Quantifying time-variant travel time distribution by multi-fidelity model in hillslope under nonstationary hydrologic conditions

The travel time distribution (TTD) is a lumped representation of groundwater discharge and solute export responding to rainfall. It reflects the mixing process of water parcels and solute particles of different ages and characterizes reactive transport progress in hillslope aquifers. As a result of the mixing process, groundwater leaving the system at a certain time is an integration of multiple water parcels of different ages from different historical rainfall events. Under nonstationary rainfall input condition, the TTD varies with transit groundwater flow, leading to the time-variant TTD. Most methods for estimating time-variant TTD are constrained by requiring either the long-term continuous hydrogeochemical data or the intensive computations. This study introduces a multi-fidelity model to overcome these limitations and evaluate time-variant TTD numerically. In this multi-fidelity model, groundwater age distribution model is taken as the high-fidelity model, and particle tracking model without random walk is taken as the low-fidelity model. Non-parametric regression by non-linear Gaussian process is applied to correlate the two models and then build up the multi-fidelity model. The advantage of the multi-fidelity model is that it combines the accuracy of high-fidelity model and the computational efficiency of low-fidelity model. Moreover, in groundwater and solute transport model with low P\\'eclet number, as the spatial scale of the model increases, the number of particles required for multi-fidelity model is reduced significantly compared to random walk particle tracking model. The correlation between high and low-fidelity models is demonstrated in a one dimensional pulse injection case. In a two dimensional hypothetical model, convergence analysis indicates that the multi-fidelity model converges well when increasing the number of high-fidelity models. Error analysis also confirms the good performance of the multi-fidelity model.

New Travel Time Reliability Methodology for Urban Arterial Corridors

The need for reliable performance measures of urban arterial corridors is increasing because of the rise in traffic congestion and the high value of users’ travel time. Consequently, travel time reliability (TTR), which attempts to capture the day-to-day variability in travel times, has recently received considerable research interest. The basis of all TTR metrics is the underlying travel time distribution (TTD) along the given link or corridor. Estimating and forecasting arterial corridor TTDs for TTR analysis is the focus of this paper. This paper proposes a TTR methodology that addresses some of the limitations of the current U.S. state-of-the-art methodology which was published in the 6th edition of the Highway Capacity Manual (HCM6). Specifically, HCM6 can only estimate average TTD and not the population TTD. However, the population TTD is needed for accurate trip decision-making by individual drivers and logistics companies. In addition, HCM6 cannot be used to analyze the effect of new technologies, such as connected and automated vehicles, nor can it be used easily for long corridors or networks. The proposed TTR methodology, which is traffic-microsimulation based, was applied on a 1.16 mi arterial testbed in Lincoln, Nebraska, U.S. It was shown that the proposed TTR methodology, when calibrated, could replicate the empirical population TTD at a 5% significance level. The population TTD could also be transformed into an average TTD that also replicated the corresponding empirical average TTD at a 5% significance level.

Flow and residence time in a laboratory aquifer recharged by rainfall

<p>During rainfall, water infiltrates the soil, and percolates through the unsaturated zone until it reaches the water table. Groundwater then flows through the aquifer, and eventually emerges into streams to feed surface runoff. We reproduce this process in a  two-dimensional laboratory aquifer recharged by artificial rainfall. As rainwater infiltrates, it forms a body of groundwater which can exit the aquifer only through one of its sides. The outlet is located high above the base of the aquifer, and drives the flow upwards. The resulting vertical flow component violates the Dupuit-Boussinesq approximation. In this configuration, the velocity potential that drives the flow obeys the Laplace equation, the solution of which crucially depends on the boundary conditions. Noting that the water table barely deviates from the horizontal, we linearize the boundary condition at the free surface, and solve the flow equations in steady state. We derive an expression for the velocity potential, which accounts for the shape of the experimental streamlines and for the propagation rate of tracers through the aquifer. This theory allows us to calculate the travel times of tracers through the experimental aquifer, which are in agreement with the observations. The travel time distribution has an exponential tail, with a characteristic time that depends on the aspect ratio of the aquifer. This distribution depends essentially on the geometry of the groundwater flow, and is weakly sensitive to the hydrodynamic dispersion that occurs at the pore scale.</p>

A Diffusion-Based Analysis of a Multiclass Road Traffic Network

This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows based on conservation laws that incorporate the macroscopic fundamental diagram (a functional relationship between vehicle density and flow). Our setup is capable of handling multiple types of vehicle densities, with general macroscopic fundamental diagrams, on a network with arbitrary topology. Interpreting our system as a spatial population process, we derive, under natural scaling, fluid, and diffusion limits. More specifically, the vehicle density process can be approximated with a suitable Gaussian process, which yield accurate normal approximations to the joint (in the spatial and temporal sense) vehicle density process. The corresponding means and variances can be computed efficiently. Along the same lines, we develop an approximation to the vehicles’ travel time distribution between any given origin and destination pair. Finally, we present a series of numerical experiments that demonstrate the accuracy of the approximations and illustrate the usefulness of the results.

Statistical modelling of bus travel time with Burr distribution

A better understanding of the travel time distribution shape or pattern could improve the decision made by the transport operator to estimate the travel time required for the vehicle to travel from one place to another. Finding the most appropriate distribution to represent the day-to-day travel time variation of an individual link of a bus route is the main purpose of this study. Klang Valley, Malaysia is the study area for the research. A consecutive of 7 months ten bus routes automatic vehicle location (AVL) data are used to examine the distribution performance. The leading distribution proposed for the research is the Burr distribution. Both symmetrical and asymmetrical distributions that have been proposed in existing studies are also used for comparison purposes. Maximum likelihood estimation is applied for parameter estimation while loglikelihood value, Akaike information criterion (AIC) and Bayesian information criterion (BIC) are applied for performance assessment of the distributions. Promising results are obtained by the leading model in all different kinds of operating environment and could be treated as the preliminary preparation for further reliability analysis.

An artificial neural network based method to uncover the value-of-travel-time distribution

This study proposes a novel Artificial Neural Network (ANN) based method to derive the Value-of-Travel-Time (VTT) distribution. The strength of this method is that it is possible to uncover the VTT distribution (and its moments) without making assumptions about the shape of the distribution or the error terms, while being able to incorporate covariates and taking the panel nature of stated choice data into account. To assess how well the proposed ANN-based method works in terms of being able to recover the VTT distribution, we first conduct a series of Monte Carlo experiments. After having demonstrated that the method works on Monte Carlo data, we apply the method to data from the 2009 Norwegian VTT study. Finally, we extensively cross-validate our method by comparing it with a series of state-of-the-art discrete choice models and nonparametric methods. Based on the promising results we have obtained, we believe that there is a place for ANN-based methods in future VTT studies.