Modelling and solving train scheduling problems under capacity constraints

Many large coal mining operations in Australia rely heavily on the rail network to transport coal from mines to coal terminals at ports for shipment. Over the last few years, due to the fast growing demand, the coal rail network is becoming one of the worst industrial bottlenecks in Australia. As a result, this provides great incentives for pursuing better optimisation and control strategies for the operation of the whole rail transportation system under network and terminal capacity constraints. This PhD research aims to achieve a significant efficiency improvement in a coal rail network on the basis of the development of standard modelling approaches and generic solution techniques. Generally, the train scheduling problem can be modelled as a Blocking Parallel- Machine Job-Shop Scheduling (BPMJSS) problem. In a BPMJSS model for train scheduling, trains and sections respectively are synonymous with jobs and machines and an operation is regarded as the movement/traversal of a train across a section. To begin, an improved shifting bottleneck procedure algorithm combined with metaheuristics has been developed to efficiently solve the Parallel-Machine Job- Shop Scheduling (PMJSS) problems without the blocking conditions. Due to the lack of buffer space, the real-life train scheduling should consider blocking or hold-while-wait constraints, which means that a track section cannot release and must hold a train until the next section on the routing becomes available. As a consequence, the problem has been considered as BPMJSS with the blocking conditions. To develop efficient solution techniques for BPMJSS, extensive studies on the nonclassical scheduling problems regarding the various buffer conditions (i.e. blocking, no-wait, limited-buffer, unlimited-buffer and combined-buffer) have been done. In this procedure, an alternative graph as an extension of the classical disjunctive graph is developed and specially designed for the non-classical scheduling problems such as the blocking flow-shop scheduling (BFSS), no-wait flow-shop scheduling (NWFSS), and blocking job-shop scheduling (BJSS) problems. By exploring the blocking characteristics based on the alternative graph, a new algorithm called the topological-sequence algorithm is developed for solving the non-classical scheduling problems. To indicate the preeminence of the proposed algorithm, we compare it with two known algorithms (i.e. Recursive Procedure and Directed Graph) in the literature. Moreover, we define a new type of non-classical scheduling problem, called combined-buffer flow-shop scheduling (CBFSS), which covers four extreme cases: the classical FSS (FSS) with infinite buffer, the blocking FSS (BFSS) with no buffer, the no-wait FSS (NWFSS) and the limited-buffer FSS (LBFSS). After exploring the structural properties of CBFSS, we propose an innovative constructive algorithm named the LK algorithm to construct the feasible CBFSS schedule. Detailed numerical illustrations for the various cases are presented and analysed. By adjusting only the attributes in the data input, the proposed LK algorithm is generic and enables the construction of the feasible schedules for many types of non-classical scheduling problems with different buffer constraints. Inspired by the shifting bottleneck procedure algorithm for PMJSS and characteristic analysis based on the alternative graph for non-classical scheduling problems, a new constructive algorithm called the Feasibility Satisfaction Procedure (FSP) is proposed to obtain the feasible BPMJSS solution. A real-world train scheduling case is used for illustrating and comparing the PMJSS and BPMJSS models. Some real-life applications including considering the train length, upgrading the track sections, accelerating a tardy train and changing the bottleneck sections are discussed. Furthermore, the BPMJSS model is generalised to be a No-Wait Blocking Parallel- Machine Job-Shop Scheduling (NWBPMJSS) problem for scheduling the trains with priorities, in which prioritised trains such as express passenger trains are considered simultaneously with non-prioritised trains such as freight trains. In this case, no-wait conditions, which are more restrictive constraints than blocking constraints, arise when considering the prioritised trains that should traverse continuously without any interruption or any unplanned pauses because of the high cost of waiting during travel. In comparison, non-prioritised trains are allowed to enter the next section immediately if possible or to remain in a section until the next section on the routing becomes available. Based on the FSP algorithm, a more generic algorithm called the SE algorithm is developed to solve a class of train scheduling problems in terms of different conditions in train scheduling environments. To construct the feasible train schedule, the proposed SE algorithm consists of many individual modules including the feasibility-satisfaction procedure, time-determination procedure, tune-up procedure and conflict-resolve procedure algorithms. To find a good train schedule, a two-stage hybrid heuristic algorithm called the SE-BIH algorithm is developed by combining the constructive heuristic (i.e. the SE algorithm) and the local-search heuristic (i.e. the Best-Insertion- Heuristic algorithm). To optimise the train schedule, a three-stage algorithm called the SE-BIH-TS algorithm is developed by combining the tabu search (TS) metaheuristic with the SE-BIH algorithm. Finally, a case study is performed for a complex real-world coal rail network under network and terminal capacity constraints. The computational results validate that the proposed methodology would be very promising because it can be applied as a fundamental tool for modelling and solving many real-world scheduling problems.

Obstacle-free range determination for rail track maintenance vehicles

Maintenance trains travel in convoy. In Australia, only the first train of the convoy pays attention to the track sig- nalization (the other convoy vehicles simply follow the preceding vehicle). Because of human errors, collisions can happen between the maintenance vehicles. Although an anti-collision system based on a laser distance meter is already in operation, the existing system has a limited range due to the curvature of the tracks. In this paper, we introduce an anti-collision system based on vision. The two main ideas are, (1) to warp the camera image into an image where the rails are parallel through a projective transform, and (2) to track the two rail curves simultaneously by evaluating small parallel segments. The performance of the system is demonstrated on an image dataset.

Dwell-time and run-time control for DC mass rapid transit railways

Dwell times at stations and inter-station run times are the two major operational parameters to maintain train schedule in railway service. Current practices on dwell-time and run-time control are that they are only optimal with respect to certain nominal traffic conditions, but not necessarily the current service demand. The advantages of dwell-time and run-time control on trains are therefore not fully considered. The application of a dynamic programming approach, with the aid of an event-based model, to devise an optimal set of dwell times and run times for trains under given operational constraints over a regional level is presented. Since train operation is interactive and of multi-attributes, dwell-time and run-time coordination among trains is a multi-dimensional problem. The computational demand on devising trains' instructions, a prime concern in real-time applications, is excessively high. To properly reduce the computational demand in the provision of appropriate dwell times and run times for trains, a DC railway line is divided into a number of regions and each region is controlled by a dwell- time and run-time controller. The performance and feasibility of the controller in formulating the dwell-time and run-time solutions for real-time applications are demonstrated through simulations.

Accident prediction model for railway-highway interfaces

Considerable past research has explored relationships between vehicle accidents and geometric design and operation of road sections, but relatively little research has examined factors that contribute to accidents at railway-highway crossings. Between 1998 and 2002 in Korea, about 95% of railway accidents occurred at highway-rail grade crossings, resulting in 402 accidents, of which about 20% resulted in fatalities. These statistics suggest that efforts to reduce crashes at these locations may significantly reduce crash costs. The objective of this paper is to examine factors associated with railroad crossing crashes. Various statistical models are used to examine the relationships between crossing accidents and features of crossings. The paper also compares accident models developed in the United States and the safety effects of crossing elements obtained using Korea data. Crashes were observed to increase with total traffic volume and average daily train volumes. The proximity of crossings to commercial areas and the distance of the train detector from crossings are associated with larger numbers of accidents, as is the time duration between the activation of warning signals and gates. The unique contributions of the paper are the application of the gamma probability model to deal with underdispersion and the insights obtained regarding railroad crossing related vehicle crashes. Considerable past research has explored relationships between vehicle accidents and geometric design and operation of road sections, but relatively little research has examined factors that contribute to accidents at railway-highway crossings. Between 1998 and 2002 in Korea, about 95% of railway accidents occurred at highway-rail grade crossings, resulting in 402 accidents, of which about 20% resulted in fatalities. These statistics suggest that efforts to reduce crashes at these locations may significantly reduce crash costs. The objective of this paper is to examine factors associated with railroad crossing crashes. Various statistical models are used to examine the relationships between crossing accidents and features of crossings. The paper also compares accident models developed in the United States and the safety effects of crossing elements obtained using Korea data. Crashes were observed to increase with total traffic volume and average daily train volumes. The proximity of crossings to commercial areas and the distance of the train detector from crossings are associated with larger numbers of accidents, as is the time duration between the activation of warning signals and gates. The unique contributions of the paper are the application of the gamma probability model to deal with underdispersion and the insights obtained regarding railroad crossing related vehicle crashes.

Probabilistic load flow in AC electrified railways

System analysis within the traction power system is vital to the design and operation of an electrified railway. Loads in traction power systems are often characterised by their mobility, wide range of power variations, regeneration and service dependence. In addition, the feeding systems may take different forms in AC electrified railways. Comprehensive system studies are usually carried out by computer simulation. A number of traction power simulators have been available and they allow calculation of electrical interaction among trains and deterministic solutions of the power network. In the paper, a different approach is presented to enable load-flow analysis on various feeding systems and service demands in AC railways by adopting probabilistic techniques. It is intended to provide a different viewpoint to the load condition. Simulation results are given to verify the probabilistic-load-flow models.

Peak power demand reduction under moving block signalling using an expert system

The concept of moving block signallings (MBS) has been adopted in a few mass transit railway systems. When a dense queue of trains begins to move from a complete stop, the trains can re-start in very close succession under MBS. The feeding substations nearby are likely to be overloaded and the service will inevitably be disturbed unless substations of higher power rating are used. By introducing starting time delays among the trains or limiting the trains’ acceleration rate to a certain extent, the peak energy demand can be contained. However, delay is introduced and quality of service is degraded. An expert system approach is presented to provide a supervisory tool for the operators. As the knowledge base is vital for the quality of decisions to be made, the study focuses on its formulation with a balance between delay and peak power demand.

Railway junction traffic control by heuristic methods

Traffic conflicts at railway junctions are very conmon, particularly on congested rail lines. While safe passage through the junction is well maintained by the signalling and interlocking systems, minimising the delays imposed on the trains by assigning the right-of-way sequence sensibly is a bonus to the quality of service. A deterministic method has been adopted to resolve the conflict, with the objective of minimising the total weighted delay. However, the computational demand remains significant. The applications of different heuristic methods to tackle this problem are reviewed and explored, elaborating their feasibility in various aspects and comparing their relative merits for further studies. As most heuristic methods do not guarantee a global optimum, this study focuses on the trade-off between computation time and optimality of the resolution.

Optimal traffic control at railway junctions

Conflict occurs when two or more trains approach the same junction within a specified time. Such conflicts result in delays. Current practices to assign the right of way at junctions achieve orderly and safe passage of the trains, but do not attempt to reduce the delays. A traffic controller developed in the paper assigns right of way to impose minimum total weighted delay on the trains. The traffic flow model and the optimisation technique used in this controller are described. Simulation studies of the performance of the controller are given.

Bottlenecks detection of track allocation schemes at rail stations by Petri nets

Robustness of the track allocation problem is rarely addressed in literatures and the obtained track allocation schemes (TAS) embody some bottlenecks. Therefore, an approach to detect bottlenecks is needed to support local optimization. First a TAS is transformed to an executable model by Petri nets. Then disturbances analysis is performed using the model and the indicators of the total trains' departure delays are collected to detect bottlenecks when each train suffers a disturbance. Finally, the results of the tests based on a rail hub linking six lines and a TAS about thirty minutes show that the minimum buffer time is 21 seconds and there are two bottlenecks where the buffer times are 57 and 44 seconds respectively, and it indicates that the bottlenecks do not certainly locate at the area where there is minimum buffer time. The proposed approach can further support selection of multi schemes and robustness optimization.

A fiber Bragg grating sensor system for train axle counting

Railway signaling facilitates two main functions, namely, train detection and train control, in order to maintain safe separations among the trains. Track circuits are the most commonly used train detection means with the simple open/close circuit principles; and subsequent adoption of axle counters further allows the detection of trains under adverse track conditions. However, with electrification and power electronics traction drive systems, aggravated by the electromagnetic interference in the vicinity of the signaling system, railway engineers often find unstable or even faulty operations of track circuits and axle counting systems, which inevitably jeopardizes the safe operation of trains. A new means of train detection, which is completely free from electromagnetic interference, is therefore required for the modern railway signaling system. This paper presents a novel optical fiber sensor signaling system. The sensor operation, field setup, axle detection solution set, and test results of an installation in a trial system on a busy suburban railway line are given.

Quantitative evaluation of route allocation solutions at large-scale passenger stations

Routing trains within passenger stations in major cities is a common scheduling problem for railway operation. Various studies have been undertaken to derive and formulate solutions to this route allocation problem (RAP) which is particularly evident in mainland China nowadays because of the growing traffic demand and limited station capacity. A reasonable solution must be selected from a set of available RAP solutions attained in the planning stage to facilitate station operation. The selection is however based on the experience of the operators only and objective evaluation of the solutions is rarely addressed. In order to maximise the utilisation of station capacity while maintaining service quality and allowing for service disturbance, quantitative evaluation of RAP solutions is highly desirable. In this study, quantitative evaluation of RAP solutions is proposed and it is enabled by a set of indices covering infrastructure utilisation, buffer times and delay propagation. The proposed evaluation is carried out on a number of RAP solutions at a real-life busy railway station in mainland China and the results highlight the effectiveness of the indices in pinpointing the strengths and weaknesses of the solutions. This study provides the necessary platform to improve the RAP solution in planning and to allow train re-routing upon service disturbances.

The conflict resolution in connected railway junctions

Purpose of study: Traffic conflicts occur when trains on different routes approach a converging junction in a railway network at the same time. To prevent collisions, a right-of-way assignment is needed to control the order in which the trains should pass the junction. Such control action inevitably requires the braking and/or stopping of trains, which lengthens their travelling times and leads to delays. Train delays cause a loss of punctuality and hence directly affect the quality of service. It is therefore important to minimise the delays by devising a suitable right-of-way assignment. One of the major difficulties in attaining the optimal right-of-way assignment is that the number of feasible assignments increases dramatically with the number of trains. Connected-junctions further complicate the problem. Exhaustive search for the optimal solution is time-consuming and infeasible for area control (multi-junction). Even with the more intelligent deterministic optimisation method revealed in [1], the computation demand is still considerable, which hinders real-time control. In practice, as suggested in [2], the optimality may be traded off by shorter computation time, and heuristic searches provide alternatives for this optimisation problem.