Travel Time Functions Research Articles

An optimization model for planning road networks that considers traffic noise impact

To reduce potential noise emissions, an optimization model for planning a road network that considers traffic noise impact is proposed. First, the urban traffic noise prediction method is constructed with the road structure as a constraint. Then, the travel time function is built based on the traffic flow model. Furthermore, the road network optimization model is presented based on the minimum network noise cost under different traffic flow states. The results of road structure optimization show the following: 1) Traffic noise cost increases but travel delay increases as travel coefficients increase; 2) The road traffic noise cost of the smaller design speed is lower; 3) The optimal road structures with various travel coefficients are recommended for distinct optimal objects. 4) The difference between the upper and lower limits of traffic noise pollution under different road structures is within 9 dB. This research can provide a reference for noise control.

Technical note: A graphical approach to the analysis of travel times in an automated storage and retrieval system

AbstractOperating time is closely related to the performance of an order‐picking system. Knowing the probability distribution of operating time will greatly facilitate system performance analysis and optimization. When using an automated storage and retrieval system (AS/RS), travels of the storage and retrieval machine can be modeled using the Chebyshev metric. However, because of the dependence among the travel legs, analyzing the variance of travel time can be quite challenging. In this paper, a graphical approach based on contour lines is proposed for deriving the probability density function (PDF) of travel time in an AS/RS. With the PDF, the expected value and variance of travel time can be obtained. To demonstrate the use of the proposed approach in evaluating the performance of an AS/RS under stochastic conditions, we derive the PDF of travel time and apply it in a queueing analysis. Based on the queueing performance measures and an overall arrival rate, the minimum number of operation requests waiting or being served occurs when the arrival rates of storage and retrieval requests are approximately equal. Also, when arrival rates of storage and retrieval requests are equal, the number of operation requests waiting or being served is minimized when the rack is square‐in‐time.

Ultralow-frequency amplitude variation with angle inversion of plane-wave primary reflection seismograms

An amplitude variation with angle (AVA) inversion method is presented for estimating density and velocities of a stratified elastic medium from reflection seismograms in the intercept time-horizontal slowness domain. The elastic medium parameters are assumed to vary continuously with depth. The seismograms are Green’s function precritical incidence primary P-wave reflections of time length [Formula: see text], assumed to obey differential equations of a model for elastic primary P-wave backscattering, similar to seismograms representing the first term in the well-known Bremmer series/Wentzel–Kramers–Brillouin–Jeffreys iterative solution model. A relation is found between the plane-wave Green’s function seismograms at each horizontal slowness and the medium properties in time. The Green’s function seismograms after normal-moveout correction are directly inverted for the medium parameters as a function of zero-offset traveltime. It is documented theoretically and verified numerically that the signal at the fundamental frequency [Formula: see text] must be present in the seismograms for the AVA method to provide the parameter trends of the elastic medium, implying that ultralow frequencies <1 Hz for [Formula: see text] s must be generated and recorded. Noise in the seismograms at ultralow frequencies is not considered because the theoretical AVA model does not handle microseisms that would be measured in real data. The main mathematical findings are illustrated by using simple model seismograms.

Development of travel time functions for disrupted urban arterials with microscopic traffic simulation

Urban traffic networks consisting of partially blocked roads often need to remain open to traffic before, during and after disasters because of their vital roles to hazard preparation, emergency response and recovery of urban communities. To conduct effective traffic planning of disrupted transportation networks highly depends on accurate prediction of travel time on partially blocked roads, which is very different from that on intact roads. Due to the lack of appropriate models, travel time prediction approaches developed for intact roads have often been directly applied to partially blocked roads, leading to inaccurate travel time estimates. Unrealistic travel time estimates of partially blocked roads as well as the whole transportation network further affect traffic planning, emergency response and other decision-makings which are heavily reliant on travel time prediction. A new approach to develop travel time functions for partially blocked roads in urban areas is proposed to close this gap based on microscopic traffic simulation. First, an improved model for simulating traffic on partially blocked roads is developed by extending the existing cellular automaton model. Second, the improved traffic model is validated at microscopic and macroscopic levels with measured traffic data from an urban road. Third, traffic simulations under various scenarios with different demand flow rates, truck ratios and blockage ratios are conducted through microscopic simulation experiments. Finally, a set of continuous traffic time functions are further developed for disrupted traffic flow with parameters estimated from the generated traffic data. The developed travel time functions for a typical urban arterial road are then compared with the standard Bureau of Public Roads function. The comparison suggests that the standard Bureau of Public Roads function would considerably underestimate the travel time on partially blocked roads and the proposed travel time functions can offer a more realistic prediction. The proposed methodology of developing the travel time functions of partially blocked roads will be helpful for accurate estimation of traffic demand of post-hazard transportation networks.

Dynamic Discretization Discovery Algorithms for Time-Dependent Shortest Path Problems

Finding a shortest path in a network is a fundamental optimization problem. We focus on settings in which the travel time on an arc in the network depends on the time at which traversal of the arc begins. In such settings, reaching the destination as early as possible is not the only objective of interest. Minimizing the duration of the path, that is, the difference between the arrival time at the destination and the departure from the origin, and minimizing the travel time along the path from origin to destination, are also of interest. We introduce dynamic discretization discovery algorithms to efficiently solve such time-dependent shortest path problems with piecewise linear arc travel time functions. The algorithms operate on partially time-expanded networks in which arc costs represent lower bounds on the arc travel time over the subsequent time interval. A shortest path in this partially time-expanded network yields a lower bound on the value of an optimal path. Upper bounds are easily obtained as by-products of the lower bound calculations. The algorithms iteratively refine the discretization by exploiting breakpoints of the arc travel time functions. In addition to time discretization refinement, the algorithms permit time intervals to be eliminated, improving lower and upper bounds, until, in a finite number of iterations, optimality is proved. Computational experiments show that only a small fraction of breakpoints must be explored and that the fraction decreases as the length of the time horizon and the size of the network increases, making the algorithms highly efficient and scalable. Summary of Contribution: New data collection techniques have increased the availability and fidelity of time-dependent travel time information, making the time-dependent variant of the classic shortest path problem an extremely relevant problem in the field of operations research. This paper provides novel algorithms for the time-dependent shortest path problem with both the minimum duration and minimum travel time objectives, which aims to address the computational challenges faced by existing algorithms. A computational study shows that our new algorithm is indeed significantly more efficient than existing approaches.

Optimization of distance between fire stations: effects of fire ignition probabilities, fire engine speed and road limitations, property values and weather conditions

A general spatial fire brigade unit network density optimization problem has been solved. The distance to a particular road, from a fire station, is approximated as a continuous variable. It is proved, via integral convolution, that the probability density function of the total travel time, PDFT, is triangular. The size of the fire, when it stopped, is a function of the time it takes until the fire brigade reaches the fire location. An explicit continuous function for the expected total cost per square kilometer, based on the cost per fire station, the PDFT, the exponential fire cost function parameters, the distance between fire stations, and the speed of fire engines, is derived. It is proved that the optimal distance between fire brigade unit positions, OFD, which minimizes the total expected cost, is unique. Then, the OFDs are replaced by integers, OFDIs, for different parameter assumptions. In this process, also the optimal expected total costs are determined. It is proved that the OFD is a strictly decreasing function of the expected number of fires per area unit, a strictly increasing function of the speed of the fire engines, a strictly decreasing function of the parameters of the exponential fire cost function, and a strictly increasing function of the cost per fire station. These effects of parameter changes are also illustrated via graphs in the numerical section.

Multi-stencils fast marching method for factored eikonal equations with quadratic anisotropy

In this study, we propose a multi-stencils fast marching method to solve the factored eikonal equations for media with quadratic anisotropy, also known as Riemannian anisotropy. Compared with the conventional fast marching method, the new method has an improved accuracy in tracing moving wavefronts via computing the solution at each grid point along several stencils. To deal with the source singularity, we solve for the viscosity solution iteratively by factorize the unknown traveltime function into a function that captures the singularity and a multiplicative factor which is differentiable at the source location. By leveraging the strengths of multi-stencils and factorisation, the newly developed algorithm is highly accurate in solving anisotropic eikonal equations. Through a series of numerical examples, we explicitly show that the algorithm (1) has an obvious first (second) order convergence rate with the first (second) order finite-difference scheme, and (2) is unconditionally stable as long as the initial time table around the source is specified. Finally, we design an eikonal-based anisotropic ray tracing technique. We test the anisotropic ray tracing technique on both radial and azimuthal anisotropy cases and the numerical results demonstrate that the usage of multi-stencils scheme increase the accuracy of the anisotropic ray paths especially for azimuthal anisotropy case. This high-accurate eikonal solver and the associated ray tracing technique can be used in high-resolution seismic anisotropic tomography and other researches in the future.

Modelling Physical Accessibility to Public Green Spaces in Switzerland to Support the SDG11

Urban sprawl has a strong impact on the provision and use of green spaces and, consequently, on the benefits that society can derive from these natural ecosystems, especially in terms of public health. In looking at the Sustainable Development Goals and other regional policy frameworks, there is a strong need for quantifying access to green spaces. This study presents and applies a methodology to model the physical accessibility at national and sub-national scales to public green spaces (i.e., urban green spaces and forests) in Switzerland, using AccessMod and ArcGIS travel time functions. We found that approximately 75% and 36% of the Swiss population can access the nearest urban green space within 5 min and 15 min, respectively, using motorized transport. For motorized access to the nearest forest patch, 72% and 52% of the population are within 5 min and 15 min, respectively. When considering only the main urban areas, approximately 55% of the population can walk to the nearest urban green space within 5 min. However, a high heterogeneity in access exists at cantonal and municipal levels, depending on road density, green space density, and population distribution. Despite some possible challenges in correctly delineating public green spaces, our methodology offers a replicable approach offering not only insights into sustainable urban development, but also the facilitation of comparison with other European countries.

Elastic train scheduling model

Train scheduling plays a significant role in the optimal use of the railway resources and satisfaction of customers. This paper presents a novel innovation, which is the elasticity of train length, or the possibility of compression and stretching of the train length in accordance with rail route conditions. The proposed sustainable model provides optimal train scheduling with minimum travel time as well as optimal revenue and cost by developing a balance between length, speed, traction power, and energy consumption of trains while there is the possibility of carrying homogeneous and heterogeneous commodities. Thus, the new model is referred to as the sustainable elastic train scheduling model. Implementing the model in a real case using an introduced genetic algorithm proves its success and increases railway revenues by at least 48 percent with the saving of 25 percent in time. Sensitivity analysis of the model reveals the model is more sensitive to changes in the objective function of travel time. In addition to 50% improvement in using railroad capacity, it is possible to achieve the minimum increase of 71% in revenue.

Freeway tunnel effect of travel time based-on a double lane traffic model

Speed limit of freeway tunnel restricts car driving behaviors. To explore the tunnel effect of travel time, a double lane traffic model is put forward, and a compensative function of mean travel time is simply introduced in this paper. The model describes the net lane-changing rate using the ratio of characteristic lane changing time to traffic relaxation time, assumes that the cars on both lanes of the tunnel have the same equilibrium speed, but the speeds on both lanes of normal section are different. It is assumed that the road length is 100 km, and the tunnel length is 7.5 km except for the case of seeking tunnel length effects. The model is used to build a simulation platform. Numerical results indicated that when the initial road density normalized by jam density is above 0.2, the tunnel causes a congestion region just upstream the tunnel inlet, provides a smooth region just downstream the tunnel outlet, can affect the traffic flow pattern significantly. But the tunnel effect of travel time is small, as the tunnel can merely slightly increase the mean travel time. The on/off ramp flows play a crucial role in the formation of traffic flow pattern.

Modelling data-driven distributionally robust risk-averse hub interdiction median problem under hypothesis test

This paper explores a hub interdiction median problem for risk-averse managers using the objective function of the total travel time. This problem mainly involves the selection of the key hub with the strongest influence on the hub network and the redesign of this network after disruptions. Motivated by the mean and conditional value-at-risk criteria (CVaR), we first study the maximum total travel time in the hub network after disruptions and propose a mean-CVaR hub interdiction median model. Then, we consider the travel time in the model as a random variable with finite sample observations. Assuming that the probability distribution of random time has the known finite discrete support, we develop a novel data-driven distributionally robust mean-CVaR hub interdiction median model by constructing an ambiguity set based on the robust optimization method and the Pearson chi-square hypothesis test. The constructed ambiguity set includes the real probability distribution of the travel time at a designated confidence level. We further derive the worst mean via robust sample average approximation approach, and obtain a data-driven cone representation of the worst CVaR under ambiguity set. Finally, by using the travel time data from a local aviation hub network in the United States, we conduct the numerical experiments in a real-world context to demonstrate the validity of our proposed model.

Automatic velocity picking from semblances with a new deep-learning regression strategy: Comparison with a classification approach

The physical basis, parameterization, and assumptions involved in root-mean-square (rms) velocity estimation have not significantly changed since they were first developed. However, these three aspects are all good targets for novel application of the recent emergence of machine learning (ML). Therefore, it is useful at this time to provide a tutorial overview of two state-of-the-art ML implementations; we have designed and evaluated classification and regression neural networks for the extraction of apparent rms velocity trajectories from semblance data. Both networks share a similar end-to-end trainable structure, except for the final layer. In the classification network, the velocity picking is performed by finding the largest amplitude trajectory through all velocity bins. The regression network, on the other hand, applies a differentiable soft-argmax function that converts the feature maps directly to apparent rms velocity values as functions of traveltime. Relative confidence maps can also be estimated from both neural networks. A large number of synthetic models with horizontal layers are created, and common-midpoint gathers are simulated from those models as training samples. Transfer learning is applied to fine-tune the networks with a small number of samples for testing with synthetic and field data from more complicated (2D) models. Tests using synthetic data show that the regression and classification networks can give reasonable velocity predictions from semblances, but the regression network gives higher accuracy.

Can dynamic ride-sharing reduce traffic congestion?

Can dynamic ride-sharing reduce traffic congestion? In this paper we show that the answer is yes if the trip density is high, which is usually the case in large-scale networks but not in medium-scale networks where opportunities for sharing in time and space become rather limited. When the demand density is high, the dynamic ride-sharing system can significantly improve traffic conditions, especially during peak hours. Sharing can compensate extra travel distances related to operating a mobility service. The situation is entirely different in small and medium-scale cities when trip shareability is small, even if the ride-sharing system is fully optimized based on the perfect demand prediction in the near future. The reason is simple, mobility services significantly increase the total travel distance, and sharing is simply a means of combating this trend without eliminating it when the trip density is not high enough. This paper proposes a complete framework to represent the functioning of the ride-sharing system and multiple steps to tackle the curse of dimensionality when solving the problem. We address the problem for two city scales in order to compare different trip densities. A city scale of 25 km2 with a total market of 11,235 shareable trips for the medium-scale network and a city scale of 80 km2 with 205,308 demand for service vehicles for the large-scale network over a 4-hour period with a rolling horizon of 20 minutes. The solutions are assessed using a dynamic trip-based macroscopic simulation to account for the congestion effect and dynamic travel times that may influence the optimal solution obtained with predicted travel times. This outperforms most previous studies on optimal fleet management that usually consider constant and fully deterministic travel time functions.

The Time-Dependent Vehicle Routing Problem with Time Windows and Road-Network Information

Most time-dependent vehicle routing problems are based on a similar modeling paradigm: travel time information is represented by travel time functions between pairs of points of interest (e.g., depot or customers). Only a few papers investigate how these functions can be computed using the available travel time information. Furthermore, most of them neglect the possibility that different paths could be selected in the road network depending on the compromises they offer between cost (distance) and travel time. In this paper, we propose a new setting where travel time functions are defined on road-network arcs. We consider the Time-Dependent Vehicle Routing Problem with Time Windows and solve it with a branch-and-price algorithm. As far as we know, this is the first exact approach for a time-dependent vehicle routing problem when travel time functions are initially defined on the segments of a road-network.

Column generation for the equilibrium route-flow traffic assignment problem

Today efficient traffic management seems to be impossible without the support of the artificial intelligence systems based on mathematical models of traffic flow assignment since a modern road network is a large-scale system with huge amounts of elements. The present paper is devoted to the route-flow traffic assignment problem, which solution is the most valuable from decision-making perspectives. The paper aims to fill the gap in the relation between the column generation process and the uniqueness of the equilibrium route-flow traffic assignment pattern. The independence of routes is showed to be highly significant when travel time functions are arc-additive. Indeed, on the one hand, the independence of routes is proved to guarantee the uniqueness of the equilibrium route-flow traffic assignment pattern. On the other hand, the independence of routes appears to be crucial for column generation when solving the route-flow traffic assignment problem since the equilibrium travel time is proven to be decreased only by adding independent candidate route. Obtained results contribute to the development of algorithms for route-flow traffic assignment based on travel times equilibration procedure.

Modeling Time-Varying Variability and Reliability of Freeway Travel Time Using Functional Principal Component Analysis

This paper presents an aproach for modeling travel time variability and reliability that accounts for time-of-day effects on travel time variations. The conditional probability density functions of travel time in each specific period play a fundamental role in the modeling of time-varying variability and reliability. Nonparametric kernel density estimation is applied to travel time data, which enhances the flexibility and accuracy in accommodating travel time distributions under various complex traffic conditions. The proposed functional travel time density model (FTTDM) uses functional principal component analysis in kernel density function estimates for modeling and depicting time-varying variability through the dependence on the departure time of day. The resulting quantile estimates are used to obtain time-varying reliability, which considers the addition of extra time to the average or the median for an on-time arrival. This study uses linked travel time data of an electronic toll collection system to estimate route travel times in the Taiwan Freeway system. As illustrated in the data applications, the FTTDM effectively captures the time-varying feature of travel time variability and reliability, and the reliability indicators identify the unreliable departure time of day of a route.

Non-linear optimization for continuous travel demand estimation

Models and methods of traffic distribution are being developed by researchers all over the world. The development of this scientific field contributes to both theory and practice. In this article, the non-linear optimization of traffic flow re-assignment is examined in order to solve continuously the travel demand estimation problem. An approach has been developed in the form of computational methodology to cope with the network optimization problem. A uniqueness theorem is proved for a certain type of road network. Explicit relations between travel demand and traffic flow are obtained for a single-commodity network of non-intersecting routes with special polynomial travel time functions. The obtained findings contribute to the theory and provide a fresh perspective on the problem for transportation engineers.

Day-to-day dynamics with advanced traveler information

This paper studies how the advanced traveler information affects the stability of the day-to-day flow evolution of a transportation system. Two scenarios are investigated regarding the types of information provided, where one type is the historical travel time and the other the forecasted travel time. Given the information, travelers are assumed to form their own perception/prediction on travel time and further choose the routes. The day-to-day dynamics under the two above-mentioned scenarios are formulated using both discrete-time and continuous-time models, and their respective local stability is analyzed. Findings from the discrete-time and continuous-time models are compared, which show that: (i) the discrete-time models behave in a more complex fashion than the continuous-time models, and (ii) the conclusions drawn from the discrete-time modeling and continuous-time modeling can be consistent, different or contradictory, which depends on the system parameters, network structure, the travel time functions and the route choice probability functions.

Lifting the Performance of a Heuristic for the Time-Dependent Travelling Salesman Problem through Machine Learning

In recent years, there have been several attempts to use machine learning techniques to improve the performance of exact and approximate optimization algorithms. Along this line of research, the present paper shows how supervised and unsupervised techniques can be used to improve the quality of the solutions generated by a heuristic for the Time-Dependent Travelling Salesman Problem with no increased computing time. This can be useful in a real-time setting where a speed update (or the arrival of a new customer request) may lead to the reoptimization of the planned route. The main contribution of this work is to show how to reuse the information gained in those settings in which instances with similar features have to be solved over and over again, as it is customary in distribution management. We use a method based on the nearest neighbor procedure (supervised learning) and the K-means algorithm with the Euclidean distance (unsupervised learning). In order to show the effectiveness of this approach, the computational experiments have been carried out for the dataset generated based on the real travel time functions of two European cities: Paris and London. The overall average improvement of our heuristic over the classical nearest neighbor procedure is about 5% for London, and about 4% for Paris.

Data-driven network loading

ABSTRACT Dynamic Network Loading (DNL) models are typically formulated as a system of differential equations where travel times, densities or any other variable that indicates congestion is endogenous. However, such endogeneities increase the complexity of the Dynamic Traffic Assignment (DTA) problem due to the interdependence of DNL, route choice and demand. In this paper, attempting to exploit the growing accessibility of traffic-related data, we suggest that congestion can be instead captured by exogenous variables, such as travel time observations. We propagate the traffic flow based on an exogenous travel time function, which has a piece-wise linear form. Given piece-wise stationary route flows, the piece-wise linear form of the travel time function allows us to use an efficient event-based modelling structure. Our Data-Driven Network Loading (DDNL) approach is developed in accordance with the theoretical DNL framework ensuring vehicle conservation and FIFO. The first simulation experiment-based results are encouraging, indicating that the DDNL can contribute to improving the efficiency of applications where the monitoring of historical network-wide flows is required. Abbreviations: DDNL – Data Driven Network Loading; DNL – Dynamic Network Loading; DTA – Dynamic Traffic Assignment; ITS – Intelligent Transportation Systems; OD – Origin Destination; TTF – Travel Time Function; LTT – Linear Travel Time; DL – Demand level