Dynamic blocking for railyards: Part II. Heterogeneous traffic

Traffic through a railroad yard is said to be heterogeneous if all the destinations are not served with the same frequency. This paper presents a study of railroad yards when traffic is heterogeneous and stationary, that is, without rush hour (or rush day) phenomena. Destinations (blocks) are grouped into categories that are served with the same frequency. The number of blocks and the frequency corresponding to each class are the only traffic characteristics that need to be known to analyze a given yard. With this information it is easy to determine the minimum number of tracks needed, and the number of switches per car; a numerical example is provided. The minimum number of required tracks is always larger than that for homogeneous traffic, but under the right conditions, the number of switches can be smaller. An approximation for large numbers of blocks is used to isolate the traffic factors that make the number of switches either large or small.     

Storage space allocation in container terminals

Container terminals are essential intermodal interfaces in the global transportation network. Efficient container handling at terminals is important in reducing transportation costs and keeping shipping schedules. In this paper, we study the storage space allocation problem in the storage yards of terminals. This problem is related to all the resources in terminal operations, including quay cranes, yard cranes, storage space, and internal trucks. We solve the problem using a rolling-horizon approach. For each planning horizon, the problem is decomposed into two levels and each level is formulated as a mathematical programming model. At the first level, the total number of containers to be placed in each storage block in each time period of the planning horizon is set to balance two types of workloads among blocks. The second level determines the number of containers associated with each vessel that constitutes the total number of containers in each block in each period, in order to minimize the total distance to transport the containers between their storage blocks and the vessel berthing locations. Numerical runs show that with short computation time the method significantly reduces the workload imbalance in the yard, avoiding possible bottlenecks in terminal operations.     

Real-time congestion pricing strategies for toll facilities

This paper analyzes the dynamic traffic assignment problem on a two-alternative network with one alternative subject to a dynamic pricing that responds to real-time arrivals in a system optimal way. Analytical expressions for the assignment, revenue and total delay in each alternative are derived as a function of the pricing strategy. It is found that minimum total system delay can be achieved with many different pricing strategies. This gives flexibility to operators to allocate congestion to either alternative according to their specific objective while maintaining the same minimum total system delay. Given a specific objective, the optimal pricing strategy can be determined by finding a single parameter value in the case of HOT lanes. Maximum revenue is achieved by keeping the toll facility at capacity with no queues for as long as possible. Guidelines for implementation are discussed.     

A comparison of different container sorting systems in modern rail-rail transshipment yards

Rail-rail transshipment yards act as central hub nodes within a railway network and enable a rapid consolidation of containers between different freight trains. To avoid an excessive movement of gantry cranes when transferring a container from one train to another, modern yards apply sorting systems where shuttle cars move containers horizontally along the spread of the yard. This paper compares four elementary sorting systems. Specifically, we compare rubber-tired and rail-mounted shuttles and differentiate whether a pure shuttle system or a lift & shuttle system is applied. In pure shuttle systems, a shuttle receives a container from a crane and transports it towards the destination crane, where it serves as a storage device until being unloaded. A lift & shuttle system applies shuttles with an integrated lifting platform, so that they are able to autonomously store and receive containers from a separate storage rack. Both alternatives exist in rubber-tired and rail-mounted versions. As the shuttles are the main driver of the investment costs, we compare the required fleet size for timely supplying given gantry crane schedules within all four systems. For this purpose, we derive suited scheduling procedures. This way, decision support for yard managers having to identify a suited sorting system and to layout a new terminal is provided.     

Real-time energy consumption minimization in railway networks

A new timetable must be calculated in real-time when train operations are perturbed. Although energy consumption is becoming a central issue both from the environmental and economic perspective, it is usually neglected in the timetable recalculation. In this paper, we formalize the real-time Energy Consumption Minimization Problem (rtECMP). It finds in real-time the driving regime combination for each train that minimizes energy consumption, respecting given routing and precedences between trains. In the possible driving regime combinations, train routes are split in subsections for which one of the regimes resulting from the Pontryagin’s Maximum Principle is to be chosen. We model the trade-off between minimizing energy consumption and total delay by considering as objective function their weighted sum. We propose an algorithm to solve the rtECMP, based on the solution of a mixed-integer linear programming model. We test this algorithm on the Pierrefitte-Gonesse control area, which is a critical area in France with dense mixed traffic. The results show that the problem is tractable and an optimal solution of the model tackled can often be found in real-time for most instances.     

Connected vehicle penetration rate for estimation of arterial measures of effectiveness

The Connected Vehicle (CV) technology is a mobile platform that enables a new dimension of data exchange among vehicles and between vehicles and infrastructure. This data source could improve the estimation of Measures of Effectiveness (MOEs) for traffic operations in real-time, allowing to perfectly monitor traffic states after being fully adopted. However, as with any novel technology, the CV adoption will be a gradual process. This research focuses on determining minimum CV technology penetration rates that would guarantee accurate MOE estimates on signalized arterials. First, we present estimation methods for various MOEs such as average speed, number of stops, acceleration noise, and delay, followed by an initial assessment of the penetration rates required to accurately estimate them in undersaturated and oversaturated conditions. Next, we propose a methodology to determine the minimum CV market penetration rates to guarantee accurate MOE estimates as a function of traffic conditions, signal settings, sampling duration, and the MOE variability. A correction factor is also provided to account for small vehicle populations where sampling is done without replacement. The methodology is tested in a simulated segment of the San Pablo Avenue arterial in Berkeley, CA. The outcomes show that the minimum penetration rate required can be estimated within 1% for most MOEs under a wide range of traffic conditions. The proposed methodology can be used to determine if MOE estimates obtained with a portion of CV equipped vehicles can yield accurate enough results. The methodology could also be used to develop and assess control strategies towards improved arterial traffic operations.     

Traffic flow on signalized streets

This paper considers a signalized street of uniform width and blocks of various lengths. Its signals are pretimed in an arbitrary pattern, and traffic on it behaves as per the kinematic-wave/variational theory with a triangular fundamental diagram. It is shown that the long run average flow on the street when the number of cars on the street (i.e. the street’s density) is held constant is given by the solution of a linear program (LP) with a finite number of variables and constraints. This defines a point on the street’s macroscopic fundamental diagram. For the homogeneous special case where the block lengths and signal timings are identical, all the LP constraints but one are redundant and the result has a closed form. In this case, the LP recipe matches and simplifies the so-called “method of cuts”. This establishes that the method of cuts is exact for homogeneous problems. However, in the more realistic inhomogeneous case the difference between the two methods can be arbitrarily large.The paper uses the LP method to obtain the macroscopic fundamental diagrams arising under four different traffic coordination schemes for streets with four different block length configurations. It is found that the best scheme depends on the prevailing density. Curiously, the popular scheme in which all the traffic green phases are started synchronously wins only in rare circumstances. Its performance is particularly underwhelming when the street’s blocks are long. The paper also presents density-aware numerical methods to optimize the signal offsets for 1-way and 2-way streets. For 1-way streets operated with a common cycle the method reduces to a simple graphical construction . In this case the resulting flow matches the flow that would arise if all of the street’s intersections except one with the shortest green phase had been eliminated.     

Design of single-track rail line for high-speed trains

This paper presents a method for designing a single-track rail line for a reliable high-speed passenger train service. We first consider deterministic train performance and describe a general method for finding the best location and length of the passing tracks. The design is then modified to include slack, which is necessary to ensure on-time performance for trains encountering unexpected delay. An analysis of the robustness of the system to small delays is presented. Robustness to large train delays and slower traffic is incorporated through the provision of additional sidings. Finally, simulation results are presented which compare the performance of a single-track line to a fully double-tracked equivalent.     

Comparative evaluation of resource cycle strategies on operating and environmental impact in container terminals

This paper examines the use of single and dual cycle operations for three types of resources, namely, quay cranes, vehicles, and yard cranes to improve the operating efficiency and reduce the energy consumption in a container terminal. Various cycle strategies are proposed and their corresponding estimation models, describing the stowage distributions of outbound and inbound containers on a ship and the storage sharing level of blocks in the yard, are formulated to estimate the total number of cycles for the resources. Statistical analyses are conducted to evaluate and compare the effect of different cycle strategies on the cycle reductions. From the experiment results, it was found that collaboration between resources with the single cycle operation always outperforms that under the dual cycle operation without collaboration.     

An improved car‐following model for railway traffic

In this paper, we propose an improved traffic model for simulating train movement in railway traffic. The proposed model is based on optimal velocity car‐following model. In order to test the proposed model, we use it to simulate the train movement with fixed‐block system. In simulations, we analyze and discuss the space–time diagram of railway traffic flow and the trajectories of train movement. Simulation results demonstrate that the proposed model can be successfully used for simulating the train movement in railway traffic. From the space–time diagram, we find some complex phenomena of train flow, which are observed in real railway traffic, such as train delays. By analyzing the trajectories of train movement, some dynamic characteristics of trains can be reproduced. Copyright © 2011 John Wiley & Sons, Ltd.     

Probabilistic risk analysis of flying ballast hazard on high-speed rail lines

Flying ballast is a significant safety concern for high-speed train operations on ballasted tracks. It is the phenomenon of a ballast particle displaced from the track, due to the aerodynamic force induced by a passing train traveling above a certain speed. Flying ballast can potentially damage tracks and rolling stock, thereby posing a risk to high-speed rail operations. This paper develops a Probabilistic Risk Analysis (PRA) model based on the information available from the field and the literature. The model enables a quantitative assessment of the probability of ballast particle displacement at a particular position on the track, as well as the probabilistic distribution of the total number of ballast particles that are expected to move. The model accounts for various risk factors, such as train speed, ballast gradation, and track position. The model application is illustrated using a ballasted track on the Yellow River Bridge on the Beijing-Shanghai high-speed rail line in China. The analysis finds that flying ballast probability increases when train speed increases, in particular, the problem of flying ballast becomes more pronounced when train speed exceeds 350 km per hour (217 miles per hour). Flying ballast probability might be reduced when the ballast profile is lower, given all else being equal. In addition, flying ballast probability is expected to be higher at the center of the track than in other positions. The proposed risk model can be further developed and ultimately be used to evaluate route-specific flying ballast risk, enabling the identification, assessment, and comparison of risk mitigation strategies in order to support emerging high-speed rail operations.     

Optimizing train operational plan in an urban rail corridor based on the maximum headway function

The train operational plan (TOP) plays a crucial role in the efficient and effective operation of an urban rail system. We optimize the train operational plan in a special network layout, an urban rail corridor with one terminal yard, by decomposing it into two sub-problems, i.e., the train departure profile optimization and the rolling stock circulation optimization. The first sub-problem synthetically optimizes frequency setting, timetabling and the rolling stock circulation at the terminal without a yard. The maximum headway function is generated to ensure the service of the train operational plan without considering travel demand, then we present a model to minimize the number of train trips, and design a heuristic algorithm to maximize the train headway. On the basis of a given timetable, the rolling stock circulation optimization only involves the terminal with a yard. We propose a model to minimize the number of trains and yard–station runs, and an algorithm to find the optimal assignment of train-trip pair connections is designed. The computational complexities of the two algorithms are both linear. Finally, a real case study shows that the train operational plan developed by our approach enables a better match of train headway and travel demand, and reduces the operational cost while satisfying the requirement of the level of service.     

Interactions between driver information,route choice,and optimal signal timing on a simple network

The interaction between driver information, route choice, and optimal traffic signal settings was investigated using a simple two-route system with a single “T” intersection and a fixed O-D demand. The logit model and the method of successive averages (MSA) were used to calculate the route choice probabilities and the stochastic equilibrium assignment. Given an assignment, signal settings which minimized average intersection delay were calculated; flow reassignment and new optimal signal settings were then obtained and this iterative process continued until convergence. The calculations were performed either directly in a combined assignment/signal optimization model or in stages using the output flows of an assignment model as inputs to TRANSYT-7F and iterating between the two models. Results show that a unique joint signal timing/assignment equilibrium is reached in all cases provided that a certain precision in drivers' perceptions is not reached. If driver information increases to this precision (bifurcation point) and beyond, results show clearly that the unique joint signal timing/assignment equilibrium no longer exists. In fact, three joint equilibria points exist after the bifurcation point. Two of these points are stable and one is not. It was found that the system yields the lowest total intersection delay when the joint equilibrium is such that all traffic and hence the major part of green time is assigned to only one of the two routes. Although this may not be feasible to implement in practice, the results indicate clearly for this simple example that there is a trade-off between a system with minimum total delay but no unique joint signal-settings/assignment equilibrium (achieved when drivers have nearly perfect information about the system) and a system with a unique joint equilibrium but with higher total delay (achieved when drivers have reasonably good but somewhat limited information). In most cases the second system seems appropriate for a number of practical reasons.     

Scheduling heterogeneous train traffic on double tracks with efficient dispatching rules

To further improve the utilization rate of railway tracks and reduce train delays, this paper focuses on developing a high-efficiency train routing and timetabling approach for double-track railway corridors in condition that trains are allowable to travel on reverse direction tracks. We first design an improved switchable policy which is rooted in the approaches by Mu and Dessouky (2013), with the analysis of possible delays caused by different path choices. Then, three novel integrated train routing and timetabling approaches are proposed on the basis of a discrete event model and different dispatching rules, including no switchable policy (No-SP), Mu and Dessouky (2013)’s switchable policy (Original-SP) and improved switchable policy (Improved-SP). To demonstrate the performance of the proposed approaches, the heterogeneous trains on Beijing–Shanghai high speed railway are scheduled by aforementioned approaches. The case studies indicate that in comparison to No-SP and Original-SP approaches, respectively, the Improved-SP approach can reduce the total delay of trains up to 44.44% and 73.53% within a short computational time. Moreover, all of the performance criteria of the Improved-SP approach are usually better than those of other two approaches.     

An integrated micro–macro approach to robust railway timetabling

With the increasing demand for railway transportation infrastructure managers need improved automatic timetabling tools that provide feasible timetables with enhanced performance in short computation times. This paper proposes a hierarchical framework for timetable design which combines a microscopic and a macroscopic model of the network. The framework performs an iterative adjustment of train running and minimum headway times until a feasible and stable timetable has been generated at the microscopic level. The macroscopic model optimizes a trade-off between minimal travel times and maximal robustness using an Integer Linear Programming formulation which includes a measure for delay recovery computed by an integrated delay propagation model in a Monte Carlo setting. The application to an area of the Dutch railway network shows the ability of the approach to automatically compute a feasible, stable and robust timetable. Practitioners can use this approach both for effective timetabling and post-evaluation of existing timetables.     

Bus Priority Using pre-signals

The need to provide efficient public transport services in urban areas has led to the implementation of bus priority measures in many congested cities. Much interest has recently centred on priority at signal controlled junctions, including the concept of pre-signals, where traffic signals are installed at or near the end of a with-flow bus lane to provide buses with priority access to the downstream junction. Although a number of pre-signals have now been installed in the U.K., particularly in London, there has been very little published research into their design, operation and optimisation. This paper addresses these points through the development of analytical procedures which allow pre-implementation evaluation of specific categories of pre-signals. The paper initially sets out three categories of pre-signal, which have different operating characteristics, different requirements for signalling and different impacts on capacity and delay. Key issues concerning signalling arrangements for these categories are then discussed, together with a summary of the analytical approach adopted and the assumptions required. Equations are developed to allow appropriate signal timings to be calculated for pre-signalised intersections. Further equations are then developed to enable delays to priority and non-priority traffic, with and without pre-signals, to be estimated with delay being taken here as the key performance criterion. The paper concludes with three application examples illustrating how the equations are applied and the impacts of pre-signals in different situations.The analyses confirm the potential benefits of pre-signals, where these signals apply to non-priority traffic only. Where buses are also subject to a pre-signal, it is shown that disbenefits to buses can often occur, unless bus detectors are used to gain priority signalling.     

Stochastic prediction of train delays in real-time using Bayesian networks

In this paper we present a stochastic model for predicting the propagation of train delays based on Bayesian networks. This method can efficiently represent and compute the complex stochastic inference between random variables. Moreover, it allows updating the probability distributions and reducing the uncertainty of future train delays in real time under the assumption that more information continuously becomes available from the monitoring system. The dynamics of a train delay over time and space is presented as a stochastic process that describes the evolution of the time-dependent random variable. This approach is further extended by modelling the interdependence between trains that share the same infrastructure or have a scheduled passenger transfer. The model is applied on a set of historical traffic realisation data from the part of a busy corridor in Sweden. We present the results and analyse the accuracy of predictions as well as the evolution of probability distributions of event delays over time. The presented method is important for making better predictions for train traffic, that are not only based on static, offline collected data, but are able to positively include the dynamic characteristics of the continuously changing delays.     

The real-time urban traffic control system CRONOS: Algorithm and experiments

The real-time urban traffic control algorithm CRONOS has been evaluated on an intersection by comparison of two reference control strategies, a local one and a centralized one. Recurrent traffic situations, from peak hour traffic to low traffic, have been studied, and the impact on the traffic from a fluidity point of view has been investigated using various criteria. The average behavior of CRONOS has also been analyzed by crossing the traffic signal colors with traffic variables. Several of the criteria are innovative, thanks to the real-time, accurate video-based traffic data collected.The results show high benefits of CRONOS on the total delay compared to the two reference control strategies, and benefits are also obtained on the total number of stops and percentage of stops, especially in comparison with the local strategy. All traffic situations (peak to low traffic) are concerned by these results. The analysis of the average behavior of CRONOS shows a higher average number of cycles per hour, more global green duration per hour at the center of the intersection, to the detriment of the entries. Moreover, CRONOS switches more often from amber to red when no vehicles are present on the link in percentage of cycles or in number of cycles per hour; it switches more often from green to amber when vehicles are present on the link in percentage of cycles per hour.     

Non-discriminatory train dispatching in a rail transport market with multiple competing and collaborative train operating companies

Train dispatching is vital for the punctuality of train services, which is critical for a train operating company (TOC) to maintain its competitiveness. Due to the introduction of competition in the railway transport market, the issue of discrimination is attracting more and more attention. This paper focuses on delivering non-discriminatory train dispatching solutions while multiple TOCs are competing in a rail transport market, and investigating impacting factors of the inequity of train dispatching solutions. A mixed integer linear programming (MILP) model is first proposed, in which the inequity of competitors (i.e., trains and TOCs) is formalized by a set of constraints. In order to provide a more flexible framework, a model is further reformulated where the inequity of competitors is formalized as the maximum individual deviation of competitors’ delay cost from average delay cost in the objective function. Complex infrastructure capacity constraints are considered and modelled through a big M-based approach. The proposed models are solved by a standard MILP solver. A set of comprehensive experiments is conducted on a real-world dataset adapted from the Dutch railway network to test the efficiency, effectiveness, and applicability of the proposed models, as well as determine the trade-off between train delays and delay equity.     

On the distribution of urban road space for multimodal congested networks

Transport systems in real cities are complex with many modes of transport sharing and competing for limited road space. This work intends to understand how space distributions for modes and interactions among modes affect network traffic performance. While the connection between performance of transport systems and general land allocation is the subject of extensive research, space allocation for interacting modes of transport is an open research question. Quantifying the impact of road space distribution on the performance of a congested multimodal transport system with a dynamic aggregated model remains a challenge. In this paper, a multimodal macroscopic fundamental diagram (MFD) is developed to represent the traffic dynamics of a multimodal transport system. Optimization is performed with the objective of minimizing the total passenger hours traveled (PHT) to serve the total demand by redistributing road space among modes. Pricing strategies are also investigated to provide a higher demand shift to more efficient modes. We find by an application to a bi-modal two-region city that (i) the proposed model captures the operational characteristics of each mode, and (ii) optimal dynamic space distribution strategies can be developed. In practice, the approach can serve as a physical dynamic model to inform space distribution strategies for policy makers with different goals of mobility.