Vehicle Departure Time Research Articles

Electric Vehicle Routing Problem with Charging Time and Variable Travel Time

An electric vehicle routing problem with charging time and variable travel time is developed to address some operational issues such as range limitation and charging demand. The model is solved by using genetic algorithm to obtain the routes, the vehicle departure time at the depot, and the charging plan. Meanwhile, a dynamic Dijkstra algorithm is applied to find the shortest path between any two adjacent nodes along the routes. To prevent the depletion of all battery power and ensure safe operation in transit, electric vehicles with insufficient battery power can be repeatedly recharged at charging stations. The fluctuations in travel time are implemented to reflect a dynamic traffic environment. In conclusion, a large and realistic case study with a road network in the Beijing urban area is conducted to evaluate the model performance and the solution technology and analyze the results.

Integrated Public Transport Timetable Synchronization and Vehicle Scheduling with Demand Assignment: A Bi-objective Bi-level Model Using Deficit Function Approach

Abstract: In the operations planning process of public transport (PT), timetable synchronization is a useful strategy utilized to reduce transfer waiting time and improve service connectivity. However, most of the studies on PT timetable synchronization design have treated the problem independently of other operations planning activities, and have focused only on minimizing transfer waiting time. In addition, the impact of schedule changes on PT users’ route/trip choice behavior has not been well investigated yet. This work develops a new bi-objective, bi-level integer programming model, taking into account the interests of PT users and operators in attaining optimization of PT timetable synchronization integrated with vehicle scheduling and considering user demand assignment. Based on the special structure characteristics of the model, a novel deficit function (DF)-based sequential search method combined with network flow and shifting vehicle departure time techniques is proposed to achieve a set of Pareto-efficient solutions. The graphical features of the DF can facilitate a decision-making process for PT schedulers for finding a desirable solution. Two numerical examples are illustrated to demonstrate the methodology developed.

Probabilistic time-dependent vehicle routing problem

The probabilistic time-dependent vehicle routing problem is presented in this paper. It is a novel variant of the vehicle routing problem. The variant is a problem of finding optimal routes for a fleet of vehicles visiting customers in order to proceed delivery or pick-up. All customers must be visited in designated times with given probabilities and services must begin within the given time windows. Each vehicle has a given capacity, which must not be exceeded. The travel time between each two locations is dependent on a vehicle departure time. The paper also contains examples and solution results of testing data sets using the adaptive large neighbourhood search algorithm.

A cell-based multiple vehicle type dynamic user equilibrium model with physical queues

This paper proposes a cell-based multiple vehicle type dynamic user equilibrium model with physical queues. A single-type traffic flow model is extended to a general case with multiple vehicle types that can be partly solved by the time-space discretization method. Then, a network version of the multiple vehicle type cell transmission model is given. An integrated variational inequality (VI) formulation is presented to capture the complex traveler choice behaviors such as route and departure time choices. Furthermore, a genetic algorithm with a flow-swapping method is adopted to solve the VI problem. Two examples are used to evaluate the properties of this formulation. The results show that the model can reflect dynamic phenomena, such as multiple vehicle type speed consistent under congested conditions, queue formation and dissipation and so on. Moreover, the solutions can approximately follow the multiple vehicle type dynamic route and departure time user equilibrium conditions.

The Generalized Consistent Vehicle Routing Problem

The consistent vehicle routing problem (ConVRP) takes customer satisfaction into account by assigning one driver to a customer and by bounding the variation in the arrival times over a given planning horizon. These requirements may be too restrictive in some applications. In the generalized ConVRP (GenConVRP), each customer is visited by a limited number of drivers and the variation in the arrival times is penalized in the objective function. The vehicle departure times may be adjusted to obtain stable arrival times. Additionally, customers are associated with AM/PM time windows. In contrast to previous work on the ConVRP, we do not use the template concept to generate routing plans. Our approach is based on a flexible large neighborhood search that is applied to the entire solution. Several destroy and repair heuristics have been designed to remove customers from the routes and to reinsert them at better positions. Arrival time consistency is improved by a simple 2-opt operator that reverses parts of particular routes. A computational study is performed on ConVRP benchmark instances and on new instances generated for the generalized problem. The proposed algorithm performs well on different variants of the ConVRP. It outperforms template-based approaches in terms of travel cost and time consistency. For the GenConVRP, we experiment with different input parameters and examine the trade-off between travel cost and customer satisfaction. Remarkable cost savings can be obtained by allowing more than one driver per customer.

A clonal selection algorithm for urban bus vehicle scheduling

The bus vehicle scheduling problem addresses the task of assigning vehicles to cover the trips in a timetable. In this paper, a clonal selection algorithm based vehicle scheduling approach is proposed to quickly generate satisfactory solutions for large-scale bus scheduling problems. Firstly, a set of vehicle blocks (consecutive trips by one bus) is generated based on the maximal wait time between any two adjacent trips. Then a subset of blocks is constructed by the clonal selection algorithm to produce an initial vehicle scheduling solution. Finally, two heuristics adjust the departure times of vehicles to further improve the solution. The proposed approach is evaluated using a real-world vehicle scheduling problem from the bus company of Nanjing, China. Experimental results show that the proposed approach can generate satisfactory scheduling solutions within 1min.

Contingent versus Deterministic Plans in Multi-Modal Journey Planning

Deterministic planning is the de facto standard in deployed multi-modal journey planning systems. However, in reality, transportation networks feature many types of uncertainty, including variations of the arrival and the departure times of public transport vehicles. Under uncertainty, deterministic plans could result in missed connections, leading to an arrival time much worse than originally planned. We contribute an empirical study using transportation network data from three European cities. We show that, in the presence of uncertainty, contingent plans can often provide significant savings in terms of travel time. We view our results as important because they advocate adopting uncertainty-aware multi-modal journey plans, shifting from the current practice based on using deterministic planning.

Transit Timetables Resulting in Even Maximum Load on Individual Vehicles

With advances in the intelligent-transportation-system technology of passenger information systems, the importance of even and clock headways in transit timetables is reduced. This allows for the creation of timetables with even average maximum passenger loads on individual vehicles. The maximum load attained is a load standard desired at the maximum-load stop. These timetables minimize overcrowding and produce more reliable and efficient schedules than other timetables from both passenger and operator perspectives. Thus, it will make the transit service more attractive. This paper provides a procedure for the creation of transit timetables to improve the correspondence of vehicle departure times with passenger demand. The algorithm developed yields departure times (a timetable) for vehicles to achieve an even maximum load on each vehicle and a smoothing consideration in the transition between time periods. A case study was carried out using the data of one bus route in Auckland, New Zealand, with modeling and simulation analyses. The results of the even maximum load on individual vehicles, in terms of the elimination of overcrowding and schedule adherence, exhibit significant improvement over timetables with even headways or with headways based on hourly even maximum loads.

Two faster algorithms for coordination of production and batch delivery: A note

This note suggests faster algorithms for two integrated production/distribution problems studied earlier, improving their complexities from O(n2V + 4) and O(n2(L + V)2) to O(n) and O(n + Vmin {V, n}) respectively, where n is the number of products to be delivered, V is the number of vehicles and L is the number of vehicle departure times.

An Approach to Optimize the Departure Times of Transit Vehicles with Strict Capacity Constraints

This paper focuses on an urban transit line which connects several residential areas and a workplace during the morning rush hours. The congestion is represented by some passengers who must wait for an extended duration and board the next or the third departure vehicles. This paper divides the time horizon equally into several small periods to measure the dynamic passenger demands. Under period-dependent demand conditions, a biobjective optimization model is developed to determine the departure times of transit vehicles at the start station with strict capacity constraints, in which a heuristic algorithm based on intelligent search and local improvement is designed to solve the model. The developed model can address the case in which more than two passengers arrive at a station simultaneously during one same period and calculate the number of boarded passengers. Finally, the model and algorithm have been successfully verified by a numerical example.

PEV Charging Profile Prediction and Analysis Based on Vehicle Usage Data

Present-day urban vehicle usage data recorded on a per second basis over a one-year period using GPS devices installed in 76 representative vehicles in the city of Winnipeg, Canada, allow predicting the electric load profiles onto the grid as a function of time for future plug-in electric vehicles. For each parking occurrence, load profile predictions properly take into account important factors, including actual state-of-charge of the battery, parking duration, parking type, and vehicle powertrain. Thus, the deterministic simulations capture the time history of vehicle driving and parking patterns using an equivalent 10 000 urban driving and parking days for the city of Winnipeg. These deterministic results are then compared to stochastic methods that differ in their treatment of how they model vehicle driving and charging habits. The new stochastic method introduced in this study more accurately captures the relationship of vehicle departure, arrival, and travel time compared to two previously used stochastic methods. It outperforms previous stochastic methods, having the lowest error at 3.4% when compared to the deterministic method for an electric sedan with a 24-kWhr battery pack. For regions where vehicle usage data is not available to predict plug-in electric vehicle load, the proposed stochastic method is recommended. In addition, using a combination of home, work, and commercial changing locales, and Level 1 versus Level 2 charging rates, deterministic simulations for urban run-out-of-charge events vary by less than 4% for seven charging scenarios selected. Using the vehicle usage data, charging scenarios simulated have no significant effect on urban run-out-of-charge events when the battery size for the electric sedan is increased. These results contribute towards utilities achieve a more optimal cost balance between: 1) charging infrastructure; 2) power transmission upgrades; 3) vehicle battery size; and 4) the addition of new renewable generation to address new electric vehicle loads for addressing energy drivers.

Optimizing departure times in vehicle routes

Most solution methods for the vehicle routing problem with time windows (VRPTW) develop routes from the earliest feasible departure time. In practice, however, temporary traffic congestion make such solutions non-optimal with respect to minimizing the total duty time. Furthermore, the VRPTW does not account for driving hours regulations, which restrict the available travel time for truck drivers. To deal with these problems, we consider the vehicle departure time optimization (VDO) problem as a post-processing of a VRPTW. We propose an ILP formulation that minimizes the total duty time. The results of a case study indicate that duty time reductions of 15% can be achieved. Furthermore, computational experiments on VRPTW benchmarks indicate that ignoring traffic congestion or driving hours regulations leads to practically infeasible solutions. Therefore, new vehicle routing methods should be developed that account for these common restrictions. We propose an integrated approach based on classical insertion heuristics.

Determination of the Skip-Stop Scheduling for a Congested Transit Line by Bilevel Genetic Algorithm

This study focuses on how to determine the skip-stop scheduling for a congested urban transit line during the morning rush hours. A transit schedule with uneven headways and skip-stop operations is adopted to match the time-dependent demands and accelerate the circulative utilizations of vehicles. This schedule allows the buses to run on unequal vehicle-departure intervals and to skip some stations. A nonlinear programming model is formulated to minimize the overall waiting times and the in-vehicle crowded costs subjected to a limited number of vehicles. According to the layered characteristics of the skip-stop scheduling, a bilevel genetic algorithm is developed to solve the proposed model. The possible departure times of vehicles at the terminal are searched by the outer genetic algorithm and the skip-stop operations are solved by the inner genetic algorithm. Finally, the proposed model and algorithm are successfully tested with the help of a real-world case.

A practical model for transfer optimization in a transit network: Model formulations and solutions

This paper studies the transit network scheduling problem and aims to minimize the waiting time at transfer stations. First, the problem is formulated as a mixed integer programming model that gives the departure times of vehicles in lines so that passengers can transfer between lines at transfer stations with minimum waiting times. Then, the model is expanded to a second model by considering the extra stopping time of vehicles at transfer stations as a new variable set. By calculating the optimal values for these variables, transfers can be better performed. The sizes of the models, compared with the existing models, are small enough that the models can be solved for small- and medium-sized networks using regular MIP solvers, such as CPLEX. Moreover, a genetic algorithm approach is represented to more easily solve larger networks. A simple network is used to describe the models, and a medium-sized, real-life network is used to compare the proposed models with another existing model in the literature. The results demonstrate significant improvement. Finally, a large-scale, real-life network is used as a case study to evaluate the proposed models and the genetic algorithm approach.

Trade-Offs Between Time, Cost, and Uncertainty by Commuters in Hyderabad, India: Stated Preference Survey Assessment

In developing countries, air quality assessments that include the transportation sector have tended to focus predominantly on assessing technological solutions to problems associated with vehicle pollutant emissions, energy consumption, and greenhouse gases. This focus can be justified on the basis of the favorable cost-effectiveness, political acceptance, and ease of quantifying technological measures—at least in the short term—but unfortunately it often leads to the exclusion of demand-oriented measures. Further, air quality and pollution policy analysts often use assumptions of exogenously determined travel demand patterns, implicitly excluding many opportunities to look at policies oriented toward travel demand as an air pollution control strategy. The air quality impacts of policy measures to influence vehicle kilometers traveled and mode shares, such as bus rapid transit, are investigated. The approach involves developing coefficients with a stated preference (SP) survey that could be used to test policies with a conventional four-step urban transportation model. The main purpose of the SP survey in this study was to examine traveler tradeoffs among time, cost, and reliability (measured as uncertainty in vehicle departure time). Some different methods of measuring reliability were tested during the pilot phase of the survey, as were the actual range of parameter values to be tested. Models were estimated using traveler cohorts based on levels of vehicle ownership. In comparing vehicle owners (cars and two-wheelers) with nonowners, owners were found to be substantially more sensitive to time and reliability while nonowners were more sensitive to price. All groups showed notable sensitivity to reliability. Policy implications of these results are discussed, with a notable conclusion being that demand-oriented measures appear to be a fruitful area for further investigation as air pollution control strategies, even when technological measures show strong effectiveness.

Bus Timetables with Even Passenger Loads as Opposed to Even Headways

Bus timetables with even headways often require passengers to adjust to given timetables instead of adjusting the timetables to fluctuating passenger demand. This expectation is a main source of unreliable service that extends passenger waiting times at bus stops and creates overcrowding. Alternative transit timetables are created to improve the correspondence of vehicle departure times with passenger demand while minimizing resources (number of buses required). An automated method is presented. With the growing problems of transit reliability, and the advance in the technology of passenger information systems, even and clock headways become less important. Therefore, more efficient schedules from both the passenger and operator perspectives can be realized. The method presented uses an informative graphic technique. This approach enables the scheduler to examine changes in bus departure times and to obtain immediate feedback on the expected average passenger loads.

Transit Service and Path Choice Models in Stochastic and Time-Dependent Networks

This paper develops a new path choice model that incorporates both time-dependent and stochastic transit service characteristics, and allows passengers to update path choice decisions while waiting. To develop this model, a new transit service model is proposed that represents route segments using a shuttle model. Such a model balances requirements for stochastic and time-dependent service modeling with the ability to aggregate to a larger transit corridor or network. This service model leads to a dynamic model of transit path choice, in which the passenger may wait until a vehicle is about to depart before making a boarding decision. A formal definition of this dynamic path choice model is given, and its differences with previous path choice models are noted. Based on this definition, two mathematical formulations of the dynamic model are developed. The first formulation assumes that the passenger will use the dynamic model for all possible vehicle departure times in the future, and is formulated as an optimal control problem. It is shown mathematically that this problem formulation is a less-constrained version of previous path choice models. However, because of some analytic and behavioral difficulties with this first model, a more well-behaved constrained formulation is also presented. A small corridor example demonstrates the significant differences in path choices and travel times between the constrained dynamic model and more traditional path choice models. Limitations of these dynamic path choice models are also discussed.

Decomposition of the reactive dynamic assignments with queues for a many-to-many origin-destination pattern

This research discusses the formulation and solution algorithm of the reactive dynamic traffic assignment with the link travel time explicitly taking into account the effects of queues under the point queue concept. In the reactive assignment, vehicles are assumed to choose their routes based on present instantaneous travel times. Time dependent many-to-many origin-destination volumes are assumed to be given; that is, the departure times of vehicles from origins are known. We first discuss the formulation of the dynamic assignment so as to satisfy the flow conservation and the First-In-First-Out queue discipline. Then, the reactive assignment is shown to be decomposed with respect to present time, since route choices of vehicles are dependent on the present traffic situation but independent of the past and future traffic condition. An algorithm is finally proposed based upon the decomposition.

Transit scheduling

AbstractThis paper provides an overview of the transit operational planning process with an emphasis on certain aspects of new methodologies in scheduling. The transit scheduling system usually consists of three interelated components: (1) creation of timetables; (2) scheduling vehicles to trips; and (3) assignment of drivers. These three components are described, but with a focus on the first component because of its importance from the user's perspective. The design of a transit timetable is discussed from both a practical and an analytical viewpoint. A methodology is presented on the construction of alternative computerized public timetables, based on procedures that improve the correspondence of vehicle departure times with passenger demand. The vehicle scheduling procedure is viewed through the minimization of the number of vehicles required to carry out a fixed or variable timetable. Finally, different approaches to the crew assignment component are briefly discussed. The overview and methodologies presented in the paper suggest that most scheduling tasks can be performed automatically or in a conversational man‐computer mode. The adoption of new scheduling procedures will undoubtedly increase the efficiency of each of the three components of the transit scheduling system.

State‐dependent gap acceptance

AbstractThis paper considers a traffic problem in which vehicles queue up according to a Poisson process on a single‐lane entrance ramp prior to merging into a major stream of vehicular traffic. In order to then prevent the ramp queue from becoming too large, a model is proposed which considers a lowering of the critical gap as the ramp queue size increases. With the critical gap assumed to be a nonincreasing function of the number of vehicles on the ramp at instances that correspond to departure times of lead vehicles from the ramp queue, the resultant model is an M/G/1 queue with state‐dependent service times. Some general results are obtained for this model and a specific case discussed in moderate detail.