column-generation-based heuristic method is developed to efficiently solve this complicated two-stage SADR model with a nonlinear objective function and continuous travel time distributions. Collaborating with the National Science and Technology Center for Disaster Reduction (NCDR), an empirical study using a potential real-world earthquake scenario occurring in Taiwan is conducted to demonstrate the usefulness and effectiveness of our proposed model and solution approach compared to the deterministic model and two current-practice heuristics.