Expected Travel Time Research Articles

Layout Planning of a Basic Public Transit Network Considering Expected Travel Times and Transportation Efficiency

Urban transit systems are crucial for modern cities, providing sustainable and efficient transportation solutions for residents’ daily commutes. Extensive research has been conducted on optimizing the design of transit systems. Among these studies, designing transit line trajectories and setting operating frequencies are critical components at the strategic planning level, and they are typically implemented in an urban integrated transportation network. However, its computational complexity grows exponentially with the expansion of urban integrated transportation networks, resulting in challenges to global optimization in large-scale cities. To address this problem, this study investigates the layout planning of a basic public transit network (BPTN) to simplify the urban integrated transportation network by filtering out road segments and intersections that are unattractive for both users and operators. A non-linear integer programming model is proposed to maximize the utility of the BPTN, which is defined as a weighted sum of expected travel times (from a user perspective) and transportation efficiency (from an operator perspective). An expected transit flow distribution (ETFD) analysis method is developed, combining different assignment approaches to evaluate the expected travel time and transportation efficiency of the BPTN under various types of transit systems. Moreover, we propose an objective–subjective integrated weighting approach to determine reasonable weight coefficients for travel time and transportation efficiency. The problem is solved by a heuristic solution framework with a topological graph simplification (TGS) process that further simplifies the BPTN into a small-scale graph. Numerical experiments demonstrate the efficacy of the proposed model and algorithm in achieving desirable BPTN layouts for different types of transit systems under variable demand structures. The scale of the BPTN is significantly reduced while maintaining a well-balanced trade-off between expected travel time and transportation efficiency.

Urban Emergency Evacuation Path Optimization Based on Uncertain Environments to Enhance Response for Symmetric and Asymmetric Evacuation Problems

Background: Serious secondary disasters caused by extreme natural weather conditions occur frequently, making it essential to establish a scientific and efficient modern emergency management system to maximize life-saving efforts. Methods: This study focuses on the uncertain environment of urban road networks and employs fuzzy theory to construct a 0–1 integer programming model for emergency evacuation paths that minimizes the average expected travel time. Results: We enhanced the neighborhood search strategy of the traditional ACO_time by incorporating the 2-opt and 3-opt perturbation mechanisms from the SA algorithm. Additionally, we utilized improved ant-volume and ant-perimeter models, along with their combinations, in the pheromone-updating mechanism of the basic ACO. The heuristic principles of the A* algorithm were integrated, introducing the joint influence of path and time into the heuristic function of the ACO algorithm. Conclusions: The IACO3 algorithm was tested on the Sioux Falls network and the Berlin Heisenheimer Center network. The computation time of the improved IACO3 algorithm was reduced by up to 20% compared to the original IACO3 algorithm in relation to the SA algorithm, with only a 4–5% increase in computation time compared to the ACO_time algorithm, which translates to an increase of merely 4–5 s. This demonstrates the superior solution efficiency of the IACO3 algorithm.

The Online Shortest Path Problem: Learning Travel Times Using a Multiarmed Bandit Framework

In the age of e-commerce, logistics companies often operate within extensive road networks without accurate knowledge of travel times for their specific fleet of vehicles. Moreover, millions of dollars are spent on routing services that fail to accurately capture the unique characteristics of the drivers and vehicles of the companies. In this work, we address the challenge faced by a logistic operator with limited travel time information, aiming to find the optimal expected shortest path between origin-destination pairs. We model this problem as an online shortest path problem, common to many last-mile routing settings; given a graph whose arcs’ travel times are stochastic and follow an unknown distribution, the objective is to find a vehicle route of minimum travel time from an origin to a destination. The planner progressively collects travel condition data as drivers complete their routes. Inspired by the combinatorial multiarmed bandit and kriging literature, we propose three methods with distinct features to effectively learn the optimal shortest path, highlighting the practical advantages of incorporating spatial correlation in the learning process. Our approach balances exploration (improving estimates for unexplored arcs) and exploitation (executing the minimum expected time path) using the Thompson sampling algorithm. In each iteration, our algorithm executes the path that minimizes the expected travel time based on data from a posterior distribution of the speeds of the arcs. We conduct a computational study comprising two settings: a set of four artificial instances and a real-life case study. The case study uses empirical data of taxis in the 17-km-radius area of the center of Beijing, encompassing Beijing’s “5th Ring Road.” In both settings, our algorithms demonstrate efficient and effective balancing of the exploration-exploitation trade-off.

Microgeographic speed, reliability, and traffic externalities

This paper estimates congestion externalities on a broad sample of roads in England’s capital region. A fixed effects approach that compares across times of day finds that 10% more traffic increases travel time by 4%, erodes reliability, and finds smallest marginal effects on high-capacity roads. I incorporate both expected travel time and reliability into a model of congestion externalities. Combining the model with travel data, I find that Central London’s Congestion Charge exceeds tolled drivers’ external costs if they only reflect travel time and reliability. Despite the large toll in London’s city centre, I find that deadweight loss in untolled parts of the city remains substantial, and that accounting for reliability increases deadweight loss by as much as 55%.

Modeling and optimization of expected travel time for multi‐aisle AS/RSs with two‐class‐based storage policy

AbstractClass‐based storage policy with optimized contour‐shaped class boundary can significantly improve storage system's performance. Surprisingly, this policy has not been explored in widely used multi‐aisle automated storage and retrieval systems (MA‐AS/RSs), which use one storage and retrieval machine to serve multiple aisles with the help of an aisle‐transfer technique. This paper investigates the two‐class‐based storage policy with contour‐shaped class boundary in MA‐AS/RSs that use a transfer car for aisle transfer. The aim is to optimize the system dimensions and class boundary by minimizing system's expected travel time. Based on the approximation of the MA‐AS/RS with a continuous cube and the proposed hierarchical procedure, analytical expected travel time expressions for systems with any dimensions and class boundary are calculated. In addition, based on several proved properties, closed‐form optimal system dimensions and class boundary are derived. Numerical results show the accuracy of our continuous cubic approximation is sufficient. By measuring the performance using the average of expected travel time over all tested systems with various dimensions, we find that (1) class‐based policy with our optimal class boundary can respectively improve the performance by at least 40%, 10%, and 50% compared to three previous policies in the case of 20/80 ABC curve; and (2) system with our optimal dimensions can improve the performance by about 20%–30%. Several managerial insights for warehouse practitioners are presented.

The impact of transportation mode, socioeconomic deprivation and rurality on travel times to radiotherapy and surgical services for patients with prostate cancer: A national population-based evaluation

BackgroundThe distances that patients have to travel can influence their access to cancer treatment. We investigated the determinants of travel time, separately for journeys by car and public transport, to centres providing radical surgery or radiotherapy for prostate cancer. MethodsUsing national cancer registry records linked to administrative hospital data, we identified patients who had radical surgery or radiotherapy for prostate cancer between January 2017 and December 2018 in the English National Health Service. Estimated travel times from the patients’ residential area to the nearest specialist surgical or radiotherapy centre were estimated for journeys by car and by public transport. ResultsWe included 13,186 men who had surgery and 26,581 who had radiotherapy. Estimated travel times by public transport (74.4 mins for surgery and 69.4 mins for radiotherapy) were more than twice as long as by car (33.4 mins and 29.1mins, respectively). Patients living in more socially deprived neighbourhoods in rural areas had the longest travel times to the nearest cancer treatment centres by car (62.0 mins for surgery and 52.1 mins for radiotherapy). Conversely patients living in more affluent neighbourhoods in urban conurbations had the shortest (18.7 mins for surgery and 17.9 mins for radiotherapy). ConclusionTravel times to cancer centres vary widely according to mode of transport, socioeconomic deprivation, and rurality. Policies changing the geographical configuration of cancer services should consider the impact on the expected travel times both by car and by public transport to avoid enhancing existing inequalities in access to treatment and patient outcomes.

Optimization of train schedule with uncertain maintenance plans in high-speed railways: A stochastic programming approach

In high-speed railways, unexpected disturbances on maintenance activities may cause serious delays of the scheduled trains and greatly affect the service quality for traveling passengers. In contrast to most existing studies that focused on deterministic maintenance activities, this paper develops a two-stage stochastic programming approach to address the optimization of train schedules under uncertain maintenance plans. Specifically, in the first stage, we aim to determine the departure times of trains from the origin station, since this information needs to be public to passengers in advanced. The objective function is to minimize the expected travel time of trains under uncertain duration time of maintenance activities. In the second stage, given the specific information of maintenance activities, we generate the train schedule by adjusting the stop patterns, train orders and the assignment of tracks at key stations. Due to the computational difficulties arising from the large number of discrete decision variables, we particularly develop a dual decomposition based solution approach to solve the two-stage stochastic model. Our approach decomposes the original problem into a set of scenario-dependent subproblems with much fewer number of variables, which greatly improves the computational efficiency. Finally, we conduct several sets of real-world instances based on the Beijing–Guangzhou high-speed railway corridor to verify the effectiveness of the proposed model and solution approach. The results demonstrate that our approach evidently outperforms state-of-art solvers (Gurobi), especially for large-scale instances that Gurobi cannot even return feasible solutions.

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.

The Structure of the Warped Io Plasma Torus Constrained by the Io Footprint

AbstractStandard models of force balance along Jovian field lines predict the location of the Io Plasma Torus to be the centrifugal equator of Jupiter’s magnetosphere, that is, the position along the magnetic field lines farthest away from Jupiter’s rotational axis. In many models, the centrifugal equator is assumed to lay on a plane, calculated from a (shifted) dipole magnetic field, rather than on a warped surface which incorporates Jupiter’s higher magnetic field moments. In this work, we use Hubble Space Telescope observations of the Io Main Footprint to constrain density, scale height, and lateral position of the Io Plasma Torus. Therefore, we employ the leading angle of the footprints to calculate expected travel times of Alfvén waves and carry out an inversion of the observations. For the magnetic field, we use the JRM33 magnetic field model. The inversion results show peak densities between ρ0 = 1,830 cm−3 and ρ0 = 2,032 cm−3 and scale heights between H = 0.92RJ and H = 0.97RJ consistent with current literature values. Using a warped multipole centrifugal equator instead of a planar dipole increases the quality of the fit by about 25%. We additionally develop two tests to confirm that the multipole centrifugal equator from the JRM33 model fits explains the applied data set better than the dipole centrifugal equator. The quadropole moments alter Io’s relative position to the torus, which changes the plasma density around Io by up to Δρ/ρ = 20%.

Optimal charging station locations and durations for a transit route with battery-electric buses: A two-stage stochastic programming approach with consideration of weather conditions

While the environmental advantages of battery-electric buses (BEBs) are well-known, their significant differences from diesel buses require alterations to both route design (i.e., charging station locations) and operations (i.e., schedule management and holding control). The location, number, charging duration, and types of charging stations must be considered as part of the planning process. Charging stations can be located at depots, termini, or en-route. This paper considers the long-term planning and optimization problem of en-route charging station locations and charging duration to optimize passengers’ waiting time and operation and capital costs while addressing the weather-induced stochasticity of ridership and battery performance of the BEBs. A linear deterministic optimization model and a two-stage stochastic programming (SP) optimization process are developed to place BEB charging stations along the route and estimate their assigned charging time for both one-way and two-way operations. The developed approaches are tested on two high-demand bus routes in Calgary. The impact of the breakdown of the charging station associated with the maximum charging time on the schedule and the cost of the BEB operation is assessed. The solution of the stochastic model is analyzed using the expected value of perfect information as an index. The results indicate that using the SP model helps decrease the expected travel time of the route while the total cost per trip increases compared to the deterministic model.

Applications of telemedicine: Plastic surgery in the COVID-19 era

Applications of telemedicine: Plastic surgery in the COVID-19 era

Joint column generation and Lagrangian relaxation technique for incident respondent location and allocation

AbstractIncident response operations require effective planning of resources to ensure timely clearance of roadways and avoidance of secondary incidents. This study formulates a mixed‐integer linear program to minimize the total expected travel time and maximize the demand covered. The model accounts for the location, severity, frequency of incidents, dispatching locations, and availability of incident respondents. An integrated methodology that includes column generation and Lagrangian relaxation with a density‐based clustering technique that defines incident hot spots is proposed. The hybrid approach is applied to an empirical case study in Raleigh, NC. A network instance with 10,672 incident sites, clustered with a search distance (ε) of 5 min, is solved efficiently with an optimality gap of 1.37% in 2 min. A Benders decomposition technique is implemented to conduct benchmark analyses. The numerical results suggest that the proposed algorithm can solve the problem efficiently and outperform the benchmark solutions.

Berlin Pankow: a 15-min city for everyone? A case study combining accessibility, traffic noise, air pollution, and socio-structural data

Cars are dominating urban traffic in cities around the world, even though daily trips in many cities are often realized with active modes of transportation or public transport. Urban transport planning processes need to adapt to this reality and the necessity of climate change mitigation. Against this background, the research project “Mobility Reporting”, a joint undertaking of the district Pankow in Berlin and researchers from TU Berlin and TU Dresden, established a new, goal-driven, and participative planning process. The process identified local mobility as one of the central planning goals. The 15-min city (FMC) was thus adduced as a benchmark to analyze the district’s current mobility system and development potential. We conducted extensive accessibility analyses to examine the status quo concerning the FMC. We calculated travel times to essential destinations in daily life by foot, public transport, and car. This analysis was accompanied by a mixed online and paper–pencil survey conducted to evaluate the perceived accessibility of people in Pankow. The survey results shed light on the question of which walking time thresholds constitute a “very good” or “good” accessibility. Further analyses included environmental and social variables, allowing us to check whether areas with different accessibility levels also differ regarding the socio-economic characteristics of their inhabitants. For example, do socially advantaged neighborhoods have better local accessibility? Is there a trade-off between exposure to environmental pollution and good accessibility? With this contribution, we shed light on what an FMC is and ought to be. Results from the survey support the normative and political vision of the FMC. Pankow generally offers the merits of a walkable city, showing the expected travel time differences between the dense inner city and the outskirts. Socially disadvantaged neighborhoods are not consistently less accessible. However, there seems to be a trade-off between good accessibility (especially PT accessibility) and correlated externalities of transport, namely air pollution and noise.

Incorporating travel time means and standard deviations into transportation network design problem: a hybrid method based on column generation and Lagrangian relaxation

ABSTRACT Travel times in real-world transportation networks are affected by many disruptions. When we conduct the network design optimization, the traffic condition and its resulting travel time variability should be taken into account. However, most of the previous network design optimizations adopted the lengths or expected travel times of links. Based on travel time means and standard deviations, we develop an arc-based model that is a nonlinear and concave integer program. By the Dantzig-Wolfe reformulation, we transform it into an equivalent column-based model that is an integer linear program with a large number of variables. Based on the column-based model, we develop a hybrid method based on column generation and Lagrangian relaxation. The restricted master problem can be settled by the linear programming solvers. The pricing subproblems incorporate independent reliable shortest path problems and a knapsack problem. In numerical experiments, the proposed method can generate feasible solutions with good integrality gaps.

A Median-Based Misery Index for Travel Time Reliability

Travel time reliability is vital for both road agencies and road users. Expected travel time reliability can be used by road agencies to assess the state of a transportation system, and by road users, to schedule their trips. Road network deficiencies, such as insufficient traffic flow capacity of a road segment or poor road design, have a negative impact on the reliability of travel times. Thus, to maintain robust and reliable travel times, the detection of road network deficiencies is vital. By continuously analyzing travel times and using appropriate travel time reliability measurements, it is possible to detect existing deficiencies or deficiencies that may eventually occur unless necessary actions are taken. In many cases, indices and measurements of travel time reliability are related to the distribution of the travel times, specifically the skewness and width of the distribution. The current paper introduces a median-based misery index for travel time reliability. The index is robust and handles travel times that follow a skewed distribution well. The index measures the relative difference between the slow travel speeds and the free-flow travel speed. The index is inspired by the median absolute deviation, and its primary application is to detect routes or road segments with potential road network deficiencies. To demonstrate the applicability of the index, we conducted an empirical case study using real travel speed data from the European route E4 in Sweden. The results from the empirical case study indicate that the index is capable of detecting road segments with slow travel speeds regardless of the travel speed distribution.

Dual Dynamic Programming for the Mean Standard Deviation Canadian Traveller Problem

This article studies the mean standard deviation (mean-std) Canadian traveller problem (CTP). Different from the canonical CTP, which aims at minimizing the traveller's expected travel time, while considering edge breakdown probabilities, we introduce the reliability version of CTP, which tries to find a routing policy with the minimal linear combination of the travel time's mean and standard deviation. With the recent development of internet-of-things (IoT) technology, the transportation network's edges' travel-time statistics, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> . <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</i> ., mean and standard deviation, as well as the traversal probabilities, are available to the end users. With those information, we propose a dual dynamic programming (DDP) method, which simultaneously estimates the first-order and the second-order moments of a given decision-list (DL) policy, and thereby makes improvements towards to the optimal one through the generalized policy iteration (GPI) scheme. We construct an open source benchmark environment to evaluate the performance of different mean-std CTP solutions, and show that the DDP method outperforms state of the arts in a range of transportation networks.

Effects of travel time VMS on urban traffic

Expected travel time information on variable message signs (VMS) supports even capacity utilization on the road network. To justify the importance of VMS in urban traffic, general user attitude to VMS was assessed and route choice decisions were investigated through stated preferences. Logit model was used to show how route choices are affected by changing expected travel time, reliability of travel time, and perceived travel time of alternative routes. Applying logistic regression, functions were defined that describe the sensitivity of route change depending on expected travel times.

Rapid intervention vehicles' impact on fire departments' response time

PurposeThe purpose of the paper is to estimate the effect of rapid intervention vehicles (RIVs)’ impact on fire department (FDs)' response time.Design/methodology/approachThe study employed multivariate regression analysis of changes in response times before and after introducing RIVs into the FD task force, controlling for expected travel time. Response time analysis based on the database of all emergency fire responses in Norway from 2016 to 2021 was carried out.FindingsIntroducing RIVs into the FDs' task force reduced response times by 53 s on average for every call where an RIV is being deployed, given an average driving length of an emergency call of 6.4 kilometers. The response time is reduced to approximately 37 s independently of driving length, and this effect increases with 2.5 s per km.Originality/valuePrecise estimation of the expected reduced response time was calculated by introducing the first RIV into the FD's task force based on advanced statistical analysis on complete emergency register data. The analysis shows that RIVs have a positive impact on response time in both urban and rural areas, while particularly strong for urban areas.

Integrated Backup Rolling Stock Allocation and Timetable Rescheduling with Uncertain Time-Variant Passenger Demand Under Disruptive Events

Railway traffic management focuses on regulating train movements and delivering improved service quality to passengers; however, such efforts are subject to many uncertainties in terms of disruptions and passenger demand on a rail transit line. In contrast to most existing studies, which focus on the rescheduling of passenger timetables in a deterministic framework, this study proposes a two-stage stochastic optimization model for allocating backup rolling stocks (BRS) to storage lines to reschedule the timetable and serve passengers delayed by disruptions. The first stage is an assignment problem to determine the optimal plan for the allocation of BRS to storage lines to achieve a good trade-off between the investment cost for the BRS and the expected travel time of delayed passengers across different stochastic scenarios. The second stage is explicitly formulated as a network flow model to optimize the timetable of the delayed trains on the tracks and the BRS from the storage lines such that the passenger travel time is minimized under each stochastic scenario. To improve the efficiency of convergence, we develop an improved L-shaped method with several accelerating techniques. Among these, we show that the classical integer L-shaped cut can be tightened given the property of the second-stage problem, which can also be generalized to other two-stage integer stochastic programs. Real-world case studies based on historical data from the Beijing metro verify the effectiveness of the proposed approach in reducing the travel time for passengers. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods &amp; Analysis. Funding: This research was supported by the National Natural Science Foundation of China [Grants 71621001, 71825004, and 71901016]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplementary Information [ https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.1233 ] or is available from the IJOC GitHub software repository ( https://github.com/INFORMSJoC ) at [ http://dx.doi.org/10.5281/zenodo.6892548 ].

A two-stage stochastic optimization model for integrated tram timetable and speed control with uncertain dwell times

Modern trams usually own passive transit signal priority (TSP) to avoid interruption from traffic signals along the route. The key to TSP depends on the stick to the recommended travel time between intersections strictly. However, the effectiveness of the TSP can be weakened by dwell time fluctuation due to uncertain passenger demand at the stations. This paper proposes a two-stage stochastic optimization model for timetable and tram control to improve the TSP reliability considering uncertain dwell times. The first stage of the model focuses on designing timetable alternatives, and the second stage evaluates the timetables through expected travel time and energy consumption under different dwell time disturbance scenarios. The Brute force algorithm is developed to attain the optimal tram control, while the non-dominated sorting genetic algorithm II (NSGA-II) and GUROBI solver are both adopted to optimize the timetables. A case study of Nanjing Tram Line 1 in China is performed to demonstrate the effectiveness of the proposed approach. The results show that compared to the existing method, the proposed method reduces energy consumption by 16.0% and the number of stops at intersections decreases by 73.7% with the same travel time.