A stochastic optimization model for transit network timetable design to mitigate the randomness of traveling time by adding slack time

Transit network timetabling aims at determining the departure time of each trip of all lines in order to facilitate passengers transferring either to or from a bus. In this paper, we consider a bus timetabling problem with stochastic travel times (BTP-STT). Slack time is added into timetable to mitigate the randomness in bus travel times. We then develop a stochastic integer programming model for the BTP-STT to minimize the total waiting time cost for three types of passengers (i.e., transferring passengers, boarding passengers and through passengers). The mathematical properties of the model are characterized. Due to its computational complexity, a genetic algorithm with local search (GALS) is designed to solve our proposed model (OPM). The numerical results based on a small bus network show that the timetable obtained from OPM reduces the total waiting time cost by an average of 9.5%, when it is tested in different scenarios. OPM is relatively effective if the ratio of the number of through passengers to the number of transferring passengers is not larger than a threshold (e.g., 10 in our case). In addition, we test different scale instances randomly generated in a practical setting to further verify the effectiveness of OPM and GALS. We also find that adding slack time into timetable greatly benefits transferring passengers by reducing the rate of transferring failure.     

Robust single-track train dispatching model under a dynamic and stochastic environment: A scenario-based rolling horizon solution approach

After a major service disruption on a single-track rail line, dispatchers need to generate a series of train meet-pass plans at different decision times of the rescheduling stage. The task is to recover the impacted train schedule from the current and future disturbances and minimize the expected additional delay under different forecasted operational conditions. Based on a stochastic programming with recourse framework, this paper incorporates different probabilistic scenarios in the rolling horizon decision process to recognize (1) the input data uncertainty associated with predicted segment running times and segment recovery times and (2) the possibilities of rescheduling decisions after receiving status updates. The proposed model periodically optimizes schedules for a relatively long rolling horizon, while selecting and disseminating a robust meet-pass plan for every roll period. A multi-layer branching solution procedure is developed to systematically generate and select meet-pass plans under different stochastic scenarios. Illustrative examples and numerical experiments are used to demonstrate the importance of robust disruption handling under a dynamic and stochastic environment. In terms of expected total train delay time, our experimental results show that the robust solutions are better than the expected value-based solutions by a range of 10-30%.     

A dynamic stochastic assignment model for the analysis of general networks

The paper adopts the framework employed by the existing dynamic assignment models, which analyse specific network forms, and develops a methodology for analysing general networks. Traffic conditions within a link are assumed to be homogeneous, and the time varying O-D travel times and traffic flow patterns are calculated using elementary relationships from traffic flow theory and link volume conservation equations. Each individual is assumed to select a departure time and a route by trading off the travel time and schedule delay associated with each alternative. A route is considered as reasonable if it includes only links which do not take the traveller back to the origin. The set of reasonable routes is not consistant but depends on the time that an individual decides to depart from his origin. Equilibrium distributions are derived from a Markovian model which describes the evolution of travel patterns from day to day. Numerical simulation experiments are conducted to analyse the impact of different work start time flexibilities on the time dependent travel patterns. The similarity between link flows and travel times obtained from static and dynamic stochastic assignment is investigated. It is shown that in congested networks the application of static assignment results in travel times which are lower than the ones predicted by dynamic assignment.     

A utility-based bicycle speed choice model with time and energy factors

Transportation - This paper presents a utility-based behavioral model of bicycle speed choice. A mathematical framework is developed with travel time, energy expenditure, and control factors....     

A shockwave profile model for traffic flow on congested urban arterials

In this paper a new traffic flow model for congested arterial networks, named shockwave profile model (SPM), is presented. Taking advantage of the fact that traffic states within a congested link can be simplified as free-flow, saturated, and jammed conditions, SPM simulates traffic dynamics by analytically deriving the trajectories of four major shockwaves: queuing, discharge, departure, and compression waves. Unlike conventional macroscopic models, in which space is often discretized into small cells for numerical solutions, SPM treats each homogeneous road segment with constant capacity as a section; and the queuing dynamics within each section are described by tracing the shockwave fronts. SPM is particularly suitable for simulating traffic flow on congested signalized arterials especially with queue spillover problems, where the steady-state periodic pattern of queue build-up and dissipation process may break down. Depending on when and where spillover occurs along a signalized arterial, a large number of queuing patterns may be possible. Therefore it becomes difficult to apply the conventional approach directly to track shockwave fronts. To overcome this difficulty, a novel approach is proposed as part of the SPM, in which queue spillover is treated as either extending a red phase or creating new smaller cycles, so that the analytical solutions for tracing the shockwave fronts can be easily applied. Since only the essential features of arterial traffic flow, i.e., queue build-up and dissipation, are considered, SPM significantly reduces the computational load and improves the numerical efficiency. We further validated SPM using real-world traffic signal data collected from a major arterial in the Twin Cities. The results clearly demonstrate the effectiveness and accuracy of the model. We expect that in the future this model can be applied in a number of real-time applications such as arterial performance prediction and signal optimization.     

A heuristic for the train pathing and timetabling problem

In a railroad system, train pathing is concerned with the assignment of trains to links and tracks, and train timetabling allocates time slots to trains. These important tasks were traditionally done manually, but there is an increasing move toward automated software based on mathematical models and algorithms. Most published models in the literature either focus on train timetabling only, or are too complicated to solve when facing large instances. In this paper, we present an optimization heuristic that includes both train pathing and train timetabling, and has the ability to solve real-sized instances. This heuristic allows the operation time of trains to depend on the assigned track, and also lets the minimum headway between the trains to depend on the trains’ relative status. It generates an initial solution with a simple rule, and then uses a four-step process to derive the solution iteratively. Each iteration starts by altering the order the trains travel between stations, then it assigns the services to the tracks in the stations with a binary integer program, determines the order they pass through the stations with a linear program, and uses another linear program to produce a timetable. After these four steps, the heuristic accepts or rejects the new solution according to a Threshold Accepting rule. By decomposing the original complex problem into four parts, and by attacking each part with simpler neighborhood-search processes or mathematical programs, the heuristic is able to solve realistic instances. When tested with two real-world examples, one from a 159.3 km, 29-station railroad that offers 44 daily services, and another from a 345 km, eight-station high-speed rail with 128 services, the heuristic obtained timetables that are at least as good as real schedules.     

A multi-period optimization model for the deployment of public electric vehicle charging stations on network

A multi-period multipath refueling location model is developed to expand public electric vehicle (EV) charging network to dynamically satisfy origin–destination (O–D) trips with the growth of EV market. The model captures the dynamics in the topological structure of network and determines the cost-effective station rollout scheme on both spatial and temporal dimensions. The multi-period location problem is formulated as a mixed integer linear program and solved by a heuristic based on genetic algorithm. The model and heuristic are justified using the benchmark Sioux Falls road network and implemented in a case study of South Carolina. The results indicate that the charging station rollout scheme is subject to a number of major factors, including geographic distributions of cities, vehicle range, and deviation choice, and is sensitive to the types of charging station sites.     

Stochastic cell transmission model (SCTM): A stochastic dynamic traffic model for traffic state surveillance and assignment

The paper proposes a first-order macroscopic stochastic dynamic traffic model, namely the stochastic cell transmission model (SCTM), to model traffic flow density on freeway segments with stochastic demand and supply. The SCTM consists of five operational modes corresponding to different congestion levels of the freeway segment. Each mode is formulated as a discrete time bilinear stochastic system. A set of probabilistic conditions is proposed to characterize the probability of occurrence of each mode. The overall effect of the five modes is estimated by the joint traffic density which is derived from the theory of finite mixture distribution. The SCTM captures not only the mean and standard deviation (SD) of density of the traffic flow, but also the propagation of SD over time and space. The SCTM is tested with a hypothetical freeway corridor simulation and an empirical study. The simulation results are compared against the means and SDs of traffic densities obtained from the Monte Carlo Simulation (MCS) of the modified cell transmission model (MCTM). An approximately two-miles freeway segment of Interstate 210 West (I-210W) in Los Ageles, Southern California, is chosen for the empirical study. Traffic data is obtained from the Performance Measurement System (PeMS). The stochastic parameters of the SCTM are calibrated against the flow-density empirical data of I-210W. Both the SCTM and the MCS of the MCTM are tested. A discussion of the computational efficiency and the accuracy issues of the two methods is provided based on the empirical results. Both the numerical simulation results and the empirical results confirm that the SCTM is capable of accurately estimating the means and SDs of the freeway densities as compared to the MCS.     

A fuzzy-stochastic optimization model for the intermodal fleet management problem of an international transportation company

ABSTRACT

In this paper, a fuzzy-stochastic optimization model is developed for an intermodal fleet management system of a large international transportation company. The proposed model integrates various strategic, tactical and operational level decisions simultaneously. Since real-life fleet planning problems may involve different types of uncertainty jointly such as randomness and fuzziness, a hybrid chance-constrained programming and fuzzy interactive resolution-based approach is employed. Therefore, stochastic import/export freight demand and fuzzy transit times, truck/trailer availabilities, the transport capacity of Ro-Ro vessels, bounds on block train services, etc. can also be taken into account concurrently. In addition to minimize overall transportation costs, optimization of total transit times and CO₂ emission values are also incorporated in order to provide sustainable fleet plans by maximizing customer satisfaction and environmental considerations. Computational results show that effective and efficient fleet plans can be produced by making use of the proposed optimization model.     

北京地铁五号线预制盾构管片的高性能混凝土研究

文章通过利用2次正交试验,对内掺4种掺合料的高性能混凝土配合比的多指标进行了评价和筛选,确定了理论配合比.与国内其他地铁管片厂家的混凝土配合比相比,该配合比的突出特点是总胶凝材料用量较低、大量使用了矿碴掺合料、水胶比和砂率较低.依据该配合比配制的混凝土试验结果表明混凝土强度达到了C50、拌合物易于浇捣、28天收缩值较纯水泥降低一半、抗渗等级为P30、碱含量仅2.4 kg/m3,满足用于潮湿条件等耐久性要求.目前用该配合比生产的预制盾构管片已在北京地铁五号线中累计使用超过1 000环,满足工程无结构缺陷、无外形缺陷、无外表缺陷和无外表油污的四无质量要求.     

非对称小净距隧道施工力学特性研究及方案优化

非对称小净距隧道合理的开挖顺序对隧道围岩稳定和支护措施优化有很大的影响。文章结合净距2.0 m非对称公路隧道工程实践,通过二维弹塑性有限元数值仿真模拟,研究分析了隧道开挖顺序对支护力学行为特性及围岩稳定性的影响,得出了先开挖较小断面隧道优于先开挖较大断面隧道的结论,为非对称小净距隧道优化设计和施工提供了科学依据。     

A new look at the rate of change of energy consumption with respect to journey time on an optimal train journey

We present a new derivation of a key formula for the rate of change of energy consumption with respect to journey time on an optimal train journey. We use a standard mathematical model (Albrecht et al., 2015b; Howlett, 2000; Howlett et al., 2009; Khmelnitsky, 2000; Liu and Golovitcher, 2003) to define the problem and show by explicit calculation of switching points that the formula also applies for all basic control subsequences within the optimal strategy on appropriately chosen fixed track segments. The rate of change was initially derived as a known strictly decreasing function of the optimal driving speed in a text edited by  Isayev (1987, Section 14.2, pp 259–260) using an empirical resistance function. An elegant derivation by Liu and Golovitcher (2003, Section 3) with a general resistance function required an underlying assumption that the optimal strategy is unique and that the associated optimal driving speed is a strictly decreasing and continuous function of journey time. An earlier proof of uniqueness (Khmelnitsky, 2000) showed that the optimal driving speed decreases when journey time increases. A subsequent constructive proof (Albrecht et al., 2013a, 2015c) used a local energy minimization principle to find optimal switching points and show explicitly that the optimal driving speed is a strictly decreasing and continuous function of journey time. Our new derivation of the key formula also uses the local energy minimization principle and depends on the following observations. If no speed limits are imposed the optimal strategy consists of a finite sequence of phases with only five permissible control modes. By considering all basic control subsequences and subdividing the track into suitably chosen fixed segments we show that the key formula is valid on each individual segment. The formula is extended to the entire journey by summation. The veracity of the formula is demonstrated with an elementary but realistic example.     

成都地铁密实砂卵石地层工程地质特性及施工方法浅析

地层的工程地质特性直接影响到支护参数及施工方法的选择。文章结合成都地铁工程实践,介绍了成都砂卵石地层的降水效应;通过对监测数据的分析,反映在CD法和台阶法两种不同施工方法条件下,地层变形及内力变化情况,为制定合理的施工方案提供借鉴和参考。     

A continuum model for the dispersion of traffic on two-lane roads

A continuum model for two-lane traffic flow is developed using the theory of kinematic waves in which the wavespeeds in the two lanes are assumed constant but unequal. The transient behaviour is found exactly using Riemann's method of characteristics and an asymptotic model of the long time flow is described. It is shown, that for large times, the traffic concentration moves with a weighted mean wavespeed of the two lanes and disperses about this mean speed as a result of interlane concentration differences generated by the relative wavespeeds. The dispersion can be described by a virtual coefficient of diffusion proportional to the square of the differences of the two wavespeeds and inversely proportional to the rate of lane changing. The technique is extended to describe three-lane traffic flow and to include the dependence of wavespeed upon concentration.     

An integrated model system and policy evaluation tool for maximizing mobility under environmental capacity constraints: A case study in Dalian City,China

This paper presents an integrated model system for mobility maximization based on a quantified specification of environmental capacity, and evaluates policy interaction and effectiveness by simulating a number of policy scenarios. The system is designed to specify the maximum level of car ownership and number of trips by private and public modes subject to an environmental capacity constraint defined as the frontier emission under maximum system efficiency. Four types of hypothetical policies (population change, urban sprawl, land-use pattern and network improvement) are designed and the effects of 13 policy scenarios are simulated using data of Dalian City, China. Results reveal that the integrated model system reacts sensitively to policy interventions. The urban sprawl reflected in a changing residential distribution from central to suburban areas is most instrumental from the perspective of pollution alleviation. If the goal is to simultaneously reduce emissions while accommodating mobility, two combinational policy scenarios outperform all others.     

A connected-vehicle-based dynamic control model for managing the bus bunching problem with capacity constraints

This paper describes a connected-vehicle-based system architecture which can provide more precise and comprehensive information on bus movements and passenger status. Then a dynamic control method is proposed using connected vehicle data. Traditionally, the bus bunching problem has been formulated into one of two types of optimization problem. The first uses total passenger time cost as the objective function and capacity, safe headway, and other factors as constraints. Due to the large number of scenarios considered, this type of framework is inefficient for real-time implementation. The other type uses headway adherence as the objective and applies a feedback control framework to minimize headway variations. Due to the simplicity in the formulation and solution algorithms, the headway-based models are more suitable for real-time transit operations. However, the headway-based feedback control framework proposed in the literature still assumes homogeneous conditions at all bus stations, and does not consider restricting passenger loads within the capacity constraints. In this paper, a dynamic control framework is proposed to improve not only headway adherence but also maintain the stability of passenger load within bus capacity in both homogenous and heterogeneous situations at bus stations. The study provides the stability conditions for optimal control with heterogeneous bus conditions and derives optimal control strategies to minimize passenger transit cost while maintaining vehicle loading within capacity constraints. The proposed model is validated with a numerical analysis and case study based on field data collected in Chengdu, China. The results show that the proposed model performs well on high-demand bus routes.     

A logit-based model for measuring the effects of transportation infrastructure on land value

Mutual interactions between transportation and land use have long been debated. Despite progress made in computational technology, the study of these interactions is not adequately developed. The most important aspect of such interactions is given by the changes in land values due to changes in transportation infrastructures. We consider the behavioural features of these interactions along with the constraints on the land and/or zoning restrictions and propose a reliable model for the first time to predict land value changes with respect to changes in transportation facilities and accessibility. The proposed model is a logit-based mathematical programming methodology where the relative price of land is predicted with respect to transportation accessibility, neighbourhood amenities, location premium, availability of land, and zoning regulations. A real-world case study is used to exhibit the applicability of the proposed methodology and demonstrate the efficacy of the algorithms and procedures.     

A link-node complementarity model and solution algorithm for dynamic user equilibria with exact flow propagations

In this paper, we propose a link-node complementarity model for the basic deterministic dynamic user equilibrium (DUE) problem with single-user-class and fixed demands. The model complements link-path formulations that have been widely studied for dynamic user equilibria. Under various dynamic network constraints, especially the exact flow propagation constraints, we show that the continuous-time dynamic user equilibrium problem can be formulated as an infinite dimensional mixed complementarity model. The continuous-time model can be further discretized as a finite dimensional non-linear complementarity problem (NCP). The proposed discrete-time model captures the exact flow propagation constraints that were usually approximated in previous studies. By associating link inflow at the beginning of a time interval to travel times at the end of the interval, the resulting discrete-time model is predictive rather than reactive. The solution existence and compactness condition for the proposed model is established under mild assumptions. The model is solved by an iterative algorithm with a relaxed NCP solved at each iteration. Numerical examples are provided to illustrate the proposed model and solution approach. We particularly show why predictive DUE is preferable to reactive DUE from an algorithmic perspective.     

A computer model for finding the time-dependent minimum path in a transit system with fixed schedules

This paper describes the development of a computer model and algorithms for finding the time-dependent minimum path between two stations in a multi-route, multi-mode transit system running to fixed schedules. Selection of the minimum path can be based either on journey time or on weighted time. A worked example using a simple transit network is given to illustrate how the model works. The model has several applications in transport planning: it can be used for generating route schedule information to guide transit users, for assisting in route schedule coordination, and for analyzing transit system accessibility.     

An integrated multi‐objective model to determine the optimal rescue path and traffic controlled arcs for disaster relief operations under uncertainty environments

This study proposes an integrated multi‐objective model to determine the optimal rescue path and traffic controlled arcs for disaster relief operations under uncertainty environments. The model consists of three sub‐models: rescue shortest path model, post‐disaster traffic assignment model, and traffic controlled arcs selection model to minimize four objectives: travel time of rescue path, total detour travel time, number of unconnected trips of non‐victims, and number of police officers required. Since these sub‐models are inter‐related with each other, they are solved simultaneously. This study employs genetic algorithms incorporated with traffic assignment and K‐shortest path methods to determine optimal rescue path and controlled arcs. To cope with uncertain information associated with the damaged network, fuzzy system reliability theory (weakest t‐norm method) is used to measure the access reliability of rescue path. To investigate the validity and applicability of the proposed model, studies on an exemplified case and a field case of Chi‐Chi earthquake in Taiwan are conducted. The performances of three rescue strategies: without traffic control, selective traffic control (i.e. the proposed model) and absolute traffic control are compared. The results show that the proposed model can maintain the efficiency of rescue activity with minimal impact to ordinary trips and number of police officers required.