We study the integration of real-time traffic management and train control by using mixed-integer nonlinear programming (MINLP) and mixed-integer linear programming (MILP) approaches. Three innovative integrated optimization approaches for real-time traffic management that inherently include train control are developed to deliver both a train dispatching solution (including train routes, orders, departure and arrival times at passing stations) and a train control solution (i.e., train speed trajectories). Train speed is considered variable, and the blocking time of a train on a block section dynamically depends on its real speed. To formulate the integrated problem, we first propose an MINLP problem (PNLP), which is solved by a two-level approach. This MINLP problem is then reformulated by approximating the nonlinear terms with piecewise affine functions, resulting in an MILP problem (PPWA). Moreover, we consider a preprocessing method to generate the possible speed profile options for each train on each block section, one of which is further selected by a proposed MILP problem (PTSPO) with respect to safety, capacity, and speed consistency constraints. This problem is solved by means of a custom-designed two-step approach, in order to speed up the solving procedure. Numerical experiments are conducted using data from the Dutch railway network to comparatively evaluate the effectiveness and efficiency of the three proposed approaches with heterogeneous traffic. According to the experimental results, the MILP approach (PTSPO) yields the best overall performance within the required computation time. The experimental results demonstrate the benefits of the integration, i.e., train delays can be reduced by managing train speed.@en

This article presents a case study determining the optimal preventive maintenance policy for a light rail rolling stock system in terms of reliability, availability, and maintenance costs. The maintenance policy defines one of the three predefined preventive maintenance actions at fixed time-based intervals for each of the subsystems of the braking system. Based on work, maintenance, and failure data, we model the reliability degradation of the system and its subsystems under the current maintenance policy by a Weibull distribution. We then analytically determine the relation between reliability, availability, and maintenance costs. We validate the model against recorded reliability and availability and get further insights by a dedicated sensitivity analysis. The model is then used in a sequential optimization framework determining preventive maintenance intervals to improve on the key performance indicators. We show the potential of data-driven modelling to determine optimal maintenance policy: same system availability and reliability can be achieved with 30% maintenance cost reduction, by prolonging the intervals and re-grouping maintenance actions.@en

We study the integration of real-time traffic management and train control by using mixed-integer nonlinear programming (MINLP) and mixed-integer linear programming (MILP) approaches. In Part 1 of the paper (Luan et al., 2018), three integrated optimization problems, namely the PNLP problem (NLP: nonlinear programming), the PPWA problem (PWA: piecewise affine), and the PTSPO problem (TSPO: train speed profile option), have been developed for real-time traffic management that inherently include train control. A two-level approach and a custom-designed two-step approach have been proposed to solve these optimization problems. In Part 2 of the paper, aiming at energy-efficient train operation, we extend the three proposed optimization problems by introducing energy-related formulations. We first evaluate the energy consumption of a train motion. A set of nonlinear constraints is first proposed to calculate the energy consumption, which is further reformulated as a set of linear constraints for the PTSPO problem and approximated by using a piecewise constant function for the PNLP and PPWA problems. Moreover, we consider the option of regenerative braking and present linear formulations to calculate the utilization of the regenerative energy obtained through braking trains. We focus on two objectives, i.e., delay recovery and energy efficiency, through using a weighted-sum formulation and an ε-constraint formulation. With these energy-related extensions, the nature of the three optimization problems remains same to Part 1. In numerical experiments conducted based on the Dutch test case, we consider the PNLP approach and the PTSPO approach only and compare their performance with the inclusion of the energy-related aspects; the PPWA approach is neglected due to its bad performance, as evaluated in Part 1. According to the experimental results, the PTSPO approach still yields a better performance within the required computation time. The trade-off between train delay and energy consumption is investigated. The results show the possibility of reducing train delay and saving energy at the same time through managing train speed, by up to 4.0% and 5.6% respectively. In our case study, applying regenerative braking leads to a 22.9% reduction of the total energy consumption.@en

Railway operations are subject to deviations from the planned schedule, i.e., delays. In those situations, high-quality traffic control actions are needed to reduce the delays. Existing studies mainly used prescriptive techniques (e.g., mathematical programming, heuristics) to identify the best control action. These methods have limitations in the firm reliance on deterministic parameters prescriptively or normatively determined beforehand, and little understandability by the practitioners. These drawbacks hinder their acceptance in practice. This study exploits instead past realization data to provide decision support for traffic control. The realized data describe the traffic control actions taken by human controllers, and their effects; those latter are more complex than a linear sum of predetermined parameters. We use decision graphs to identify which traffic control action leads to the best solution, in terms of reduction of delays, based on the past performance of the same action in similar conditions. We are also able to explain the reasons and the factors that lead to each suggested action. We focus on the relevant case of merging stations, where multiple lines merge as one line, deciding the relative order between two consecutive trains. The method determines the stochastic effects of the two possible decisions at merge points, which allows for choosing the best one. Compared within the framework of realized data, the action suggested is the best out of a series of benchmarks, including simple rules and optimization, improving (reducing delays) approximately 11.7% on the common benchmarks. The variables with the highest impact on the utility are the length of the planned dwell time and the planned presence of an overtaking. The variables influencing the utility most are the actual delays of trains, the train type, and the order actually implemented.@en

Railway operations are subject to deviations from the planned schedule, i.e., delays. In those situations, high-quality traffic control actions are needed to reduce the delays. Existing studies mainly used prescriptive techniques (e.g., mathematical programming, heuristics) to identify the best control action. These methods have limitations in the firm reliance on deterministic parameters prescriptively or normatively determined beforehand, and little understandability by the practitioners. These drawbacks hinder their acceptance in practice. This study exploits instead past realization data to provide decision support for traffic control. The realized data describe the traffic control actions taken by human controllers, and their effects; those latter are more complex than a linear sum of predetermined parameters. We use decision graphs to identify which traffic control action leads to the best solution, in terms of reduction of delays, based on the past performance of the same action in similar conditions. We are also able to explain the reasons and the factors that lead to each suggested action. We focus on the relevant case of merging stations, where multiple lines merge as one line, deciding the relative order between two consecutive trains. The method determines the stochastic effects of the two possible decisions at merge points, which allows for choosing the best one. Compared within the framework of realized data, the action suggested is the best out of a series of benchmarks, including simple rules and optimization, improving (reducing delays) approximately 11.7% on the common benchmarks. The variables with the highest impact on the utility are the length of the planned dwell time and the planned presence of an overtaking. The variables influencing the utility most are the actual delays of trains, the train type, and the order actually implemented.@en

Optimization models for railway traffic rescheduling in the last decade tend to develop along two main streams. On the one hand, train scheduling models strive to incorporate any relevant detail of the railway infrastructure having an impact on the feasibility and quality of the solutions from the viewpoint of infrastructure managers. On the other hand, delay management models focus on the impact of rescheduling decisions on the quality of service perceived by the passengers, and in the interest of the train operating company. Models in the first stream are mainly microscopic, while models in the second stream are mainly macroscopic. This paper aims at merging these two streams of research by developing microscopic delay management approaches. A variety of solution algorithms are proposed, that compute a solution to the studied problem; the obtained solutions correspond to Nash equilibria of the strategic interaction of the players (train operating company and infrastructure manager). Computational results based on a real-world Dutch railway network quantify the trade-off between the minimization of train delays and passenger travel times, and show that good compromise solutions can be found within a limited computation time.@en

The reliability assessment of the railway services is a complex procedure that is affected by many different factors. A railway system is reliable when the trains arrive at their destination within the allowed delay threshold. The objective of this study is to investigate the effect of the infrastructure doubling and electrification on the reliability of the train schedules. In this study, advanced event-driven stochastic simulation software is developed to determine the reliability of the train movements. The calculation of the average train delay as a benchmark is provided to evaluate performance. We compared average train delay with the acceptable delay to define a new benchmark to determine the reliability of the train movements. We also analyzed the delay cascading effect along the railway line in order to better illustration of a number of correlations between the arrival and departure delays at different stations. The model has been validated through a real-world case study of Iranian railway. Successful validation of the developed simulation system demonstrated that the model provides accurate reliability estimations in both congested and non-congested situations. Furthermore, the experimental results showed that electrification and doubling improve the reliability significantly.@en

The reliability assessment of the railway services is a complex procedure that is affected by many different factors. A railway system is reliable when the trains arrive at their destination within the allowed delay threshold. The objective of this study is to investigate the effect of the infrastructure doubling and electrification on the reliability of the train schedules. In this study, advanced event-driven stochastic simulation software is developed to determine the reliability of the train movements. The calculation of the average train delay as a benchmark is provided to evaluate performance. We compared average train delay with the acceptable delay to define a new benchmark to determine the reliability of the train movements. We also analyzed the delay cascading effect along the railway line in order to better illustration of a number of correlations between the arrival and departure delays at different stations. The model has been validated through a real-world case study of Iranian railway. Successful validation of the developed simulation system demonstrated that the model provides accurate reliability estimations in both congested and non-congested situations. Furthermore, the experimental results showed that electrification and doubling improve the reliability significantly.@en

A wide literature is available on models and tools for the optimal real-time management of railway traffic, but the knowledge of their effects on real operations is still blurry and very limited due to the scarce implementation of these systems in practice. This paper analyses how these tools perform when interfaced in a closed-loop setup with a realistic traffic environment. A framework is developed that couples the rescheduling tool ROMA with the microscopic simulation model EGTRAIN. Railway traffic is managed for different perturbed scenarios using a rolling horizon scheme where optimal plans are periodically computed based on current traffic information and implemented in the simulation model. The closed-loop setup is investigated for different combinations of its parameters relatively to quality and stability of rescheduling plans. A comparison is performed against a typical open-loop approach that implements only the plan computed on the basis of expected train entrance delays. Both the closed-loop and the open-loop approaches are evaluated against the case in which no rescheduling is considered and trains keep on following the original timetable. Results obtained for the Dutch corridor Utrecht-Den Bosch show that the closed-loop always outperforms the open-loop in terms. @en

Air traffic is growing, putting increasing stress to airports and air traffic control. The introduction of optimized approaches, based on mathematical optimization paradigms for planning and real time control, can be a possible solution to this issues. We investigate the practical setting of an advanced optimization algorithm in a real-life setting of a major airport where traffic is diverse, belonging to multiple companies. We compare to the incumbent practice (based on First Come First Served) in order to determine a gap with optimized solutions computed by advanced algorithms. Those are based on a job shop scheduling model and solved by a commercial solver. This paper analyses the benefit for the involved operators of such approaches by associating a monetary cost/benefit to operations. Cooperative game theory tools have been used in the analysis. In particular, we use the Shapley value to determine the fair distribution of the costs based on the marginal improvement that the optimization of the traffic belonging to any airline brought to the system. The main conclusions of this study are the determination of the superior performance in terms of minimising the delay experienced by the whole airport, which reaches more than 25 %. The benefit allocation gives share of benefits more insightful than a simple proportional approaches based on share of traffic, or share of delay. The practical implications of the analysis with regard to variety in benefits as well as possible implementations by the different operators and companies are also analysed.@en

Passenger transit modes typical of the urban setting, including bus, tram, metro, and train, have been described in Chap. 2, along with less conventional modes such as BRT and cable. Then, Chaps. 6 and 7 have provided network assignment models that address primarily the passenger side, dealing with route choice situations and behaviour, the individual exposure to traffic conditions, and the contribution of individual users to local flows. In these models, the transit mode is represented as a set of lines, each of which is abstracted into its topology (nodes and links) and some features of traffic operations: run time, dwell time, and some capacity parameters. In such an abstract setting, no distinction has been made between, for instance, bus and railway services, apart from their respective parameter values.@en

In the Netherlands, the main port Rotterdam, is confronted with a steady growth in total volume, mostly resulting in a direct increase of the road transport; the resulting road congestion led to various initiatives increasing the share of transport over water and rail. Overall, this intermodal situation is vulnerable to many sources of uncertainty, ranging from relatively common, low impact events, to relatively rare, high impact events.@en

Employing regenerative braking in trains contributes to reducing the amount of energy used, especially when applied to commuter trains and to those used on very dense suburban networks. This paper presents a method to fine-tune the periodic timetable to improve the utilization of regenerative energy and to shave power peaks while maintaining the structure and robustness of the original timetable. First, a mixed-integer linear programming model based on the periodic event scheduling framework is proposed. A set of feasible timetables is determined and optimized with the aim of increasing synchronized acceleration and braking events at the same station, and maintaining the timetable robustness at the specified level. Next, a local search algorithm is developed to optimize the timetable such that the power peak value is minimized. The max-plus system model is adopted to estimate the delay propagation. Monte Carlo simulation is used to evaluate the utilization of regenerative energy and power peaks in random delayed circumstances. The proposed method was adopted to fine-tune the 2019 timetable for a sub-network of the Dutch railway. In the case of on- time scenarios, the optimized timetable increases the regenerative energy usage by almost 290% and decreases the 15-minute power peaks by 8.5%. In the case of delay scenarios, the optimized timetable outperforms the original timetable in terms of using regenerative energy and shaving power peaks.@en

We introduce a distributed optimization method for improving the computational efficiency of real-time traffic management approaches for large-scale railway networks. We first decompose the whole network into a pre-defined number of regions by using an integer linear optimization approach. For each resulting region, a mixed-integer linear programming approach is used to address the traffic management problem, with micro details of the network and incorporated with the train control problem. For handling the interactions among regions, an alternating direction method of multipliers (ADMM) algorithm based solution approach is developed to solve the subproblem of each region through coordination with the other regions in an iterative manner. A priority rule based solution approach is proposed to generate feasible suboptimal solutions, in case of lack of convergence. Numerical experiments are conducted based on the Dutch railway network to show the performance of the proposed solution approaches, in terms of effectiveness and efficiency. We also show the trade-off between solution quality and computational efficiency.@en

This work tackles the problem of controlling operations at an automated container terminal. In the context of large supply chains, there is a growing trend for increasing productivity and economic efficiency. New optimization models and algorithms are provided for scheduling and routing equipment that is moving containers in a quay area, loading/unloading ships, transporting them via Automated Guided Vehicles (AGVs) to Automated Stacking Cranes (ASCs), organizing them in stacks. In contrast with the majority of the approaches in the related literature, this work tackles two dynamics of the system, a discrete dynamic, characteristic of the maximization of operations efficiency, by assigning the best AGV and operation time to a set of containers, and a continuous dynamic of the AGV that moves in a geographically limited area. As an assumption, AGVs can follow free range trajectories that minimize the error of the target time and increase the responsiveness of the system. A novel solution framework is proposed in order to tackle the two system dynamics. Various metaheuristic algorithms are tested to solve the problem in a near-optimal way. Computational experiments are presented in order to show the feasibility of the proposed framework on a practical case study, and to assess the performance of advanced scheduling and routing algorithms on numerous system settings.@en

Wheel impact load detectors are widespread railway systems used for measuring the wheel–rail contact force. They usually measure the rail strain and convert it to force in order to detect high impact forces and corresponding detrimental wheels. The measured strain signal can also be used to identify the defect type and its severity. The strain sensors have a limited effective zone that leads to partial observation from the wheels. Therefore, wheel impact load detectors exploit multiple sensors to collect samples from different portions of the wheels. The discrete measurement by multiple sensors provides the magnitude of the force; however, it does not provide the much richer variation pattern of the contact force signal. Therefore, this paper proposes a fusion method to associate the collected samples to their positions over the wheel circumferential coordinate. This process reconstructs an informative signal from the discrete samples collected by multiple sensors. To validate the proposed method, the multiple sensors have been simulated by an ad hoc multibody dynamic software (VI-Rail), and the outputs have been fed to the fusion model. The reconstructed signal represents the contact force and consequently the wheel defect. The obtained results demonstrate considerable similarity between the contact force and the reconstructed defect signal that can be used for further defect identification.@en

This paper addresses the real-time problem of coordinating aircraft ground and air operations in an airport area. At a congested airport, airborne decisions are related to take-off and landing operations, while ground (taxiway) decisions consist of scheduling aircraft movements between the gates and the runways. Since the runways are the initial/terminal points of both decisions, coordinated actions have a great potential to improve the overall performance. However, in the traffic control practice the different decisions are taken by different controllers, at least in large airports. Weak coordination may result in long queues at the runways, with increasing aircraft delays and energy consumption. This paper investigates models, methods and policies for improving the coordination between taxiway scheduling and airborne scheduling. The performance of a solution is measured in terms of delay and travel time, the latter being related to the energy consumption of an aircraft. A microscopic mathematical formulation is adopted to achieve reliable solutions. Exact and heuristic methods have been analysed in combination with the different policies, based on practical-size instances from Amsterdam Schiphol airport, in the Netherlands. Computational experience shows that good quality solutions can be found within limited time, compatible with real-time operations.@en

Intelligent decision support systems for the real-time management of landing and take-off operations can be very effective in helping air traffic controllers to limit airport congestion at busy terminal control areas. The key optimization problem to be solved regards the assignment of airport resources to take-off and landing aircraft and the aircraft sequencing on them. The problem can be formulated as a mixed integer linear program. However, since this problem is strongly NP-hard, heuristic algorithms are typically adopted in practice to compute good quality solutions in a short computation time. This paper presents a number of algorithmic improvements implemented in the AGLIBRARY solver (a state-of-the-art optimization solver to deal with complex routing and scheduling problems) in order to improve the possibility of finding good quality solutions quickly. The proposed framework starts from a good initial solution for the aircraft scheduling problem with fixed routes (given the resources to be traversed by each aircraft), computed via a truncated branch-and-bound algorithm. A metaheuristic is then applied to improve the solution by re-routing some aircraft in the terminal control area. New metaheuristics, based on variable neighbourhood search, tabu search and hybrid schemes, are introduced. Computational experiments are performed on an Italian terminal control area under various types of disturbances, including multiple aircraft delays and a temporarily disrupted runway. The metaheuristics achieve solutions of remarkable quality, within a small computation time, compared with a commercial solver and with the previous versions of AGLIBRARY.@en