Travel Time Distribution Research Articles

Performance Analysis for Puzzle-based Movable Racks System with Diagonal Movements

High-density warehouses are now necessary due to quick delivery services. The puzzle-based storage system is a workable solution to increase storage density, although the retrieval process is challenging. The Logistics 4.0 Lab at NTNU and Norwegian company Wheel.me have unveiled a new solution called a puzzle-based movable rack system. It uses autonomous wheels to move storage racks in any direction, including diagonally, potentially achieving high throughput. Retrieval performance depends on the system’s features even though it is the most practical approach. For this study, we considered performance analysis of the PBMR system in terms of travel time distribution and number of movements considering different scenarios. The results of the scenario analysis show that 70% of the time, travel time is lower than 1 unit while the number of movements is less than 10% of the storage capacity units 50% of the time when we used the proposed PBMR system with diagonal movements. This has yielded valuable insights into the efficiency and functionality of the designed system.

Investigating the Seasonal Variations of Event, Recent, and Pre-Recent Runoff Components in a Pre-Alpine Catchment using Stable Isotopes and an Iterative Hydrograph Separation Approach

An analysis of the runoff generation processes in terms of event, recent, and pre-recent runoff components is demonstrated for the Swiss pre-Alpine Alp catchment (46.4 km2) and two smaller tributaries (Erlenbach, 0.7 km2, and Vogelbach, 1.6 km2), whereas, recent water is understood as the contribution of the respective three prior rainfall-runoff events. A four-years time series of daily stable water isotope data in stream water and precipitation is used for the analysis of seasonal variations. In addition, high-frequency data (10 minutely intervals) are used for a detailed visualization of the rapid mobilization of recent water for single events. An iterative extension of the standard two-component hydrograph separation method is applied; this approach can be interpreted as a discretization of the catchment water and tracer mass balance along the event and pre-event time axis. Furthermore, the calculated event, recent, and pre-recent runoff components can be used to estimate time-varying backward travel time distributions.

AN AGENT BASED MODEL TO IMPROVE TRAFFIC FLOW AND ASSESS THE IMPACT OF SMART TRAFFIC LIGHT

The Traffic in developing country undergoes severs perturbations due to either a misunderstanding of the physical phenomenon or in bad calibration of equipments such as traffic light. Due to this high complexity, mathematical models fail to well represent different scenario. Those issues are mostly due to the high amount of parameter which should be taken into consideration when dealing with some mathematical model and the drivers behaviors. Since agent-based model is a computational simulation that represents individual entities (called agents) and their interactions within a defined environment. It is a powerful tools used to investigate human behavior impact in a mathematical model. Therefore, this paper proposed a novel agent-based approach framework for effectively making traffic light timing dynamic according to traffic density. Moreover, based on different rules such as lane changing, stop and goat the traffic light, we develop an Agent based model to represent the relationships between the traffic changing and its environment. The use of agent-based models for traffic light time optimization offers a more granular, adaptive, and integrative approach that better capture the complexities of real-world traffic scenarios. Finally, the experimental result is applied on synthetic data and compared to other results in almost the same context for both static and dynamic traffic light. The results show that the travel time distribution is less for dynamic traffic light.

A generative adversarial network-based framework for network-wide travel time reliability prediction

This paper introduces a generative model named the travel time reliability-generative adversarial network (TTR-GAN) model for predicting network-wide TTR using automatic vehicle identification data. The TTR-GAN model is capable of generating predicted travel time samples, enabling the assessment of network-wide TTR without the need to assume a specific travel time distribution. In the TTR-GAN model, a combination of graph convolutional networks and long short-term memory (LSTM) neural networks is employed within the GAN framework. When training the TTR-GAN model, special attention is given to adjusting the mean and standard deviation of the generated samples, aiming for a closer resemblance to real samples. Experiments conducted on a road network in China demonstrate the predictive capability of the proposed TTR-GAN model, surpassing several benchmark models such as the LSTM neural network, moving average model, and GAN model in terms of statistical, buffer time, and probability distribution measures. By incorporating the mean and standard deviation into the loss function, the TTR-GAN model achieves an 18.2% reduction in Jensen‒Shannon divergence between predicted and real samples. Furthermore, the model's performance in real-world applications is illustrated through a sensitivity test.

GE-DDRL: Graph Embedding and Deep Distributional Reinforcement Learning for Reliable Shortest Path: A Universal and Scale Free Solution

This paper studies the reliable shortest path (RSP) problem in stochastic transportation networks. State-of-the-art RSP solutions usually target one specific RSP problem; moreover, the corresponding algorithm’s computational complexity scales at least linearly with the size of the underlying transportation network. While in this paper, we propose a graph embedding and deep distributional reinforcement learning (GE-DDRL) method, which serves as a universal and scale-free solution to the RSP problem. GE-DDRL uses deep distributional reinforcement learning (DDRL) to estimate the full travel-time distribution of a given routing policy, and improves the given routing policy with the generalized policy iteration (GPI) scheme. Further, in order to achieve the generalization ability to new destination nodes, we employ one of the canonical graph embedding techniques (Skip-Gram) to compress the nodes’ representation into <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$</tex-math> </inline-formula> -dimensional real-valued vectors. With the properly compressed node features, GE-DDRL is able to generalize its estimation of the routing policy’s travel-time distribution to untrained destination nodes, and hence achieve the ‘all-to-all’ navigation functionality. To the best of our knowledge, GE-DDRL serves as the first RSP planner, which applies simultaneously to almost all RSP objectives and in the meanwhile, is scale free with the size of the transportation network in terms of the online decision-making time and memory complexity. Experimental results and comparisons with state of the arts show the efficacy and efficiency of GE-DDRL in a range of transportation networks.

Estimating Probability Distributions of Travel Times by Fitting a Markovian Velocity Model

Estimating Probability Distributions of Travel Times by Fitting a Markovian Velocity Model

A new approach to simulate watershed sediment graphs

Soil loss management requires reliable data for assessing the conditions prevailing in a watershed. Suspended sediment concentration (SSC) is one of the indicators of soil loss, and its data and associated properties are essential for integrated watershed management. However, until now, practical methods for estimating the temporal variation of SSC at the watershed scale, i.e., a sediment graph (SG), using measured data have been given less attention. Therefore, the current study was planned to simulate the SG through conceptual modeling of the soil erosion process and sediment yield. The Galazchai Watershed in West Azerbaijan Province, Iran, was selected as a case study. In this regard, the isochrone histograms were initially prepared using two methods of the longitudinal channel profile and spatially distributed travel time. Soil erosion was calculated in each isochrone segment using the Revised Universal Soil Loss Equation (RUSLE), applying the lumped and cellular automata approach. The soil erosion between isochrones was subsequently routed using the Hadley, WaTEM/SEDEM, and newly modified U.S. Forest Service methods. The last method was developed based on seven standardized variables for the current research. Synthetic SGs were ultimately derived from 12 different combinations of the study methods. The modeling performance was assessed using 38 storm events collected over several years. The base time, time to peak, peak value, and total sediment load of the simulated and observed SGs were evaluated using relative error. Comparison based on the evaluation indicators indicated better performance of the combination of the spatially distributed travel time method, cellular automata, and modified U.S. Forest Service method with the coefficient of efficiency and the normalized coefficient of efficiency varying from −1.16 to 0.99 and from 0.32 to 0.99 for the calibration and validation stages, respectively. However, none of the models were simulating satisfactorily the entire sediment graphs.

Probabilistic Forecasting of Bus Travel Time with a Bayesian Gaussian Mixture Model

Accurate forecasting of bus travel time and its uncertainty is critical to service quality and operation of transit systems: it can help passengers make informed decisions on departure time, route choice, and even transport mode choice, and it also support transit operators on tasks such as crew/vehicle scheduling and timetabling. However, most existing approaches in bus travel time forecasting are based on deterministic models that provide only point estimation. To this end, we develop in this paper a Bayesian probabilistic model for forecasting bus travel time and estimated time of arrival (ETA). To characterize the strong dependencies/interactions between consecutive buses, we concatenate the link travel time vectors and the headway vector from a pair of two adjacent buses as a new augmented variable and model it with a mixture of constrained multivariate Gaussian distributions. This approach can naturally capture the interactions between adjacent buses (e.g., correlated speed and smooth variation of headway), handle missing values in data, and depict the multimodality in bus travel time distributions. Next, we assume different periods in a day share the same set of Gaussian components, and we use time-varying mixing coefficients to characterize the systematic temporal variations in bus operation. For model inference, we develop an efficient Markov chain Monte Carlo (MCMC) algorithm to obtain the posterior distributions of model parameters and make probabilistic forecasting. We test the proposed model using the data from two bus lines in Guangzhou, China. Results show that our approach significantly outperforms baseline models that overlook bus-to-bus interactions, in terms of both predictive means and distributions. Besides forecasting, the parameters of the proposed model contain rich information for understanding/improving the bus service, for example, analyzing link travel time and headway correlation using covariance matrices and understanding time-varying patterns of bus fleet operation from the mixing coefficients. Funding: This research is supported in part by the Fonds de Recherche du Quebec-Societe et Culture (FRQSC) under the NSFC-FRQSC Research Program on Smart Cities and Big Data, the Canadian Statistical Sciences Institute (CANSSI) Collaborative Research Teams grants, and the Natural Sciences and Engineering Research Council (NSERC) of Canada. X. Chen acknowledges funding support from the China Scholarship Council (CSC). Supplemental Material: The e-companion is available at https://doi.org/10.1287/trsc.2022.0214 .

Empowering A* Algorithm With Neuralized Variational Heuristics for Fastest Route Recommendation

Fastest route recommendation (FRR) is crucial for intelligent transportation systems. The existing methods treat it as a pathfinding problem on dynamic graphs, and extend A* algorithm with neuralized travel time estimators as cost functions. However, they fail to provide effective heuristic cost due to the neglect of its admissibility and the utilization of noise path information, resulting in sub-optimal results and inefficiency. Besides, path sequentiality is also ignored, affecting algorithm accuracy as well. In this paper, we propose a variational inference based fastest route recommendation method, which follows the framework of A* algorithm and provides effective costs for routing. Specifically, we first adopt a sequential estimator to accurately estimate the travel time of a specific path. More importantly, we design a variational inference based estimator, which models the distribution of travel time between two nodes and provides an effective heuristic cost with high probability of being admissible. We further take advantage of adversarial learning to enrich the fastest path information. To the best of our knowledge, we are the first to use variational estimator to consider the admissibility of heuristics in FRR. Extensive experiments are conducted on two real-world datasets. The results verify the performance advantage of our proposed method.

The impact of COVID-19 on travel mobility of older passengers on Xi'an urban rail in China

The COVID-19 outbreak has led to unprecedented changes in people's lives and travel. Public transportation operators must understand individual mobility during COVID-19. Few studies have focused on the impact of COVID-19 on the travel behaviors of vulnerable older adults. To fill this research gap, this study is conducted using smartcard data from the Xi'an urban rail transit during the time of COVID-19 from February 1, 2020 to April 30, 2020. This study first divides the research objects, that is, passengers, into two groups of young adults and older adults, and periods into three stages: the outbreak, post-pandemic, and recovery. Indicators of travel distance, travel frequency, and activity duration were introduced for the two passenger groups to quantify their travel mobility in different stages. To evaluate the spatiotemporal performance of travel mobility, the travel time distribution of the two groups of passengers in each stage was continuously tracked and the returning passengers were proposed to measure the spatial distribution of station-level ridership. In summary, this study provides not only a deeper understanding of the mobility of older passengers during COVID-19 but also useful insights for urban rail transit managers to make more effective decisions for older adults.

Self‐adaptive search optimization‐based vehicle path prediction and traffic light controller in vehicular ad hoc network

SummaryIn recent days, VANET is considered as the main hopeful equipment in the system of transportation since traffic congestion arises regularly and thus occurred road accidents very easily. Besides, the network traffic is increasing due to the huge quantity of information generated in region of urban. Therefore, one of the primary challenges faced by Intelligent Transportation System (ITS) is ensuring the accurate transmission of information in both vehicle‐to‐vehicle (V2V) and vehicle‐to‐road (V2R) sensing unit communications. So, here, an adaptive routing controller (ARC) is utilized to improve the data transmission between vehicle and road sensing unit (RSU) and to minimize the traffic density in VANET, and the self‐adaptive search optimization is developed in VANET clustering to prioritize vehicles in the lane, in which the multi‐objective function is intended depending on the energy of the node, acceleration, jitter, priority, velocity, and trust factors. The traffic light control is done to facilitate the effective communication in the network. Thus, the proposed technique is calculated in terms of throughput, jitter, quadratic mean of acceleration (QMA), and spatially distributed travel time (SDTT), which acquired the values of 0.53 s, 36.07 kmph, 3.472 s, and 43.572%, respectively, while using 50 vehicles at 50 s.

Lane changing and congestion are mutually reinforcing?

This study presents a comprehensive analysis of the relationship between congestion and lane changing, using vehicle trajectory data from the M1 motorway in Sydney. We establish a connection between the distribution of travel time and lane changing frequency and employ a Poisson process to describe the intensity of lane changing occurrences in different travel time ranges. From an individual perspective, lane changing does not bring significant speed benefits in most cases, except when the speed range is between 45 and 50 ​km/h. From a system perspective, the relationship between lane change rate and speed depends on the purpose of the lane changes. In merging, diverging, and lane restriction areas, for instance, mandatory lane changes dominate. In most sections of the motorway, discretionary lane changes are motivated by the expectation of improving speed and/or safety. Additionally, we demonstrate a mutual causality relationship between lane changing and congestion through the Granger causality test. This relationship is more pronounced in general areas during peak periods and contributes to the deterioration of the driving environment.

DRL Router: Distributional Reinforcement Learning-Based Router for Reliable Shortest Path Problems

This article studies reliable shortest path (RSP) problems in stochastic transportation networks. The term reliability in the RSP literature has many definitions, e.g., 1) maximal stochastic on-time arrival probability, 2) minimal travel time with a high-confidence constraint, 3) minimal mean and standard deviation combination, and 4) minimal expected disutility. To the best of our knowledge, almost all state-of-the-art RSP solutions are designed to target one specific RSP objective, and it is very difficult, if not impossible, to adapt them to other RSP objectives. To bridge the gap, this article develops a distributional reinforcement learning (DRL)-based algorithm, namely, DRL-Router, which serves as a universal solution to the four aforementioned RSP problems. DRL-Router employs the DRL method to approximate the full travel time distribution of a given routing policy and then makes improvements with respect to the user-defined RSP objective through a generalized policy iteration scheme. DRL-Router is 1) universal, i.e., it is applicable to a variety of RSP objectives; 2) model free, i.e., it does not rely on well calibrated travel time distribution models; 3) it is adaptive with navigation objective changes; and 4) fast, i.e., it performs real-time decision making. Extensive experimental results and comparisons with baseline algorithms in various transportation networks justify both the accuracy and efficiency of DRL-Router.

Spatio-Temporal Characterization of Stochastic Dynamic Transportation Networks

This paper addresses the problem of modeling stochastic dynamic transportation networks, where travel times are random variables with time-varying distributions and spatio-temporal dependencies. It presents a taxonomy of modeling approaches used in the literature and defines extended taxonomic categories to better capture the characteristics of transportation networks. A two-part approach is presented to characterize transportation networks spatially and temporally based on the network structure and observed travel time data. The first part implements a community detection approach from network science modified for the application to transportation networks. The community detection approach is further adapted to use dynamic time warping distance to measure the dissimilarity between time series of link travel times. The second part implements a change point detection approach that identifies points in time when there are changes in the underlying link travel time distributions generating the observed time series. The proposed approach is tested via sensitivity analysis using the large-scale Chicago network and its corresponding travel time data. Sensitivity analysis with varying model parameters demonstrates the robustness of the network characterization and helps determine the most suitable parameter values. The sensitivity analysis with respect to varying weather conditions and demand patterns in the network demonstrates that the spatial and temporal characteristics are robust with respect to changing exogenous and endogenous conditions.

Travel time variation and its impact on the elasticity of route choice model parameters

Travel time is an uncertain variable with inherited uncertainty for many reasons, such as measurement error, perception error, and temporal aggregation variation impacts. Many researchers have considered travel time as an exact value for different limitations, including models’ restrictions and being unaware of the travel time distribution. However, previous studies have shown that standard logit and probit models can result in biased estimations with uncertain variables or variables with errors (EIV). Nevertheless, limited evidence is available on the magnitude of this bias and the impact of the uncertain variable distribution on the estimated parameters. In this paper, we use a simulation-based approach to explore the uncertainty of variables in the models’ estimation. We check the difference between standard and simulation-assisted models for four previously observed distributions with uncertainty values in the range of common coefficient of variation (Cov) of travel time. Results show that the logit's coefficients and elasticity values with EIV consideration can be 63% and 70% different from those of a standard logit model. The probit coefficients and elasticity differ up to 75% and 124%, respectively, in a binary choice situation. Changing the data and models for a multinomial situation shows that logit has 60% biasedness again while probit undergoes up to 800%. A sensitivity analysis on elasticity values of CoV is done, which unveils that both models’ elasticities change according to a similar pattern but with different intensities. The results suggest that the standard logit handles uncertainty better than the probit model. Yet we cannot present any intuitive reason to support this observation or against it. Procedures like those implemented in this research are suggested to address the biasedness of the results.

Study on the Shortest Reliable Path of Stochastic Time-Dependent Transportation Networks considering Waiting Time at Signalized Intersections

Theoretical research is conducted on finding the shortest path with stochastic and time-dependent characteristics of link travel time in urban road networks. Considering the influence of signalized intersections on travel time, the research first presents a function of waiting time at signalized intersections and analyzes its characteristics. Then, considering the reliability of travel time, the travel time model under the min-max theorem is established, and a mathematical proof that the stochastic time-dependent traffic networks can be reduced to a deterministic time-dependent network is presented by using the first mathematical induction. Finally, based on analyzing the characteristics of the shortest path and minimum travel time, which vary with the start time, we propose solving the shortest path problem with a shortest path algorithm based on Dijkstra’s algorithm that takes the waiting time at signalized intersections into consideration. The research results showed that the algorithm proposed in this study does not depend on the acquisition of the probability distribution of travel time compared with the traditional algorithm. The range of uncertain travel time can be derived from historical data and travelers’ experiences, and the obtained shortest path has more robust time reliability.

Distributionally Robust Chance-Constrained p-Hub Center Problem

The p-hub center problem is a fundamental model for the strategic design of hub location. It aims at constructing p fully interconnected hubs and links from nodes to hubs so that the longest path between any two nodes is minimized. Existing literature on the p-hub center problem under uncertainty often assumes a joint distribution of travel times, which is difficult (if not impossible) to elicit precisely. In this paper, we bridge the gap by investigating two distributionally robust chance-constrained models that cover, respectively, an existing stochastic one under independent normal distribution and one that is based on the sample average approximation approach as a special case. We derive deterministic reformulations as a mixed-integer program wherein a large number of constraints can be dynamically added via a constraint-generation approach to accelerate computation. Counterparts of our models in the emerging robust satisficing framework are also discussed. Extensive numerical experiments demonstrate the encouraging out-of-sample performance of our proposed models as well as the effectiveness of the constraint-generation approach. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods &amp; Analysis. Funding: This work is partially supported by the National Natural Science Foundation of China [Grants 72101187 and 72021002] and Early Career Scheme from the Hong Kong Research Grants Council General Research Fund [Grant 9043424] and NSFC/RGC Joint Research Scheme N_CityU105/21. Y. Zhao is supported by the Ministry of Education, Singapore, under its 2019 Academic Research Fund Tier 3 grant call [Grant MOE-2019-T3-1-010]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0113 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0113 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

The Role of Anomalous Transport in Long‐Term, Stream Water Chemistry Variability

AbstractWe investigate the occurrence of anomalous (non‐Fickian) transport in an hydrological catchment system at kilometer scales and over a 36‐year period. Using spectral analysis, we examine the fluctuation scaling of long‐term time series measurements of a natural passive tracer (chloride), for rainfall and runoff. The scaling behavior can be described by a continuous time random walk (CTRW) based on a power‐law distribution of transition times, which indicates two distinct power‐law regimes in the distribution of overall travel times in the catchment. The CTRW provides a framework for assessing anomalous transport in catchments and its implications for water quality fluctuations.

Study on Tram Travel-Time Reliability Characteristics for Optimal Traffic Signal Control

This paper quantitatively investigates the effects of the number of intersections between adjacent stations [Formula: see text] and different periods on tram travel-time reliability to provide a decision basis for adopting optimal signal-control methods. Station spacing data, intersection information on the line, 10 day planned operation schedules, and actual operation data of Zhangjiang tram line 1 were collected. The tram travel-time distributions were analyzed under seven typical scenarios (i.e., N = 0, 1, 2, 3, off-peak hours, morning peak hours, and evening peak hours). The results showed that the lognormal distribution described the tram travel time better than did the normal and gamma distributions. It was demonstrated that scenarios [Formula: see text], [Formula: see text], and off-peak hours were of high reliability; morning peak hours and evening peak hours were of medium reliability; and scenarios [Formula: see text] and [Formula: see text] were of low reliability. The unreliability of travel time increased along with the increase of the mean and the fluctuation of travel time. An optimized signal-control strategy based on travel-time reliability was put forward and VISSIM simulation of an interval was conducted, verifying the effectiveness of the proposed strategy. The findings will help tram-management agencies to adopt suitable and flexible signal-control strategies according to the actual varying condition.

Numerical evaluation of photosensitive tracers as a strategy for separating surface and subsurface transient storage in streams

We numerically evaluated photosensitive tracers as a potential strategy for separating the effects of surface and hyporheic storage zones (SSZs and HSZs, respectively) on stream corridor transport. Correctly separating HSZ and SSZ effects is critical to estimating the hydro-biogeochemical function of a stream because HSZs and SSZs expose solutes to significantly different biogeochemical conditions, like sunlight exposure, microbial processes, and oxygen availability. Our numerical experiments used a multiscale river-corridor transport model implemented in the ATS code, which accommodates multiple storage zones with distinct travel time distributions and biogeochemical reactions. For parameter inferences, we used Bayesian inverse modeling. We found that breakthrough curves for photo-decaying tracers from day and night injection can delineate surface and hyporheic transient storage contributions, but only when interpreted jointly through a two-storage zone model. Numerical experiments that used only daytime injection or interpreted breakthrough curves with a single storage zone model yielded good fit to breakthrough curves, but parameter estimates were biased and controlling processes misattributed, examples of good model fits for the wrong reasons. Using those biased parameter estimates in reactive transport simulations resulted in significantly different projections of denitrification, which underscores the potential for stream function to be mischaracterized if tracer tests are interpreted through an inappropriately simplified model for transient storage. More generally, this study highlights the role of modeling in evaluating the experimental design and identifying the potential of system mischaracterization and its implications.