A railway capacity determination model and rail access charging methodologies

This article discusses approaches to the determination of railway capacity and the significance of the following factors on capacity: mix of trains, length and weight of trains, direction of train travel, acceleration and deceleration, stopping protocols of trains, location and length of crossing loops, location of signals, length of sections, dwell times and sectional running times. A more accurate method to calculate railway capacity is developed using previously unaddressed aspects for capacity determination. Capacity and pricing are two key issues for organizations involved with open track access regimes. A train access charging methodology is therefore developed and incorporated into a railway capacity determination model.     

Estimation of train dwell time at short stops based on track occupation event data: A study at a Dutch railway station

Train dwell time is one of the most unpredictable components of railway operations, mainly because of the varying volumes of alighting and boarding passengers. However, for reliable estimations of train running times and route conflicts on main lines, it is necessary to obtain accurate estimations of dwell times at the intermediate stops on the main line, the so‐called short stops. This is a great challenge for a more reliable, efficient and robust train operation. Previous research has shown that the dwell time is highly dependent on the number of boarding and alighting passengers. However, these numbers are usually not available in real time. This paper discusses the possibility of a dwell time estimation model at short stops without passenger demand information by means of a statistical analysis of track occupation data from the Netherlands. The analysis showed that the dwell times are best estimated for peak and off‐peak hours separately. The peak‐hour dwell times are estimated using a linear regression model of train length, dwell times at previous stops and dwell times of the preceding trains. The off‐peak‐hour dwell times are estimated using a non‐parametric regression model, in particular, the k‐nearest neighbor model. There are two major advantages of the proposed estimation models. First, the models do not need passenger flow data, which is usually impossible to obtain in real time in practice. Second, detailed parameters of rolling stock configuration and platform layout are not required, which makes the model more generic and eases implementation. A case study at Dutch railway stations shows that the estimation accuracy is 85.8%–88.5% during peak hours and 80.1% during off‐peak hours, which is relatively high. We conclude that the estimation of dwell times at short stop stations without passenger data is possible. Copyright © 2016 John Wiley & Sons, Ltd.     

Integrated modeling of high performance passenger and freight train planning on shared-use corridors in the US

This paper studies strategic level train planning for high performance passenger and freight train operations on shared-use corridors in the US. We develop a hypergraph-based, two-level approach to sequentially minimize passenger and freight costs while scheduling train services. Passenger schedule delay and freight lost demand are explicitly modeled. We explore different solution strategies and conclude that a problem-tailored linearized reformulation yields superior computational performance. Using realistic parameter values, our numerical experiments show that passenger cost due to schedule delay is comparable to in-vehicle travel time cost and rail fare. In most cases, marginal freight cost increase from scheduling more passenger trains is higher than marginal reduction in passenger schedule delay cost. The heterogeneity of train speed reduces the number of freight trains that can run on a corridor. Greater tolerance for delays could reduce lost demand and overall cost on the freight side. The approach developed in the paper could be applied to other scenarios with different parameter values.     

Express guideway transit: A case for further development in transit automation

Safe and reliable coupling and decoupling of cars from a moving train is feasible with further developments in linear motor propulsion and control of transit vehicles. This allows the last car of a train to decouple and stop at a station for a relative long dwell time, before it accelerates and is coupled to a following train. Controlled doors in front and rear of the transit vehicle permit passengers to walk through the train to the car which stops at their destination. A proposed transit system using these features is described and compared to Bombardier's Advanced Rapid Transit. Potential advantages are high schedule speed, uncrowded trains, smaller and more stations, low energy requirements and a smaller vehicle fleet.     

Train scheduling simulation that minimises operational conflicts due to service constraints

This paper presents an attempt made to facilitate re‐scheduling of trains to minimize operational delays and accommodate uniform headways for off peak sub urban services subject to resource constraints such as locomotive availability, poor track conditions and stations without siding facilities. The paper describes the computer simulation model designed to optimize train schedules on single‐track rail lines. Using this simulation program it is possible to plan and optimize timetables for railway networks with train runs within short time periods for both single track and double track conditions. The paper describes the capabilities of presenting the results of the simulation runs. These include the time‐distance graph, the network with train movements, dialog boxes with information about selected trains. The programme is capable of changing the starting point, departure time, train destinations and adding or deleting a stop etc. from the user interface. Four objects of array variables are used in the simulation process to keep train and station data. Two object arrays are used for the train movements in up and down directions. The stations' data are stored in the other two object arrays. One of these arrays of stations contains all the stations of the line while the other one contains only the stations with siding facilities. A case study that covers a 61 km long single‐track line with 14 stations is presented to highlight the model capabilities.     

The train platforming problem: The infrastructure management company perspective

If railway companies ask for station capacity numbers, their underlying question is in fact one about the platformability of extra trains. Train platformability depends not only on the infrastructure, buffer times, and the desired departure and arrival times of the trains, but also on route durations, which depend on train speeds and lengths, as well as on conflicts between routes at any given time. We consider all these factors in this paper. We assume a current train set and a future one, where the second is based on the expected traffic increase through the station considered. The platforming problem is about assigning a platform to each train, together with suitable in- and out-routes. Route choices lead to different route durations and imply different in-route-begin and out-route-end times. Our module platforms the maximum possible weighted sum of trains in the current and future train set. The resulting number of trains can be seen as the realistic capacity consumption of the schedule. Our goal function allows for current trains to be preferably allocated to their current platforms.Our module is able to deal with real stations and train sets in a few seconds and has been fully integrated by Infrabel, the Belgian Infrastructure Management Company, in their application called Ocapi, which is now used to platform existing and projected train sets and to determine the capacity consumption.     

Mining missing train logs from Smart Card data

This paper shows how to recover the arrival times of trains from the gate times of metro passengers from Smart Card data. Such technique is essential when a log, the set of records indicating the actual arrival and departure time of each bus or train at each station and also a critical component in reliability analysis of a transportation system, is missing partially or entirely. The procedure reconstructs each train as a sequence of the earliest exit times, called S-epochs, among its alighting passengers at each stations. The procedure first constructs a set of passengers, also known as reference passengers, whose routing choices are easily identifiable. The procedure then computes, from the exit times of the reference passengers, a set of tentative S-epochs based on a detection measure whose validity relies on an extreme-value characteristic of the platform-to-gate movement of alighting passengers. The tentative S-epochs are then finalized to be a true one, or rejected, based on their consistencies with bounds and/or interpolation from prescribed S-epochs of adjacent trains and stations. Tested on 12 daily sets of trains, with varying degrees of missing logs, from three entire metro lines, the method restored the arrival times of 95% of trains within the error of 24 s even when 100% of logs was missing. The mining procedure can also be applied to trains operating under special strategies such as short-turning and skip-stop. The recovered log seems precise enough for the current reliability analysis performed by the city of Seoul.     

A hierarchical line planning approach for a large-scale high speed rail network: The China case

Planning a set of train lines in a large-scale high speed rail (HSR) network is typically influenced by issues of longer travel distance, high transport demand, track capacity constraints, and a non-periodic timetable. In this paper, we describe an integrated hierarchical approach to determine line plans by defining the stations and trains according to two classes. Based on a bi-level programming model, heuristics are developed for two consecutive stages corresponding to each classification. The approach determines day-period based train line frequencies as well as a combination of various stopping patterns for a mix of fast trunk line services between major stations and a variety of slower body lines that offer service to intermediate stations, so as to satisfy the predicted passenger transport demand. Efficiencies of the line plans described herein concern passenger travel times, train capacity occupancy, and the number of transfers. Moreover, our heuristics allow for combining many additional conflicting demand–supply factors to design a line plan with predominantly cost-oriented and/or customer-oriented objectives. A range of scenarios are developed to generate three line plans for a real-world example of the HSR network in China using a decision support system. The performance of potential train schedules is evaluated to further examine the feasibility of the obtained line plans through graphical timetables.     

Reduced dwell times resulting from train–platform improvements: the costs and benefits of improving passenger accessibility to metro trains

Abstract

This paper examines whether a dwell time reduction on a high-intensity metro service, as a result of a series of accessibility enhancements, can contribute to an increased level of service and accessible public transport for passengers together with a reduction in costs for the operator. Actual train operation data were collected by on-site observations and from London Underground Ltd. A simple simulation is built to represent the effect on the overall cycle times of trains if certain parameters (e.g. dwell time) are changed. Four models are developed, concerning: (1) step height between train and platform, (2) an assumption of passenger service time to be no longer than 20 s, (3) door width and (4) the combination of step height and door width. From the application of the models it appears that the fourth model provides the highest reduction in dwell time and diminishes the overall cycle times of trains. However, it is the most expensive to implement as it requires work to raise platforms and the purchase of new rolling stock.     

Coordination of last train transfers using automated fare collection (AFC) system data

This paper studies last train coordination problem for metro networks, aiming to maximize the total number of passengers who can reach their destinations by metro prior to the end of operation. The concept of last boarding time is defined as the latest time that passengers can board the last trains and reach final destinations. The corresponding method for calculating last boarding time is also put forward. With automatic fare collection system data, an optimization model for coordinating last trains is proposed. The objective function optimizes the number of passengers who can reach their final destinations during the train period using departure times and headways of last trains for each line as decision variables. Afterwards, an adaptive genetic algorithm is put forward to solve this model and is applied to a case study of the Shanghai metro system. Copyright © 2017 John Wiley & Sons, Ltd.     

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.     

高速铁路列车运行图均衡性研究

以相邻间隔时间期望方差及相间间隔时间均值和方差为计算指标,描述车站的列车分布及顺序均衡性。运用均衡性指标矩阵及均衡度指标向量来评价列车实际与计划运行图的均衡性。结果表明,由于干扰影响列车间隔时间大小波动明显,列车到达均衡性整体优于列车出发均衡性,长沙南站时间间隔分布及顺序均衡性最差,衡山西站、株洲西站、长沙南站到发均衡度最差,应结合列车晚点情况重点考虑运行图结构优化。     

Travel itinerary problem

In this study, we propose a travel itinerary problem (TIP) which aims to find itineraries with the lowest cost for travelers visiting multiple cities, under the constraints of time horizon, stop times at cities and transport alternatives with fixed departure times, arrival times, and ticket prices. First, we formulate the TIP into a 0–1 integer programming model. Then, we decompose the itinerary optimization into a macroscopic tour (i.e., visiting sequence between cities) selection process and a microscopic number (i.e., flight number, train number for each piece of movement) selection process, and use an implicit enumeration algorithm to solve the optimal combination of tour and numbers. By integrating the itinerary optimization approach and Web crawler technology, we develop a smart travel system that is able to capture online transport data and recommend the optimal itinerary that satisfies travelers’ preferences in departure time, arrival time, cabin class, and transport mode. Finally, we present case studies based on real-life transport data to illustrate the usefulness of itinerary optimization for minimizing travel cost, the computational efficiency of the implicit enumeration algorithm, and the feasibility of the smart travel system.     

Joint optimization of tram timetables and signal timing adjustments at intersections

This paper explores at the planning level the benefits of coordinating tram movements and signal timings at controlled intersections. Although trams may have dedicated travel lanes, they mostly operate in a mixed traffic environment at intersections. To ensure tram progression, pre-set signal timings at intersections are adjusted by activating Transit Signal Priority (TSP) actions, which inevitably add delays to the auto traffic. A mixed integer program is proposed for jointly determining tram schedules for a single tram line and modifying signal timings at major controlled intersections. The objective is to minimize the weighted sum of the total tram travel time and TSP’s negative impacts on other traffic. A real-world case study of Line 5 of the Shenyang Hunnan Modern Tramway shows that by extending the dwell time or link travel time we can significantly reduce the TSP’s negative impacts on the auto traffic while only slightly increasing tram travel times.     

Improving recovery-to-optimality robustness through efficiency-balanced design of timetable structure

To improve the service quality of the railway system (e.g., punctuality and travel times) and to enhance the robust timetabling methods further, this paper proposes an integrated two-stage approach to consider the recovery-to-optimality robustness into the optimized timetable design without predefined structure information (defined as flexible structure) such as initial departure times, overtaking stations, train order and buffer time. The first-stage timetabling model performs an iterative adjustment of all departure and arrival times to generate an optimal timetable with balanced efficiency and recovery-to-optimality robustness. The second-stage dispatching model evaluates the recovery-to-optimality robustness by simulating how each timetable generated from the first-stage could recover under a set of restricted scenarios of disturbances using the proposed dispatching algorithm. The concept of recovery-to-optimality is examined carefully for each timetable by selecting a set of optimally refined dispatching schedules with minimum recovery cost under each scenario of disturbance. The robustness evaluation process enables an updating of the timetable by using the generated dispatching schedules. Case studies were conducted in a railway corridor as a special case of a simple railway network to verify the effectiveness of the proposed approach. The results show that the proposed approach can effectively attain a good trade-off between the timetable efficiency and obtainable robustness for practical applications.     

A bi-level model for single-line rail timetable design with consideration of demand and capacity

This paper proposes a bi-level model to solve the timetable design problem for an urban rail line. The upper level model aims at determining the headways between trains to minimize total passenger cost, which includes not only the usual perceived travel time cost, but also penalties during travel. With the headways given by the upper level model, passengers’ arrival times at their origin stops are determined by the lower level model, in which the cost-minimizing behavior of each passenger is taken into account. To make the model more realistic, explicit capacity constraints of individual trains are considered. With these constraints, passengers cannot board a full train, but wait in queues for the next coming train. A two-stage genetic algorithm incorporating the method of successive averages is introduced to solve the bi-level model. Two hypothetical examples and a real world case are employed to evaluate the effectiveness of the proposed bi-level model and algorithm. Results show that the bi-level model performs well in reducing total passenger cost, especially in reducing waiting time cost and penalties. And the section loading-rates of trains in the optimized timetable are more balanced than the even-headway timetable. The sensitivity analyses show that passenger’s desired arrival time interval at destination and crowding penalty factor have a high influence on the optimal solution. And with the dispersing of passengers' desired arrival time intervals or the increase of crowding penalty factor, the section loading-rates of trains become more balanced.     

Door-to-door travel times in RP departure time choice models: An approximation method using GPS data

A common way to determine values of travel time and schedule delay is to estimate departure time choice models, using stated preference (SP) or revealed preference (RP) data. The latter are used less frequently, mainly because of the difficulties to collect the data required for the model estimation. One main requirement is knowledge of the (expected) travel times for both chosen and unchosen departure time alternatives. As the availability of such data is limited, most RP-based scheduling models only take into account travel times on trip segments rather than door-to-door travel times, or use very rough measures of door-to-door travel times. We show that ignoring the temporal and spatial variation of travel times, and, in particular, the correlation of travel times across links may lead to biased estimates of the value of time (VOT). To approximate door-to-door travel times for which no complete measurement is possible, we develop a method that relates travel times on links with continuous speed measurements to travel times on links where relatively infrequent GPS-based speed measurements are available. We use geographically weighted regression to estimate the location-specific relation between the speeds on these two types of links, which is then used for travel time prediction at different locations, days, and times of the day. This method is not only useful for the approximation of door-to-door travel times in departure time choice models, but is generally relevant for predicting travel times in situations where continuous speed measurements can be enriched with GPS data.     

Fuzzy modeling approach to the rail freight car inventory problem

Techniques to improve freight car fleet use are of considerable interest to the railroad industry. In this paper, we present a fuzzy inventory control approach applied to the sizing of empty cars on a rail network. We address the problem of deciding the optimal inventory level and the optimal ordering quantity for a rail freight car fleet system in which demand and travel time are uncertain variables represented as triangular fuzzy numbers. Based on the fuzzy economic order quantity (EOQ) formula, a modified fuzzy EOQ model is set up and the optimal policy is developed using the signed distance method to defuzzify the fuzzy total cost. Computational results made for the Serbian rail network case verify the proposed model as well as the efficiency of the approach.     

Scheduling and platforming trains at busy complex stations

We consider the problem of train planning or scheduling for large, busy, complex train stations, which are common in Europe and elsewhere, though not in North America. We develop the constraints and objectives for this problem, but these are too computationally complex to solve by standard combinatorial search or integer programming methods. Also, the problem is somewhat political in nature, that is, it does not have a clear objective function because it involves multiple train operators with conflicting interests. We therefore develop scheduling heuristics analogous to those successfully adopted by train planners using “manual” methods. We tested the model and algorithms by applying to a typical large station that exhibits most of the complexities found in practice. The results compare well with those found by traditional methods, and take account of cost and preference trade-offs not handled by those methods. With successive refinements, the algorithm eventually took only a few seconds to run, the time depending on the version of the algorithm and the scheduling problem. The scheduling models and algorithms developed and tested here can be used on their own, or as key components for a more general system for train scheduling for a rail line or network.Train scheduling for a busy station includes ensuring that there are no conflicts between several hundred trains per day going in and out of the station on intersecting paths from multiple in-lines and out-lines to multiple platforms, while ensuring that each train is allowed at least its minimum required headways, dwell time, turnaround time and trip time. This has to be done while minimizing (costs of) deviations from desired times, platforms or lines, allowing for conflicts due to through-platforms, dead-end platforms, multiple sub-platforms, and possible constraints due to infrastructure, safety or business policy.     

Joint modeling of evacuation departure and travel times in hurricanes

Hurricanes are costly natural disasters periodically faced by households in coastal and to some extent, inland areas. A detailed understanding of evacuation behavior is fundamental to the development of efficient emergency plans. Once a household decides to evacuate, a key behavioral issue is the time at which individuals depart to reach their destination. An accurate estimation of evacuation departure time is useful to predict evacuation demand over time and develop effective evacuation strategies. In addition, the time it takes for evacuees to reach their preferred destinations is important. A holistic understanding of the factors that affect travel time is useful to emergency officials in controlling road traffic and helps in preventing adverse conditions like traffic jams. Past studies suggest that departure time and travel time can be related. Hence, an important question arises whether there is an interdependence between evacuation departure time and travel time? Does departing close to the landfall increases the possibility of traveling short distances? Are people more likely to depart early when destined to longer distances? In this study, we present a model to jointly estimate departure and travel times during hurricane evacuations. Empirical results underscore the importance of accommodating an inter-relationship among these dimensions of evacuation behavior. This paper also attempts to empirically investigate the influence of social ties of individuals on joint estimation of evacuation departure and travel times. Survey data from Hurricane Sandy is used for computing empirical results. Results indicate significant role of social networks in addition to other key factors on evacuation departure and travel times during hurricanes.