Travel Time Uncertainty Research Articles

Modeling and Estimating the Effect of a Mix of Varying Levels of Automated Vehicles on Operational Performance of Urban Freeways

Automated vehicles (AVs) will likely influence various aspects of the existing transportation system in the next few decades. Existing literature documents the operational benefits of AVs at different penetration rates. However, estimating the effect of the mix of different levels of AVs on the operational performance of traffic flow has not been explored in the past. This study employs a microsimulation approach to model and estimate the potential effect of varying levels of AVs on the operational performance of freeways. The proposed approach involves a two-step process for calibrating the simulation model. In the first step, the model is calibrated from an operational perspective. In the second step, the calibration is performed from a safety perspective. Thirteen scenarios were generated considering varying penetration rates of different levels of AVs. Congestion index (CI), buffer time (BT), travel time uncertainty (TTU), and delay were computed for each scenario and segment type. The estimations indicate that increasing the penetration of level 3 to level 5 AVs significantly reduces CI, BT, TTU, and delay. In contrast, the effect of level 1 and 2 AVs on freeway operational performance is negligible. Notably, the operational benefits are more pronounced with higher penetration of level 3 and higher AVs. Additionally, the reduction in delay is greater on interchange segments compared with basic freeway segments. The study findings are valuable insights concerning the operational performance of freeways under varying penetration of different levels of AVs, assisting practitioners in formulating AVs-inclusive policies.

Have a Good Travel Time in Routing: Bibliometric Analysis, Literature Review, and Future Directions

ABSTRACTTravel time serves as a critical factor in routing problems, affecting routing decisions, congestion avoidance, and environmental sustainability. In this study, a thorough bibliometric and network analysis is presented based on 1752 documents collected from Web of Science published in the past three decades. CiteSpace is adopted to generate research clusters for topological analysis that graphically illustrate the publications' evolution over time and identify the current state and the emerging trends of routing problems with travel time focus. The collaboration network explores the cooperation patterns between countries and institutions. Attention toward the time‐dependency, uncertainty, dynamic characteristics of travel time, and the influence of travel speed on emissions, is uncovered through document co‐citation analysis. Furthermore, a comprehensive review of the literature has been conducted from an information quality and evolution perspective. Realistic scenarios such as fuel consumption and traffic conditions are eliciting more attention. Significant emphasis is increasingly placed on the time dependency, reliability, uncertainty, and dynamics of travel time. This study systematically reviews and analyzes relevant research on routing problems with travel time focus, identifying key emerging trends and knowledge gaps, and offering valuable insights for future research.

Robust convoy movement problem under travel time uncertainty

A convoy represents a collection of vehicles traveling with a spacing of 50–100 m between them for tactical purposes. The convoy movement problem is a variant of the vehicle routing problem, an NP-hard problem aimed at determining the paths and schedules of convoys. Given the uncertainties in travel times during wartime, attributable to various factors such as road conditions and enemy threats, it is essential to consider uncertain travel times when determining convoy paths and schedules. Therefore, this study introduces a robust convoy movement problem under travel time uncertainty. A polyhedral set for uncertain travel times is used to derive a robust counterpart for the problem. To solve the proposed problem, we establish an exact algorithm that determines optimal solutions by iteratively generating and integrating multiple paths of convoys. This algorithm involves four steps: generation of k-th robust shortest paths, construction of path combinations, adjustment of departure times, and conduction of optimality check. These steps are iterated sequentially until the optimal solution is obtained. In computational experiments, the exact algorithm demonstrates superior performance and reduced computation time compared with the commercial solver CPLEX on both real instances and randomly generated instances. In addition, we conduct a sensitivity analysis for several parameters related to the problem, providing valuable managerial insights for decision-makers.

A multi-objective optimization approach for sustainable and personalized trip planning: A self-adaptive evolutionary algorithm with case study

In the modern tourism landscape, the fusion of sustainability and personalized travel plans marks a significant paradigm shift. This paper presents a novel multi-objective optimization approach for crafting sustainable and personalized tourist trip plans. The proposed model is designed to provide tailored recommendations to tourists, simultaneously minimizing total costs, environmental impacts, and maximizing individual preferences. These recommendations encompass choices such as hotel and resting place selection, daily sequence of attractions, precise visit schedules, and preferred modes of transportation. Addressing intricacies within an urban multi-modal transport system, including factors like traffic lights, weather conditions, and distinct features of each transport mode, the model ensures that tourists can explore scenic spots within their available time windows. To tackle uncertainties in travel time, travel costs, and visit durations, a practical fuzzy optimization approach is employed. For efficient resolution of the multi-objective optimization model, a self-adaptive evolutionary algorithm based on Non-Dominated Sorting Genetic Algorithm II (SA-NSGAII) is developed. The effectiveness of the proposed solution method is verified through comparisons with Augmented ε-Constraint (AUGMECON) and NSGA-II methods, utilizing various benchmark examples. Employing real data from Montreal, an empirical case study is conducted to illustrate the application of the sustainable and personalized trip planning model. The analysis of the solution results demonstrates how this approach can assist tourists in achieving a harmonious balance between sustainability objectives and making well-informed decisions based on their individual preferences.

GPU-accelerated parallel all-pair shortest path routing within stochastic road networks

All-pair shortest path routing within stochastic road networks is often more complicated and computationally challenging than routing in deterministic networks because uncertainties in travel time are introduced. We develop and test a GPU-enabled approach to resolve this computational challenge. This approach is based on a simulation framework that includes four steps: simulation of road networks impedances, computation of candidate paths using an all-pair shortest path algorithm, travel time estimation across candidate paths, and all-pair optimal path calculations. We developed GPU algorithms to accelerate the second and third steps, which are computationally demanding for large road networks. We used the road network of Wuhan, China as a case study. Our experiments indicate that the GPU approach leads to thousands of times in improvement of acceleration, which makes all-pair shortest path routing within stochastic road networks computationally feasible.

Co-optimizing electric bus dispatching and charging considering limited resources and battery degradation

This paper aims to formulate a mathematical model for a multi-type electric bus scheduling problem to determine the optimal fleet composition, bus-to-trip assignment, and partial charging schedule, where the battery degradation, nonlinear charging, and the constraint of charging station capacity are considered. A time-expanded network is proposed to represent the bus-to-trip assignment and partial charging. An adaptive large neighborhood search algorithm is designed to solve the problem. Using a multi-line bus network in Nanjing as the case, empirical operational data is used to generate monthly timetable samples to simulate the uncertainty of trip travel time and energy consumption. The result shows that the charging station capacity can be reduced from 20 (real-world case) to 12, considering the cost-effectiveness and robustness of the bus system. The result of this study also provides suggestions on the charging duration choices and the starting state-of-charge for different periods of the day. In peak and off-peak hours, 20-30-minute charging is recommended for electric buses with state-of-charge lower than 30 %, and 10-minute charging is more recommended when the state-of-charge of the electric bus is between 30 % and 70 %.

Stochastic and robust truck-and-drone routing problems with deadlines: A Benders decomposition approach

Time-definite delivery service requires efficient and punctual delivery within specified deadlines. Enhancing the service level of delivery in last-mile logistics prompted the application of a truck-and-drone cooperative system. However, the inherent uncertainty in travel time contributes to frequent service delays. To address this challenge, our study addresses the stochastic and robust truck-and-drone routing problems with deadlines, aiming to minimize service delay risk under uncertainty. We leverage the sample average approximation (SAA) and robust optimization (RO) approaches to handle uncertainty in scenarios involving both big and small datasets. Benders decomposition (BD) algorithms are developed to solve the SAA and RO truck-and-drone routing problems efficiently. Numerical experiments showcase the algorithms’ effectiveness and reveal interesting insights. These findings suggest the importance of tailoring the approach to data availability for optimizing truck-and-drone delivery under uncertainty. Furthermore, the proposed model formulations and algorithms are generalized to address truck-and-drone routing problems under more complex scenarios, such as that with uncertainty of service time, or with nonlinear objective functions.

Computing the worst-case due dates violations with budget uncertainty

We study the problem of maximizing the violation of due dates when considering either the total violation, or the number of jobs that are tardy. We consider classical completion times and a variant useful in heuristics. The four problems arise when solving (exactly or heuristically) robust scheduling problems with release and due dates/deadlines and processing time uncertainty, and also routing problems with (soft) time windows and travel time uncertainty. We provide polynomial dynamic programming algorithms for the four problems.

Measuring Reliable Accessibility to High-Speed Railway Stations by Integrating the Utility-Based Model and Multimodal Space–Time Prism under Travel Time Uncertainty

Measuring Reliable Accessibility to High-Speed Railway Stations by Integrating the Utility-Based Model and Multimodal Space–Time Prism under Travel Time Uncertainty

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

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

Optimizing business location for small and medium enter¬prises considering travel time uncertainty, natural disasters, and density population: a study case in Jakarta

Optimizing business location for small and medium enter¬prises considering travel time uncertainty, natural disasters, and density population: a study case in Jakarta

An adaptive deep multi-task learning approach for citywide travel time collaborative estimation

The provision of accurate travel time information holds paramount significance for optimizing traffic operations and management. However, existing approaches typically address multiple travel time learning tasks independently, neglecting the correlation of tasks and necessitating the construction of separate models for each task. As the scale of the road network expands, this practice becomes increasingly infeasible. To bridge this gap, this paper presents an adaptive deep multi-task learning model to solve multiple travel time estimation tasks collaboratively from a citywide perspective. The novel model seamlessly integrates geographical, environmental, and spatial-correlated features, capturing the complex non-linear characteristics of travel time in the urban road network through a deep network learning feature representations layer by layer from the input data. Through the paradigm of deep multi-task collaborative learning, the knowledge learned from one task serves as an inductive bias for other tasks, thereby facilitating the learning of related tasks. By modeling the uncertainty of travel time with a probabilistic model, the weights of jointly learned tasks are adaptively fine-tuned in a principled way. Additionally, a novel algorithm is devised to fully leverage the information embedded within the data with partial information. The proposed methodology is evaluated through a case study on the citywide road network in Beijing, China. Empirical results of extensive experiments demonstrate the adeptness of the proposed model in effectively harnessing information transferred from parallel tasks, adaptively fine-tuning the weights of joint learning tasks, and proficiently exploiting data characterized by incomplete labels, therefore leading to superior performance compared to competing methods. The average estimation error of the four jointly learned travel time estimation tasks is about 28.48%, yielding an improvement of over 4% compared to single-task learning models. The results verify the effectiveness and robustness of the proposed model for travel time estimation in the urban road network.

A general variable neighborhood search for the traveling salesman problem with time windows under various objectives

The traveling salesman problem with time windows (TSPTW) has wide practical applications in transportation and scheduling operations. We study the TSPTW in the deterministic case as well as under travel time uncertainty. We consider the three classical TSPTW variants with the objectives of minimizing cost, completion time, and tour duration. In addition, a new TSPTW variant that maximizes the minimum slack of a tour, i.e., the smallest time buffer between the arrival time and the end of the time window over all nodes visited on the tour, is introduced. We further address a variant of the TSPTW in which the arc travel times are uncertain. This problem is modeled by means of an uncertainty set, and the goal is to determine a tour that remains feasible in the worst case within a budget stipulating the sum of all travel time deviations from their nominal values. To solve all targeted problem variants, we develop a two-phase general variable neighborhood search (GVNS) that applies an efficient move evaluation approach within the local search. Extensive numerical experiments on benchmark instances from the literature show that our GVNS finds high-quality solutions that are competitive with those obtained by the state-of-the-art heuristics for all problem variants.

Measuring route diversity in spatial and spatial-temporal public transport networks

Route diversity is a pivotal metric for evaluating the redundancy of transportation networks, a fundamental aspect of system resilience. This study provides a comprehensive exploration of route diversity in multimodal public transport systems, specifically considering the unique characteristics of bus networks. Our research introduces a two-pronged approach to measuring route diversity within spatial public transport networks, delving into service-based and infrastructure-based perspectives. The former assesses redundancy against transit service disruptions by factoring in transit line overlaps, while the latter evaluates redundancy against infrastructure-related interruptions by considering overlapping road segments on which transit lines rely. In addition, the study advances by modelling public transport systems as multilayer spatial-temporal networks, integrating time-variable service frequency and travel time uncertainty, which enables us to derive route diversity for origin-destination (O-D) pairs across different time periods.We present a case study of the multimodal public transport network in Jiading District, Shanghai, revealing a power-law distribution of the route diversity. The results unveil O-D pairs with lower route diversity, underscoring their lack of resilience against various disturbances. Lower service-based route diversity suggests the necessity of enhancing service frequency and bolstering cross-line combined transit scheduling, while lower infrastructure-based route diversity could warrant the design of road-diversified transit lines, especially within bus corridors. Besides, relative route diversity between the two indices highlights specific O-D pairs with notable disparities in service and infrastructure redundancy. This difference is correlated with the distance between O-D pairs and the road network's configuration. This analysis underscores the method's potential to offer more relevant insights to public transport planners and operators for adjusting transit lines and schedules through a resilience-focused lens.

Reinforcement learning for humanitarian relief distribution with trucks and UAVs under travel time uncertainty

Effective humanitarian relief operations are challenging in the aftermath of disasters, as trucks are often faced with considerable travel time uncertainties due to damaged transportation networks. Efficient deployment of Unmanned Aerial Vehicles (UAVs) potentially mitigates this problem, supplementing truck fleets in an impactful manner. To plan last-mile relief distribution in this setting, we introduce a multi-trip, split-delivery vehicle routing problem with trucks and UAVs, soft time windows, and stochastic travel times for last-mile relief distribution, formulated as a stochastic dynamic program. Within a finite time horizon, we aim to maximize a weighted objective function comprising the number of goods delivered, the number of different locations visited, and late arrival penalties. Our study offers insights into dealing with travel time uncertainty in humanitarian logistics by (i) deploying Unmanned Aerial Vehicles (UAVs) as partial substitutes for trucks, (ii) evaluating dynamic solutions generated by two deep reinforcement learning (RL) approaches – specifically value function approximation (VFA) and policy function approximation (PFA) – and (iii) comparing the RL solutions with solutions stemming from mathematical programming and dynamic heuristics. Experiments are performed on both Solomon-based instances and two real-world cases. The real-world cases – the 2015 Nepal earthquake and the 2018 Indonesia tsunami – are based on locally collected field data and real-world UAV specifications, and aim to provide practical insights. The experimental results show that dynamic decision-making improves both performance and robustness of humanitarian operations, achieving reductions in lateness penalties of around 85% compared to static solutions based on expected travel times. Furthermore, the results show that replacing half of the trucks with UAVs improves the weighted objective value by 11% to 56%, benefitting both reliability and location coverage. The results indicate that both the deployment of UAVs and the use of dynamic methods successfully mitigate travel time uncertainties in humanitarian operations.

Electric bus fleet scheduling under travel time and energy consumption uncertainty

The public transportation system is experiencing a substantial shift due to the rapid expansion of electromobility infrastructure and operations. This transformation is anticipated to contribute to decarbonizing and promoting environmental sustainability significantly. Among the most pressing planning issues in this area is the optimization of operational and strategic costs associated with electric fleets, which has recently garnered the attention of researchers. This paper investigates the scheduling and procurement problem of electric fleets under travel time and energy consumption uncertainty. A novel mixed-integer linear programming model is proposed, which determines the number of buses required to cover all trips, yields the schedule of the trips, and creates bus charging plans. The robust optimization paradigm is employed to address uncertainty, and a new budget uncertainty set is introduced to control the robustness of the solution. The efficiency of the model is evaluated through an extensive Monte Carlo simulation. Additionally, a case study is conducted on the off-campus college transport network at Binghamton University to demonstrate the real-world applicability of the model. The numerical results have shown that ignoring uncertainty can lead to schedules where up to 48% of the trips are affected, which are either delayed or missed. The proposed approach can also be applied to other transportation networks with similar characteristics and uncertainties.

Using long-range transmissions in the Beaufort Gyre to test the sound-speed equation at high pressure and low temperature.

An ocean acoustic tomography array with a radius of 150 km was deployed in the central Beaufort Gyre during 2016-2017 for the Canada Basin Acoustic Propagation Experiment. Five 250-Hz transceivers were deployed in a pentagon, with a sixth transceiver at the center. A long vertical receiving array was located northwest of the central mooring. Travel-time anomalies for refracted-surface-reflected acoustic ray paths were calculated relative to travel times computed for a range-dependent sound-speed field from in situ temperature and salinity observations. Travel-time inversions for the three-dimensional sound-speed field consistent with the uncertainties in travel time [∼2 ms root mean square (rms)], receiver and source positions (∼ 3 m rms), and sound speed calculated from conductivity-temperature-depth casts could not be obtained without introducing a deep sound-speed bias (below 1000 m). Because of the precise nature of the travel-time observations with low mesoscale and internal wave variability, the conclusion is that the internationally accepted sound-speed equation (TEOS-10) gives values at high pressure (greater than 1000 m) and low temperature (less than 0 °C) that are too high by 0.14-0.16 m s-1.

Sustainable group tourist trip planning: An adaptive large neighborhood search algorithm

The tourism industry is a key driver of economic growth and contributes to the achievement of sustainability goals. This paper presents a multi-objective group tourist planning problem that considers economic, environmental, and social dimensions simultaneously. The proposed model minimizes total cost and environmental impacts while maximizing the total collected prizes from tourists' interests. We introduce the lost profit opportunity for the cost of tours from an economic perspective for the first time. From an environmental perspective, the model minimizes both carbon emissions for transportation and the waste produced by tourists. Social satisfaction is addressed by considering tourists' preferences for visiting tourist sites and their interests in participating in group tours, maximizing total collected prizes. Uncertainties in travel time and prize values are addressed by using a fuzzy programming approach. A multi-objective adaptive large neighborhood search (ALNS) algorithm is developed to solve the proposed multi-objective group tourist planning problem, offering various removal, insertion, and local search heuristic procedures. Extensive analyses and computations are conducted to demonstrate the performance of the proposed multi-objective optimization model and the ALNS metaheuristic algorithm in solving large-scale instances. The results demonstrate the effectiveness of our approach in aiding tourism managers to make informed decisions that balance economic, environmental, and social objectives.

Reliable dynamic wireless charging infrastructure deployment problem for public transport services

Dynamic wireless power transfer (DWPT) technology offers the promise of eliminating the limited driving range of electric buses (EBs), providing greater convenience and safety benefits through the ability to charge EBs in motion. It may be possible to effectively circumvent the drawbacks of EBs such that it becomes mainstream in the future EB market. In this paper, we study the robust DWPT deployment problem for an EB system, aiming to determine the DWPT facility deployment, battery size, and en-route charging schedule simultaneously. We first formulate the deterministic problem as a novel mixed-integer linear programming (MILP) model. Next, we consider the energy consumption uncertainty and travel time uncertainty to develop a two-stage robust model. We further analyze the structural properties of our proposed model, and implement the column-and-constraint generation (C&CG) method to solve it optimally. Finally, a series of experiments based on a test bus network and the National University of Singapore internal bus network are carried out to verify the efficiency and effectiveness of our models and algorithms. Some managerial insights are also provided that public transit (PT) operators could use to enhance the efficiency of the EB system in the future.

A kriging interpolation model for geographical flows

The kriging model can accommodate various spatial supports and has been extensively applied in hydrology, meteorology, soil science, and other domains. With the expansion of applications, it is essential to extend the kriging model for new spatial support of high-dimensional data. Geographical flows can depict the movements of geographical objects and imply the underlying mobility patterns in geographical phenomena. However, due to the bias, sparsity, and uneven quality of flow data in the real world, research about flows remains hindered by the lack of complete flow data and effective flow interpolation methods. In this study, we design a kriging interpolation model for flows based on several flow-related concepts and the autocorrelation of flows. We also analyze the second-order stationarity and anisotropy in the flow spatial random field. To illustrate the effectiveness and applicability of our method, we conduct two case studies. The former case study compares several experiments of flow density interpolation using Beijing mobile signaling data and illustrates the conditions of applicable areas. The latter case study extends our model to other flow attributes, such as travel time uncertainty, using Beijing taxi origin-destination flow data. The results of these cases demonstrate the effectiveness and high accuracy of our model.