Path Travel Time Research Articles

A novel modelling framework for real-time prediction of path travel times using both traffic and weather data

The problems of path travel time predictions have been studied over decades. Traditional approaches to this challenge have relied on different traffic data. However, in metropolitan cities with frequent rainfall, there is a need to consider the weather effects on real-time prediction of path travel times. Hence, this research integrates traffic data with weather data, including rainfall intensity data and weather forecast data to consider the temporal relationships between weather data and path travel times. The proposed modelling framework is evaluated with data from a major expressway and an urban arterial road in Hong Kong. Results unequivocally demonstrate that incorporating weather data significantly boosts prediction accuracy. This study also examines the impact of different frequencies on weather data, as well as weather forecast correctness, on prediction accuracy. Finally, the applicability of the proposed modelling framework has been verified without and with the input of ground truth on path travel times.

Data driven origin–destination matrix estimation on large networks—A joint origin–destination-path-choice formulation

This paper presents a novel approach to data-driven time-dependent origin–destination (OD) estimation using a joint origin–destination-path choice formulation, inspired by the well-known equivalence of doubly constraint gravity models and multinomial logit models for joint O–D choice. This new formulation provides a theoretical basis and generalizes an earlier contribution. Although including path choice increases the dimensionality of the problem, it also dramatically improves the quality of the data one can directly use to solve it (e.g. measured path travel times versus coarse centroid-to-centroid travel times); and opens up possibilities to combine different assimilation techniques in a single framework: (1) fast shortest path set computation using static (e.g. road type) and dynamic (speed, travel time) link properties; (2) predicting a “prior OD matrix” using the resulting path-shares and (estimated or measured) production and attraction totals; and (3) scaling/constraining this prior using link flows (informative of demand). If the resulting system of equations has insufficient rank, we use principal component analysis to reduce the dimensionality, solve this reduced problem, and transform that solution back to a full OD matrix. Comprehensive tests and sensitivity analysis on 7 networks with different sizes and characteristics give an empirical underpinning of the extended equivalence principle; demonstrate good accuracy and reliability of the OD estimation method overall; and suggest that the method is robust with respect to major assumptions and contributing factors.

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.

Enhancement of Harris Hawks optimization applied in path planning for an indoor navigation mobile application

The research focuses on the enhancement of Harris Hawks Optimization (HHO) algorithm in achieving an efficient path planning, specifically in indoor environments. It solves problems encountered in HHO; firstly, the exploration operator of HHO is modified to incorporate the survival of the fittest principle, this ensures a controlled diversity by using an Exponential Ranking selection method. The method aims to guide the algorithm to find a more optimal solution while allowing it to search for alternative paths. Secondly, Linear Path Strategy is used to reduce the number of nodes in the paths, therefore minimizing its length and simplifying trajectories. In addition, Linear Path Strategy aims to create smoother paths and avoid obstacles, improving the overall performance of the algorithm. Lastly, general multi-objective formula is defined to evaluate path length and travel time. Considering these factors established a balanced evaluation metric, which provided a detailed assessment of path quality for scenarios like indoor navigation. Comparative analysis was done, and results highlighted the effectiveness of EHHO in generating better paths, in comparison with Ant Colony Optimization (ACO), Grey Wolf Optimization (GWO), and with the current HHO algorithm. It outperformed the algorithms compared in terms of path length, travel time, and efficiency of the execution, especially in a complex environment. In conclusion, EHHO algorithm showed promising results in providing shorter, faster, and more efficient routes, with potential applications across different domains that requires optimal path planning solutions.

Non-additive network pricing with non-cooperative mobility service providers

This study addresses a mobility network pricing problem in a competitive environment. We consider a multimodal transportation network where the links are operated by multiple profit-maximizing, mobility service providers (MSPs). We take the perspective of a network regulator that aims to increase ridership in a target mobility network by providing non-additive, path-based subsidies to travelers. We model paths’ attractiveness using generalized cost functions that combine path travel time and path cost, and we use linear elastic travel demand functions to capture the proportion of demand served by a path. MSPs are non-cooperative and adjust link fares according to the subsidy policy implemented by the regulator. The goal of the network regulator is to solve a budget-constrained mobility network pricing problem under MSP competition. This game-theoretical framework is modeled as a single-leader multi-follower game (SLMFG) wherein the leader player represents the network regulator and multiple follower players represent the MSPs. We conduct a theoretical analysis of this SLMFG by identifying necessary and sufficient conditions for the existence of solutions to the parameterized generalized Nash equilibrium problem (GNEP) that is played amongst MSPs. We show that this GNEP is jointly convex and we use this property to develop an exact numerical approach to solve the SLMFG based on customized branch-and-bound algorithms. Numerical results reveal the impact of MSP competition in this mobility network pricing problem and shed novel insights into the design of optimal path-based subsidy policies.

Dynamic path planning via Dueling Double Deep Q-Network (D3QN) with prioritized experience replay

Path planning is a key requirement for mobile robots employed for different tasks such as rescue or transport missions. Conventional methods such as A* or Dijkstra to tackle path planning problem need a premise map of the robot's environment. Nowadays, dynamic path planning is a popular research topic, which drives mobile robots without prior static requirements. Deep reinforcement learning (DRL), which is another popular research area, is being harnessed to solve dynamic path planning problem by the researchers. In this study, Deep Q-Networks, which is a subdomain of DRL are opted to solve dynamic path planning problem. We first employ well known techniques Double Deep Q-Networks (D2QN) and Dueling Double Deep Q-Networks (D3QN) to train a model which can drive a mobile robot in environments with static and dynamic obstacles within 3 different configurations. Then we propose D3QN with Prioritized Experience Replay (PER) extension in order to further optimize the DRL model. We created a test bed to measure the performance of the DRL models against 99 randomly generated goal locations. According to our experiments, D3QN-PER method performs better than D2QN and D3QN in terms of path length and travel time to the goal without any collisions. Robot Operating System and Gazebo simulation environment is utilized to realize the training and testing environments, thus, the trained DRL models can be deployed to any ROS compatible robot seamlessly.

Acoustic arrival patterns in the Beaufort duct using normal mode and ray trace acoustic prediction models

The stratification of the Beaufort Sea has experienced significant changes over the last few decades resulting in a subsurface duct between 100- and 300-meters depths, known as the Beaufort Duct. This duct allows for long-range acoustic transmissions due to little interaction with the seafloor or sea surface. Acoustic arrival predictions for broadband acoustic sources centered around 250 Hz, such as those deployed in the Beaufort Sea in 2016–2017 show a peak acoustic arrival prior to the final cutoff centered on the sound speed minimum in the duct. This reverse dispersion feature in the acoustic time front can be connected back to the unique ducting features in the sound-speed profile. This relationship is explored using normal mode modeling and geometric optics. Modal speed predictions and ray path lengths and travel times are used to interpret the acoustic arrival patterns, particularly the dispersion feature present in the acoustic time front.

A Reliability-Based Network Equilibrium Model with Electric Vehicles and Gasoline Vehicles

With the popularity of electric vehicles, they have become an indispensable part of traffic flow on the road network. This paper presents a reliability-based network equilibrium model to realise the traffic flow pattern prediction on the road network with electric vehicles and gasoline vehicles, which incorporates travel time reliability, electric vehicles’ driving range and recharge requirement. The mathematical expression of reliable path travel time is derived, and the reliability-based network equilibrium model is formulated as a variational inequality problem. Then a multi-criterion labelling algorithm is proposed to solve the reliable shortest path problem, and a column-generation-based method of the successive average algorithm is proposed to solve the reliability-based network equilibrium model. The applicability and efficiency of the proposed model and algorithm are verified on the Nguyen-Dupuis network and the real road network of Sioux Falls City. The proposed model and algorithm can be extended to other road networks and help traffic managers analyse traffic conditions and make sustainable traffic policies.

Equilibrium condition-based optimization models for network-wide travel time estimation using limited observed data

This paper presents a series of optimisation models to estimate network-wide travel times under equilibrium conditions. The proposed models estimate the upper and lower bounds (ULB) of the maximum total travel time (MTTT), path travel time (PTT), and link travel time (LTT). The uncertainty range of travel time is obtained by subtracting the upper bound of travel time from the corresponding lower bound. To minimise the uncertainty ranges of the estimated travel times, the relationship of PTTs is introduced as a generalised equilibrium condition. Numerical experiments show that adopting the equilibrium condition can minimise the uncertainty ranges of the travel time estimation. The proposed method can also more accurately estimate the travel times even when the observed data are limited in the entire network. These findings provide a basis for further research on the travel time observability problem of travel time estimation for the whole territory of the network.

Enhancing remote sensing of water temperature using acoustic tomography and 3-D-RPS algorithm

Remote sensing of water temperature and flow dynamics is of paramount importance for water environment management. Coastal acoustic tomography (CAT), an innovative method for remote sensing in underwater environments, utilizes the dual-way travel time of multiple sound paths to reconstruct the underwater temperature field. However, the transmission experiments are susceptible to data noise caused by station drift and inaccuracies in travel time extraction. In this study, a three-dimensional Rousseeuw Phase-Space (3-D-RPS) thresholding algorithm is proposed to remove outliers in the travel time data obtained from Huangcai Reservoir using three CAT systems on September 16, 2020. Additionally, this work includes grid partitioning based on sound path propagation, calculation of sound path lengths, and reference transmission time within each grid, construction of a sparse matrix, and inversion of the two-dimensional temperature field and its associated inversion error. The accuracy and applicability of the proposed method are confirmed through a comparison with data obtained from temperature–depth (TD) sensors. The results demonstrate the precision and suitability of this approach. By effectively mitigating the impact of station drift and extraction accuracy issues, this method provides a reliable temperature field estimation.

Real-time estimation of multi-class path travel times using multi-source traffic data

In practice, most of the intelligent transportation systems provide average travel times of all vehicles on selected paths in real time on a regular basis. However, path travel times of different vehicles could vary widely under different traffic conditions. There is a need to consider the differences in vehicle classes for path travel time estimation. This paper proposes a novel modeling framework that considers variance–covariance relationships between vehicle classes for real-time estimation of multi-class path travel times with use of multi-source traffic data collected from various types of sensors. The proposed methodology is examined with a case study of a selected urban expressway in Hong Kong with data obtained from multiple sources. The path travel time estimates by vehicle class are validated and the results demonstrate the merits and performance of the proposed framework.

Studying inner core and lower mantle structure with a combination of PKP and converted SKP and PKS waves

SUMMARYStructure of the inner core is often measured through traveltime differences between waves that enter the inner core (PKPdf) and waves that travel through the outer core only (PKPab and PKPbc). Here we extend the method to converted waves PKSdf and SKPdf and compare results to PKP wave measurements. PKSdf and SKPdf have a very similar path to PKPdf and if velocity variations are present in the inner core, all three wave types should experience them equally. Since traveltime deviations can be due to velocity changes (either isotropic or anisotropy) as well as wave path deviations born from heterogeneity, we simultaneously investigate wave path directions and traveltimes of PKP, SKP and PKS waves for several source-array combinations. One of the path geometries is the anomalous polar corridor from South Sandwich to Alaska, which has strong traveltimes anomalies for PKPdf relative to more normal equatorial path geometries. Here we use array methods and determine slowness, traveltime and backazimuth deviations and compare them to synthetic data. We find that path deviations from theoretical values are present in all wave types and paths, but also that large scatter exists. Although some of the path deviations can be explained by mislocation vectors and crustal variations, our measurements argue that mantle structure has to be considered when investigating inner core anisotropy. Our polar path data show similar traveltime residuals as previously published, but we also find slowness residuals for this path. Interestingly, SKPdf and PKSdf for the South Sandwich to Alaska path show traveltime residuals that are partly opposite to those for PKPdf, possibly due to an interaction with a localized ultra-low velocity zone where waves enter the core.

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.

Travel Time Probability Prediction Based on Constrained LSTM Quantile Regression

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

Dynamic Path Optimization Based on Improved Ant Colony Algorithm

Dynamic path optimization is an important part of intelligent transportation systems (ITSs). Aiming at the shortcomings of the current dynamic path optimization method, the improved ant colony algorithm was used to optimize the dynamic path. Through the actual investigation and analysis, the influencing factors of the multiobjective planning model were determined. The ant colony algorithm was improved by using the analytic hierarchy process (AHP) to transform path length, travel time, and traffic flow into the comprehensive weight-influencing factor. Meanwhile, directional guidance and dynamic optimization were introduced to the improved ant colony algorithm. In the simulated road network, the length of the optimal path obtained by the improved ant colony algorithm in the simulation road network is 3.015, which is longer than the length of the optimal path obtained by the basic ant colony algorithm (2.902). The travel time of the optimal path obtained by the improved ant colony algorithm (376 s) is significantly shorter than that of the basic ant colony algorithm (416.3 s). The number of iterations of the improved ant colony algorithm (45) is less than that of the basic ant colony algorithm (58). In the instance network, the number of iterations of the improved ant colony algorithm (18) is less than that of the basic ant colony algorithm (26). The travel time of the optimal path obtained by the improved ant colony algorithm (377.1 s) is significantly shorter than that of the basic ant colony algorithm (426 s) and the spatial shortest distance algorithm (424 s). Compared with the basic ant colony algorithm and the spatial shortest distance algorithm, the results of the optimal path obtained by the improved ant colony algorithm were more accurate, and the effectiveness of the improved ant colony algorithm was verified.

General solution scheme for the static link transmission model

Most static traffic assignment models, both in the literature and in practice, are neither capacity constrained nor storage constrained. They allow flows to exceed the link capacity and/or queues to exceed the link length. Recent studies in this area have resulted in novel approaches that do consider capacity constraints, resulting in residual queues, and sometimes even storage constraints, resulting in possible queue spillback. We build upon the results of these works and in particular on the model formulated in Bliemer and Raadsen (2020) that introduced a static network loading model formulation that is both capacity constrained as well as storage constrained. Their static network loading model formulation is derived from – and consistent with - the link transmission model, a well-established dynamic network loading model. It is referred to as the static link transmission model (sLTM) in this paper. This model considers a general concave fundamental diagram for each link and a general first order node model. It is well known that ignoring queue spillback can result in significant underestimation of path travel times. This is especially true for paths that do not traverse any of the bottleneck(s) directly, but that are affected by space occupied by queues that are spilling back. The prospect of being able to capture queuing and spillback effects in static assignment provides new opportunities for improving the modelling capabilities of this paradigm. In this paper, we propose a solution scheme to sLTM capable of finding a solution on large scale networks. This is the first time that an algorithm is proposed for solving an analytical static model with queue spillback. The inclusion of a node model in a static context - while enhancing the model's capabilities – generally results in the absence of a guaranteed convergent algorithm, and introducing spillback exacerbates the issue. Given the challenges of finding a stable solution, we discuss a base solution scheme and three (configurable) extensions. Further, we investigate algorithmic settings with respect to convergence and its impact on computational cost. A large-scale case study demonstrates the feasibility of the proposed scheme by finding solutions under the most challenging of conditions in a real-world setting. We show that improving convergence capabilities negatively affects computational efficiency. To this end, several potential improvements based on our findings are discussed. Lastly, we discuss the potential of this line of research in more general terms, highlighting strengths and weaknesses following our experiences.

Penerapan Algoritma Dijkstra pada Pendistribusian Bahan Bakar Minyak di Pontianak

Determination of the shortest path or the fastest travel time is a problem that occurs to drivers of trucks loaded with fuel oil (BBM) when delivering their tanks to one of the public refueling stations (SPBU) in Pal Lima. To get to the destination, several paths that can be passed. This study aims to determine the shortest path and fastest travel time using Dijkstra's algorithm. Dijkstra's algorithm can be used on both directed and weighted graphs. The first step that must be done is to determine the starting node and destination node. After that, the calculation is carried out from the initial departure node to the neighboring node, the node with the smallest weight is used as the next calculation node. The same is done until all nodes are evaluated. Crossroads are assumed as vertices and between intersections as edges in Dijkstra's algorithm. From the results of the study, the shortest path was obtained through the Kapuas 2 Toll Road, Jl. Adi Sucipto, Jl. Imam Bonjol, Jl. Tanjung Pura, Jl. Rahadi, Jl. Mr. Love, Jl. Hassanudin, Jl. H. Rais, Pal III, Pal V with a minimum distance of 12,768 Km. For the fastest route, it is through the Kapuas 2 Toll Road, Jl. Major Alianyang, Jl. Arteri Supadio, Jl. General Ayani, Jl. Abdurrahman, Jl. Sultan Syahrir, Dr. Sutomo, Jl. Dr. Wahidin, Jl. Pal V with the fastest travel time of 27 minutes.

On the Characterization of Eco-Friendly Paths for Regional Networks

Macroscopic traffic models represent a promising tool to design strategies for ecological routing. To benefit from this tool, we must first characterize the relationship between path emissions and distance traveled or travel time on aggregated networks, i.e., a regional network. This paper investigates this relationship between two toy networks and a real urban network representing the city of Innsbruck (Austria). We utilize an accumulation-based model based on the Macroscopic Fundamental Diagram to mimic the traffic dynamics in the network and utilize the COPERT IV model to estimate the travel emissions, focusing on the carbon dioxide CO2. We show that there is a linear relationship between the total emissions of CO2 and the average travel time of internal paths, i.e. paths that take place completely within a single region. We also show that in some cases, there is a linear relationship between the total emissions and the average travel distance or travel time of paths that cross multiple regions in the network. However, the latter is not always true as traffic dynamics play an important role in path emissions. In other words, eco-friendly paths on regional networks do not necessarily follow the shortest paths in terms of distance or time.

An Algorithm of Acoustic Emission Location for Complex Composite Structure

Acoustic emission (AE) is widely used in engineering and rock mechanics. The algorithm of AE location based on homogeneous medium or single velocity structure is confronted with lower accuracy when it is applied to the actual working conditions that are prevailing complicated and heterogeneous. In this paper, an AE location algorithm based on complex composite structure (CCS) is proposed via carrying out the following studies: (1) A new travel time calculation scheme suitable for CCS with step-like velocity change is proposed based on an optimized shortest path algorithm. By doing this, a reasonable ray path that is only deflected at the interface is obtained to improve the travel time accuracy. The time complexity of the new algorithm is O(nlog2n). (2) The availability of the new algorithm is verified via a theoretical analysis under a one-dimensional velocity structure as well as an AE experiment using a complex structure under artificial excitation. (3) The AE location during the failure of a simulated CCS in the laboratory indicates that the new algorithm can effectively calculate the travel time and ray path of the sample.

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

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