Headway Constraints Research Articles

Periodic timetabling with integrated track choice for railway construction sites

We propose a mixed-integer linear programming model to generate and optimize periodic timetables with integrated track choice in the context of railway construction sites. When a section of a railway network becomes unavailable, the nearby areas are typically operated close to their capacity limits, and hence carefully modeling headways and allowing flexible routings becomes vital. We therefore discuss first how to integrate headway constraints into the Periodic Event Scheduling Problem (PESP) that do not only prevent overtaking, but also guarantee conflict-free timetables in general and particularly inside stations. Secondly, we introduce a turn-sensitive event-activity network, which is able to integrate routing alternatives for turnarounds at stations, e.g., turning at a platform vs. at a pocket track for metro-like systems. We propose several model formulations to include track choice, and finally evaluate them on six real construction site scenarios on the S-Bahn Berlin network.

Neural Network-Based Subway Regenerative Energy Optimization With Variable Headway Constraints

For subway regenerative energy optimization, the essential idea is to maximize the amount of regenerative energy absorption (AREA) between accelerating trains and braking trains by adjusting train timetable. The bottlenecks preventing the theoretical research from being used to industrial practice lie in the time-consuming simulation of AREA and the constant setting of headway threshold, which seriously reduces the computational efficiency and compresses the solution space. For addressing these issues, we formulate neural networks to speed up the AREA simulation, develop a bisection algorithm to dynamically adjust the headway threshold under moving block mechanism, and then establish a hybrid heuristic method integrating neural networks, genetic algorithm, variable neighborhood search and simulated annealing to determine the timetable, including dwell time distribution (DTD) at stations and headway time distribution (HTD) among consecutive trains. The effectiveness of the proposed method is confirmed by numerical experiments based on the real ATO data of Beijing Subway Changping Line. The results reveal that the neural networks could save 98.96% of the computational time at the expense of 1.76% of the accuracy loss, such that the hybrid heuristic algorithm could save 75.68% of the computational time. Benchmarked with the constant headway constraints used in literature, the variable headway constraints could achieve an average improvement of AREA by 8.94%. In addition, the joint optimization of DTD and HTD could increase the AREA by 15.28% on average, compared to the single optimization of HTD. This research is of great significance to improve the practicability of subway regenerative energy optimization algorithms.

A Hierarchical MPC Approach to Car-Following via Linearly Constrained Quadratic Programming

Single-lane car-following is a fundamental task in autonomous driving. A desirable car-following controller should keep a reasonable range of distances to the preceding vehicle and do so as smoothly as possible. To achieve this, numerous control methods have been proposed: some only rely on local sensing; others also make use of non-local downstream observations. While local methods are capable of attenuating high-frequency velocity oscillation and are economical to compute, non-local methods can dampen a wider spectrum of oscillatory traffic but incur a larger cost in computing. In this letter, we design a novel non-local tri-layer MPC controller that is capable of smoothing a wide range of oscillatory traffic and is amenable to real-time applications. At the core of the controller design are 1) an accessible prediction method based on ETA estimation and 2) a robust, light-weight optimization procedure, designed specifically for handling various headway constraints. Numerical simulations suggest that the proposed controller can simultaneously maintain a variable headway while driving with modest acceleration and is robust to imperfect traffic predictions.

Hardware-in-the-loop exploration of energy versus emissions trade-off in eco-following scenarios for connected automated vehicles

Studies on eco-driving have mostly taken an energy-centric view and considered driving performance, while less attention has been paid on emissions behavior. This work extends in an experimentally verified way our understanding of the trade-offs among fuel economy, driving aggressiveness, and, especially, emissions in connected automated diesel-powered vehicles. Experiments are performed with a 6.7-L Ford Powerstroke diesel engine, a urea-SCR based NOx aftertreatment system, and a full model for a Ford F250 medium-duty truck in the loop to provide realistic assessment of fuel consumption, tailpipe emissions, and driving style performances. An energy and emissions conscious speed planner is leveraged to follow the traffic. This planner offers flexibility in prioritizing energy or emissions while satisfying user-defined headway constraints, and thus allows exploration of different calibrations in a unified way. Results show how various calibrations of the flexible leader following policy yield 8%–14% decrease in total fuel consumption and 64%–70% decrease in tailpipe emissions compared with a strictly constrained following policy.

Delay propagation cellular automata model based on max-plus algebra for robustness evaluations of non-periodic train operation plans

Based on discrete-event dynamic system theory, train operation events in high-speed railway transportation systems are regarded as the basic elements of these dynamic systems. For non-periodic timetable railways in China, based on a max-plus algebra method, a delay propagation cellular automata model is proposed to evaluate the robustness of high-speed train operation plans. The cellular automata evolution rules that can reproduce the delay propagation state of trains mainly consider train safety headway constraints, passenger transfer constraints, and electric multiple unit (EMU) connection constraints. A simulation analysis of actual cases is performed. The simulation results show that the model can be used to evaluate the robustness of the train operation plan. The numerical results show that in the preparation of train operation plans, the proposed model can predict which trains have significant influences on delays in advance and improve the possibility of reducing the occurrence of delays to maintain high-quality service.

A matheuristic for transfer synchronization through integrated timetabling and vehicle scheduling

Long transfer times often add unnecessary inconvenience to journeys in public transport systems. Synchronizing relevant arrival and departure times through small timetable modifications could reduce excess transfer times, but may also directly affect the operational costs, as the timetable defines the set of feasible vehicle schedules. Therefore better results in terms of passenger service, operational costs, or both, could be obtained by solving these problems simultaneously.This paper addresses the tactical level of the integrated timetabling and vehicle scheduling problem as a bi-objective mixed integer programming problem that minimizes transfer costs and operational costs. Given an initial non-cyclical timetable, and time-dependent service times and passenger demand, the weighted sum of transfer time cost and operational costs is minimized by allowing modifications to the timetable that respect a set of headway constraints. Timetable modifications consist of shifts in departure time and addition of dwell time at intermediate stops with transfer opportunities.A matheuristic is proposed that iteratively solves the mathematical formulation of the integrated timetabling and vehicle scheduling problem allowing timetable modifications for a subset of timetabled trips only, while solving the full vehicle scheduling problem. We compare different selection strategies for defining the sub-problems. Results for a realistic case study of the Greater Copenhagen area indicate that the matheuristic is able to find better feasible solutions faster than a commercial solver and that allowing the addition of dwell time creates a larger potential for reducing transfer costs.

Resolving Infeasibilities in Railway Timetabling Instances

One of the key assumptions of timetabling algorithms is that a solution exists that meets the pre-specified constraints, like driving times, transfer constraints and headway constraints. If this assumption is satisfied, in most cases a timetable can be found rapidly. Nowadays, railways are being used more intensively, which leads to a higher utilization of the network. Due to this increased utilisation, capacity conflicts occur, so that no feasible solution to the timetabling models can be found, without making subtle but non-trivial changes to the initial input. Resolving these conflicts is essential for railway companies with high utilization of infrastructure. In this paper, we consider infeasible timetabling instances together with a list of allowed modifications of the constraints. We iteratively identify local conflicts in these instances and resolve them by adapting some of the constraints, until there are no more conflicts. The adaptations of the constraints are changes in the right-hand sides that we try to make as small as possible but that resolve the infeasibility. We empirically show that our method can be improved by enriching the initial minimal conflicts found with more constraints. In order to keep the problems tractable, an iterative procedure is used to find solutions to subproblems corresponding to conflicts in the complete timetabling instance. In a case study on instances from the Dutch railway network, we show that these instances can be made feasible within a few minutes.

Integrated Frequency Allocation and User Assignment in Multimodal Transit Networks

This paper presents an integrated solution method to the frequency-setting problem using optimization and assignment simulation. With a bilevel solution framework, an optimization problem is run at the upper level under the assumption that the total transit demand is fixed. The objective is to maximize wait time savings under the budget, fleet size, vehicle load, and policy headway constraints. At the lower level, an assignment and simulation algorithm is run; the algorithm models the demand response to the new frequency setting and transmits updated ridership and flow values to the upper level. The procedure is repeated until the improvement in the wait time savings converges. The platform is tested on the Chicago Transit Authority network in Illinois for the morning peak. The wait time savings in this experiment are converging and are found to be comparable with the results of a stand-alone frequency-setting algorithm that finds optimal solutions. Results are comparable with the optimal results of a stand-alone platform introduced in another study that modeled the demand response locally by using elasticities as opposed to networkwide modeling using assignment. The integrated platform can be used for medium-term strategic and long-term planning decisions.

An iterative optimization framework for delay management and train scheduling

Delay management determines which connections should be maintained in case of a delayed feeder train. Recent delay management models incorporate the limited capacity of the railway infrastructure. These models introduce headway constraints to make sure that safety regulations are satisfied. Unfortunately, these headway constraints cannot capture the full details of the railway infrastructure, especially within the stations. We therefore propose an optimization approach that iteratively solves a macroscopic delay management model on the one hand, and a microscopic train scheduling model on the other hand. The macroscopic model determines which connections to maintain and proposes a disposition timetable. This disposition timetable is then validated microscopically for a bottleneck station of the network, proposing a feasible schedule of railway operations. We evaluate our iterative optimization framework using real-world instances around Utrecht in the Netherlands.

The periodicity and robustness in a single-track train scheduling problem

The most important operating problem in any railway industry is to produce robust train timetables with minimum delays. The train scheduling problem is defined as an application of job shop scheduling which is considered to be one of the most interesting research topics. This paper deals with scheduling different types of trains in a single railway track. The authors have focused on the robust and periodic aspects of produced timetables. This paper is also concerned with some applicable constraints, such as the acceleration and deceleration times, station capacity and headway constraints. The periodic timetable for railways is modeled based on the periodic event scheduling problem (PESP). Furthermore, a fuzzy approach is used to reach a tradeoff among the total train delays, the robustness of schedules, and the time interval between departures of trains from the same origins. To solve large-scale problems, a meta-heuristic algorithm based on simulated annealing (SA) is utilized and validated using some numerical examples on a periodic robust train scheduling problem. Finally, a robustness measure is defined in order to assure the effectiveness of the proposed SA to find robust solutions.