A new rail optimisation model by integration of traffic management and train automation

Transportation Research Part C 71 (2016) 382–405

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Transportation Research Part C journal homepage: www.elsevier.com/locate/trc

A new rail optimisation model by integration of traffic management and train automation q Xiaolu Rao Ph.D. a,⇑, Markus Montigel Ph.D. a, Ulrich Weidmann Ph.D. b a b

Systransis Ltd., Switzerland Institute for Transport Planning and Systems, ETH Zurich, Switzerland

a r t i c l e

i n f o

Article history: Received 11 January 2016 Received in revised form 11 August 2016 Accepted 21 August 2016

Keywords: Traffic management Train automation Integration Decision-making Optimisation

a b s t r a c t This paper reviews and classifies the traffic optimisation schemes of current mainline railway into two groups. One is to improve the efficiency of traffic management by providing resolutions for traffic conflicts, while the other is to improve trains’ driving behaviour by providing driver assistance or introducing train automation. Based on a comparison of these two groups, this paper proposes to combine the functions of traffic management and train automation into an integrated optimisation model. This model includes the following contributions. First, in the function of traffic management, this paper explores the flexibility in generating different train running trajectories to prevent potential traffic conflicts. The trajectory can improve traffic flow by avoiding unplanned train stops. This is regarded as a supplementary conflict resolution to train reordering or rerouting or retiming. Second, this paper defines a series of train control commands to determine different intensities of the train’s tractive force and braking force. These commands are seen as the key to train automation. Moreover, a decision-making procedure is introduced to select the most attractive train running trajectory or train control command according to different optimisation objectives. Lastly, this paper proves the importance of bidirectional communication between traffic management and train automation based on a case study. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction The current process of manual rail operation is based on a superimposition of two closed control loops (Lüthi et al., 2007), as shown in Fig. 1. The outer control loop supervises the status of traffic and infrastructure, detects deviations and conflicts, develops a new schedule (rescheduling) and transmits it to train operation. This rescheduling mainly depends on the expertise of the dispatcher. The inner control loop is responsible for executing the production plan, which depends on the expertise of the driver. In this paper, the manual operation is termed non-optimised railway operation. Currently, the focus of railway optimisation is either on improving efficiency for the dispatcher in the outer control loop or on improving driving performance for the driver in the inner control loop. Traffic management can resolve traffic conflicts by using centralised train data in its controlled network, but it can neither avoid the inaccuracy of conflict detection due to incomplete train data and untimely data transmission, nor guarantee that each train will execute the conflict resolution as accurately as expected.

q

This article belongs to the Virtual Special Issue on: Integer Rail Optimization.

⇑ Corresponding author.

E-mail addresses: [email protected], [email protected] (X. Rao). http://dx.doi.org/10.1016/j.trc.2016.08.011 0968-090X/Ó 2016 Elsevier Ltd. All rights reserved.

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Fig. 1. Non-optimised railway operation depending on the expertise of the dispatcher and the driver.

Train automation has the most complete and updated train data to minimise the deviation between control targets and the supervised train states, but it depends on two supports. One is an additional onboard support to provide train’s overspeed protection and to keep a safe headway between trains, such as the Automatic Train Protection (ATP) system. The other is infrastructure support to provide dynamic traffic regulation to avoid traffic conflicts, such as the Automatic Train Supervision (ATS) system used in metro railway. Since the mainline railway has much more complicated infrastructure situations, currently train automation is mainly applied in metro railway. Therefore, for the mainline railway, this paper aims to provide an integrated optimisation model to combine the strength of traffic management and train automation. An initial concept of this model is illustrated in Fig. 2, which highlights bidirectional communication between traffic management and train automation. This paper endeavours to complete the design of this integrated optimisation model. First, this paper reviews and classifies different optimisation schemes in Section 2. Based on the comparison of different optimisation schemes, this paper points out that the optimisation methods of traffic management and train automation are complementary. Section 3 proposes an integrated optimisation model and introduces the key in the functions of traffic management and train automation. Further, Section 4 shares an important finding that the bidirectional communication between traffic management and train automation is necessary. Lastly, Section 5 makes conclusions and describes remaining questions for future studies. 2. Review and classification of railway optimisation schemes 2.1. Optimisation schemes in traffic management 2.1.1. Principle Traffic Management System (TMS) comprises all functions necessary for enabling trains to run safely and efficiently on the railway infrastructure (Lochman, 2009). With the growing demand for transportation, more trains are expected to be in service. This could increase traffic conflicts and harm train service quality. It is a challenge for mainline railway to increase rail capacity and improve service quality at the same time. A more functional TMS is required to reduce the impact of traffic conflicts by applying different real-time automatic solutions. This paper classifies these solutions into two categories. The first is to reschedule the traffic when the current timetable is detected with a conflict, which means two or more trains request the same infrastructure resource at the same time. The solution is to find a new conflict-free schedule by train reordering, rerouting or retiming. The second, one focus of this paper, is to optimise train speed when the train is predicted

Fig. 2. A basic concept of the integrated optimisation model proposed in this paper.

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Fig. 3. Optimisation with the Decision Support System (DSS) for dispatchers.

to have unplanned stops. In this case, the train might have a delay at its destination and a conflict might happen in current schedule. The solution is to generate train running trajectories (train position-speed-time diagrams) to avoid unplanned stops. This paper refers to the former as Decision Support System (DSS) while the latter as Driver Advisory System - Central (DAS-C). 2.1.2. Decision Support System (DSS) for dispatchers DSS, which is prevalent today and shown in Fig. 3, focuses on resolving traffic conflicts by generating control advices (train reordering and rerouting or retiming) to the dispatcher. An extensive literature is available on models and algorithms for DSS. A general overview on real-time rescheduling can be found in D’Ariano et al. (2014). According to the level of detail used to represent the infrastructure, DSS can be distinguished between macroscopic and microscopic models. The former focuses on the events associated with stations but neglecting the details of tracks, switches, signalling systems. Related research of real-time train rescheduling based on the macroscopic model can be found in Acuna-Agost et al. (2011a,b), Kumazawa et al. (2008), Törnquist and Persson (2005, 2007) and Törnquist (2012). The microscopic model instead considers more detailed information on each track, switch and signal. It is a trend to use microscopic models for DSS. Related research can be found in D’Ariano et al. (2008), Corman et al. (2010), Caimi et al. (2011), Lamorgese and Mannino (2015), Mannino (2011), Pellegrini et al. (2014), Flamini and Pacciarelli (2008) and so on. The latest research from Kersbergen et al. (2016) proposes several Distributed Model Predictive Control (DMPC) methods to solve railway management problem for entire (national) railway networks. Meng and Zhou (2014) and Meng et al. (2015) introduce a cumulative flow variables-based integer programming model for dispatching trains under a stochastic environment on a general railway network. Corman et al. (2016) merges the microscopic models of train scheduling and the macroscopic models of delay management by developing microscopic passenger-centric models, solution algorithms and lower bounds. Yin et al. (2016) implements an approximate dynamic programming approach for metro train rescheduling problem. The practical implementation of DSS can be found in Milan metro station, where its DSS uses the branch and bound method to identify suitable routing and establish an optimum schedule (Mannino and Mascis, 2009). DSS is also applied to the regional lines in Italy with (sub) optimal solutions, which uses the Mixed Integer Linear Programs (MILP) method and decomposes the rescheduling problem into master problem associated with the line and the slave problem associated with the stations (Lamorgese and Mannino, 2015). 2.1.3. Driver Advisory System - Central (DAS-C) DAS-C, as shown in Fig. 4, is another solution to reduce the impact of traffic conflicts by generating train speed advice for the driver. DAS-C computes the optimal train running trajectory to avoid the predicted unplanned train stops. Based on the trajectory, a series of train speed advice is generated and sent to the train. The speed advice can inform the driver to reduce

Fig. 4. Optimisation with the Driver Advisory System - Central (DAS-C).

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train speed in anticipation of the conflict detected ahead, and to increase train speed in anticipation of the conflict resolved. Therefore, the driver’s knowledge of traffic conflict is extended to avoid predicted unplanned train stops by optimising train speed. It is noted that the unplanned train stops can be discovered earlier than train delays at destinations or trains’ routes conflict at some block sections. This provides us possibilities to resolve potential traffic conflicts without changing current schedule, but to resolve potential traffic conflicts by optimising train speed. So far, DAS-C has often been seen as supplementary to DSS but not a substitute for it. A practical example of DAS-C is the commercial product Automatic Function (AF) applied in the Lötschberg Base Tunnel in Switzerland. This application increases capacity and saves energy costs (Mehta et al., 2010). To our knowledge, this is the first practical application of DAS-C in a mixed-traffic mainline railway. Related introduction can be found in Montigel (2009), Lüthi et al. (2007), and Rao et al. (2013a,c). Based on the experience from the DAS-C in Lötschberg Base Tunnel, this paper improves the computation of the optimal train running trajectory, which will be introduced in Section 3.2. 2.2. Optimisation schemes in train automation 2.2.1. Principle Train automation is applied to reduce the loss of capacity due to manual train operation. The basic functions of train automation include automatic train speed control (accelerating, braking, cruising and coasting), precise train parking and door control. The International Association of Public Transport (UITP) defines the Grades of Automation (GoA) depending on the distribution of responsibilities between the staff and the train automation system itself. The five GoAs are summarised in Table 1. However, it seems that those definitions tend to fit better for metro railway, but less so for mainline railway, where train drivers can be supported by Driver Advisory System (DAS). DAS is actually an automation level between GoA 1 and GoA 2. It provides drivers with additional driving advice to keep the train at the optimum speed. Apart from the DAS-C scheme in traffic management (Section 2.1.3), Driver Advisory System - On-board (DAS-O) is a similar scheme but installed onboard. Automatic Train Operation (ATO) is another optimisation scheme onboard including GoA 2, GoA 3 and GoA 4, which controls train speed automatically. 2.2.2. Driver Advisory System - Onboard (DAS-O) DAS-O, as illustrated in Fig. 5, is an alternative approach to generate train speed advice for the driver. DAS-O which is installed on the train concentrates on improving train driving behaviour rather than resolving traffic conflicts. DAS-O has a predefined train speed profile, which is a standard driving guidance for riding accuracy, riding comfort, energy saving and other onboard optimisation goals. DAS-O can generate a series of speed advice to minimise the deviation between the predefined train speed profile and the observed train states (train position, speed and time).

Table 1 Grades of Automation (UITP, 2011). Grade of automation GoA GoA GoA GoA GoA

0 1 2 3 4

Type of train operation

Train speed control

Train stopping

Train door control

Operation in event of disruption

On-sight by driver ATP with driver STO DTO UTO

Driver Driver Automatic Automatic Automatic

Driver Driver Automatic Automatic Automatic

Driver Driver Driver Train attendant Automatic

Driver Driver Driver Train attendant Automatic

ATP: Automatic Train Protection, DTO: Driverless Train Operation, STO: Semi-automatic Train Operation, UTO: Unattended Train Operation.

Fig. 5. Optimisation with Driver Advisory System - Onboard (DAS-O).

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DAS-O is often used as a complement to the driver training system for practising and improving driving skills. Currently, most existing DAS belong to DAS-O with the focus on energy-efficient driving, such as Computer Aided Train Operation (CATO) system in Sweden (Yang et al., 2013), InLineFAS in Germany (Albrecht and Dasigi, 2014) and GreenSpeed in Denmark (Bergendorff et al., 2012). In short, DAS-O can be seen as an interim step to achieve ATO. 2.2.3. Automatic Train Operation (ATO) ATO, as illustrated in Fig. 6, generates a series of train control commands to adjust train speed directly, rather than the speed advice for the driver. The train control command can decide how much train force (tractive and braking force) is inserted. Moreover, ATO has to resolve the Multi-objective Optimisation Problems (MOPs) with two or more (often conflicting) objectives. This can be achieved with various intelligent control algorithms, such as fuzzy logic control, expert control, predictive control, neural network control, genetic algorithm, differential evolutionary algorithm and integrated intelligent methods (Rao et al., 2012). A general evolutionary algorithm review for MOPs can be found in Coello (2006). Mattson et al. (2004) proposes using a smart Pareto filter to control the size of the optimal set and the degree of trade-off representation among objectives. Shapiro (1996) considers the MOPs where the objective function is not given explicitly and should be estimated by simulation. Currently, there are two branches of ATO methods to resolve MOPs. The first generates train speed profiles as the set of optimal solutions for MOPs, which can be found in Domínguez et al. (2014, 2011), and Wang et al. (2013, 2011). ATO generates train control commands to minimise the deviation between this optimal train speed profile and actual train states. The second generates train control commands as the set of optimal solutions for MOPs. This method takes the train speed profile as one of the optimisation factors to be considered and it evaluates the influence of different train control commands on multiple optimisation objectives. Related research can be found in Miyamoto et al. (1987), Oshima et al. (1988), Chang and Xu (2000), Yasunobu et al. (2002), Liu and Golovitcher (2003), and Rao et al. (2012, 2013b). This paper seeks to extend the second method, which will be discussed in Section 3.3. When the set of optimal solutions to MOPs is generated, the next is to select the most attractive solution from this set as the final output to control the train. ATO is applied in almost every metro system. ATO is not just eye-catching technology to urban residents, but it is a necessity for efficient metro operation. Metro railways have a frequent stop-and-go operation mode. The introduction of ATO has reduced the burden of train drivers with repeated operation (train start, accelerating, cruising, coasting and braking) and it has helped to avoid manual errors. Some metro stations have equipped the platform screen doors, which can be seen as one main challenge for train drivers but it is easier for ATO to achieve a precise train stopping. Compared to the mainline railway, metro railways have a much simpler timetable design and infrastructure topology. In many cases each metro line is independent of other lines and the trains of metro lines are very homogeneous sets of vehicles. In most cases, there is little influence on the braking capabilities of trains by the weather and the danger of obstacles on the track is considered much lower than on an open line. ATO has not been applied in the mainline railway primarily for several reasons. First, there are two safety concerns. One is to detect obstacles on the track. Another is to detect passenger safety while exiting and entering trains. Most mainline railways are open lines and their stations are not equipped with the platform screen doors. Therefore, additional solutions are required for these two safety concerns. Moreover, the mainline railway has a much more complicated situation than metro railway, because it varies in infrastructure topology, signalling system, locomotive types, timetable and many other aspects. Therefore, it is necessary that the ATO for mainline railway is adaptable for different conditions. 2.3. Comparison of optimisation schemes In order to better distinguish these schemes, Table 2 compares their features in several aspects:

Fig. 6. Optimisation with the Automatic Train Operation (ATO).

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387

Table 2 Comparison of railway optimisation schemes.


Current application domains – The non-optimised operation is widely applied in today’s railway, of which the efficiency and service quality depend largely on the expertise of dispatchers and drivers. – DSS has been used prevalently to prevent and resolve traffic conflict, particularly in dense traffic lines. It supports the dispatcher’s work by generating advice on train reordering, rerouting and retiming. – DAS-C provides additional method to prevent potential traffic conflict (unplanned stops) by adjusting train speed and generating advice to the driver. So far, DAS-C has been a supplementary function to DSS. – DAS-O focuses on improving the driver’s manual operation in accordance with the pre-defined train speed profile. However, the pre-defined train speed profile is usually not adaptable to the real-time situation of the traffic network. – ATO has adequate onboard computing power to deal with a large amount of train dynamic calculation. By replacing the driver’s operation, ATO can achieve an accurate train operation in accordance with the pre-defined train speed profile. ATO is often applied in a frequent stop-and-go operation (such as in metro railway), which relieves the driver of many functions and delivers a high accuracy in achieving multiple optimisation objectives.
Scope and installation entity – DSS and DAS-C are installed in the traffic management centre so that they can prevent traffic conflict by analysing the traffic network data. However, DSS and DAS-C offer no improvement for onboard functionality that all trains’ dynamic calculations are carried out in the traffic management centre. When the conflict case grows to a certain extent, there will be a concern about whether traffic management centre can handle such a heavy computing workload. Additionally, the computation of DSS and DAS-C is based on the transmitted data in the outer control loop. In this regard, another concern is about whether the transmitted data is complete, accurate and updated in real-time. Therefore, the lack of advanced onboard functionality and the quality of transmitted data are seen to be the main obstacles for the further development of traffic management. – DAS-O and ATO are installed in each train with enhanced onboard functionality. Each train carries on with its own dynamic calculation. The train states are measured and transmitted in real-time in the inner control loop. Therefore, the increased onboard computing power and the improved quality of data transmission are seen as the advantages of DAS-O and ATO. However, DAS-O and ATO cannot avoid unplanned train stops that they need external support for traffic conflict prediction. The comparison result shows that the optimisation schemes applied in traffic management (DSS and DAS-C) and train automation (DAS-O and ATO) are complementary. This paper endeavours to integrate their optimisation advantages into a new optimisation model. This model is expected to have bidirectional communication between traffic management and train automation. Trains can avoid potential traffic conflicts by reacting to the proposals from traffic management, while traffic management can improve its calculation according to the real-time feedback from train automation.

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3. The proposed integrated optimisation model 3.1. Overview Based on the review of different optimisation schemes, this paper proposes combining four optimisation schemes (DSS, DAS-C, DAS-O and ATO) into one, as an integrated optimisation model (Fig. 7). Inspired by the proposed railway network decomposition from Caimi (2014), this paper suggests that DSS is mainly applied in condensation zones (i.e. with high traffic density) to deal with major disruptions, while DAS-C is mostly applied in compensation zones (i.e. with low traffic density) to prevent potential traffic conflicts at an earlier phase. In compensation zones, the choice of appropriate trains’ speed profiles is the most important degree of freedom to be exploited (Caimi, 2014). Therefore, this paper will pay particular attention to DAS-C, which explores the flexibility in generating different train running trajectories to prevent potential traffic conflicts. Based on the trajectory, a series of control-target points (position, time and speed) can be generated as discrete information sent to the train in real-time, rather than sending a complete train running trajectory or sending only train speed advice. The choice of DAS-O or ATO depends on the practical requirements of GoA (Section 2.2.1). The core function, optimised train speed control, is the same for both DAS-O and ATO. The deviation between the received control-target points and the observed train states is calculated onboard. According to the deviation, DAS-O can generate corresponding advice for the driver (either train speed advice or additional train control command advice), while ATO can implement train control commands directly to adjust train speed automatically. Since the generation of trains’ control commands and the choice of appropriate commands have not been fully discussed, this paper seeks to make progress in this subject as well. 3.2. The computation of train running trajectory to avoid unplanned train stops 3.2.1. Preparation to compute train running trajectory: distinguish crossing conflict and follow-up conflict Since the strategies of generating train running trajectory vary from case to case, it is necessary to distinguish the conflict types between two trains at first. The conflict detection module is in charge of identifying which train is predicted to have an unplanned stop, where and when this unplanned train stop is predicted to happen, where and when this unplanned train stop is predicted to be resolved. Based on the prediction information, this paper distinguishes two types of traffic conflicts: crossing conflict and follow-up conflict. As illustrated in Fig. 8, the key to distinguishing these two types is whether the conflict start block section equals the conflict end block section. Each block section (track or switch) can only be reserved or occupied by one train. The first train (slower or delayed) is the one causing the potential conflict, and the second train (faster) is the one affected by it. Therefore, the second train is the one to receive optimisation instructions.
In the crossing conflict, two trains move in different directions and the conflict start block equals the conflict end block. The second train is predicted to have an unplanned stop in front of the signal 60 V at mileage 59950. In cases whereby the first train is faster than the second train, no further conflict may occur.
In the follow-up conflict, two trains move in the same directions on single tracks, but the conflict start block differs from the conflict end block. The second train is predicted to have an unplanned stop in front of the conflict start block and several unplanned stops between the conflict start block and the conflict end block. In cases whereby the first train is faster than the second train, there might be only one conflict occurring in the conflict start block, which will be treated as the crossing conflict case. 3.2.2. Key to computing train running trajectory: main-target point 3.2.2.1. The definition of main-target point. The key to computing the trajectory is to identify the main-target point, which consists of three-dimensional information: target position, target speed and target time. As long as the train affected by

Fig. 7. The integrated optimisation model combining optimisation schemes of DSS, DAS-C, DAS-O and ATO.

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Fig. 8. Examples of the crossing conflict and the follow-up conflict based on the double vertex graph.

the conflict can achieve the main-target point, this train can avoid unplanned stops in the most efficient way by using the minimum travel time. Subsequent subsections will introduce the calculation of main-target point to resolve the crossing conflict and the follow-up conflict separately. 3.2.2.2. Compute the main-target point to resolve the crossing conflict. In the crossing conflict, the main-target is determined by the estimated non-optimised trajectory and the estimated conflict resolution time. As shown in Fig. 9, the non-optimised trajectory is the red-dashed1 line, which assumes that there is no conflict prediction or conflict resolution provided. The non-optimised trajectory consists of four phases: 1. The train affected by the crossing conflict, travels with its normal train speed until it hits the braking curve according to the End of Movement Authority (EoA) position in front of the conflict block. 2. Braking to standstill at the EoA position in front of the conflict block. 3. Standstill until the train receives a new EoA to proceed over the conflict block. 4. Accelerating to the target speed.

1

For interpretation of color in Figs. 9, 10, and 17, the reader is referred to the web version of this article.

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Fig. 9. The computation of train running trajectory for preventing the crossing conflict.

The model used for calculating these phases (except for the standstill phase) is based on the standard train dynamics model contained in Hürlimann (2001). The standstill time relates to the estimation of the conflict resolution time (see Eq. (1)), which depends on the prediction of the first train (causing the conflict). If the train receives a new EoA before it brakes to standstill, then the phase of standstill is not required.

tconfResol ¼

jpconf  pcur j

v cur

þ t cur þ tadd ;

ð1Þ

where tconfResol pconf pcur tcur

v cur tadd

is is is is is is

the the the the the the

estimated conflict resolution time, exit position of the conflict start/end block, current position of the first train causing the conflict, current time, current speed of the first train causing the conflict, estimated additional time for reservation, signal switching and track clearing.

Fig. 9 illustrates an example of optimised trajectory (solid-green line) according to the main-target point. As shown in Eq. (2), the main-target position (ptar ) is the braking enter position of Service Brake Intervention (SBI) (Patrick, 2011) in the nonoptimised trajectory, the main-target time (t tar ) is the estimated conflict resolution time (it estimates when the train causing the conflict will release the conflict block), and the main-target speed (v tar ) is the maximum permitted speed at the maintarget position (ptar ):

8 > < ptar ¼ pbsp ¼ peoa  DSnonOpBr Main-targetcc ¼ v tar ¼ maxfv ðpbsp Þg ; > : t tar ¼ tconfResol

where Main-targetcc ptar

is the main-target point of the crossing conflict, is the main-target position,

ð2Þ

X. Rao et al. / Transportation Research Part C 71 (2016) 382–405

pbsp peoa DSnonOpBr

is is is is is is is

v tar

maxfv ðpbsp Þg t tar t confResol

the the the the the the the

391

braking start position of SBI, EoA position in front of the conflict block, braking distance in the non-optimised trajectory between pbsp and peoa , main-target speed, maximum permitted train speed at pbsp , main-target time, estimated conflict resolution time (see Eq. (1)).

3.2.2.3. Compute the main-target point to resolve the follow-up conflict. In the follow-up conflict (Fig. 10), its main-target point is determined by the estimated travel time of the first train causing the conflict and the safety restriction of the second train affected by the conflict. Since the conflict start block and the conflict end block are different, there are two different estimated conflict resolution time. The first is the estimated conflict resolution time for releasing the conflict start block (Eq. (3)), the second is the time for releasing the conflict end block (Eq. (4)).

tconfResolstart ¼ tconfResolend ¼

jpconfstart  pcur j

v cur

jpconfend  pcur j

v cur

þ tcur þ t add ;

þ tcur þ t add ;

ð3Þ

ð4Þ

where t confResolstart pconfstart t confResolend pconfend pcur t cur

is is is is is is is is

v cur t add

the the the the the the the the

estimated conflict resolution time for the conflict start block, exit location of the conflict start block, estimated conflict resolution time for the conflict end block, exit location of the conflict end block, current position of the first train causing the conflict, current time, current speed of the first train causing the conflict, estimated additional time for reservation, signal switching and track clearing.

The trajectory of the first train causing the conflict is represented by a red dashed line in Fig. 10. Based on this trajectory, the safety restriction is determined by considering the EoA position of the second train affected by the conflict, and the minimum headway distance between two trains.

8 ptrain2nd 6 peoa ; if ptrain1st < pconfstart ; > > >

t train2nd ðpconfstart Þ P t confResolstart > > : t train2nd ðpconfend Þ P tconfResolend

ð5Þ

where Resfc ptrain1st ptrain2nd peoa Hdis t train2nd ðpÞ pconfstart pconfend t confResolstart t confResolend

is is is is is is is is is is

the estimated safety restriction in the follow-up conflict, the position of the first train causing the conflict, the position of the second train affected by the conflict, the position of the EoA for the second train affected by the conflict before the conflict start block, headway between two trains in distance, the time of the second train affected by the conflict at the location of p, the exit position of the conflict start block, the exit position of the conflict end block, the estimated conflict resolution time for the conflict start block, the estimated conflict resolution time for the conflict end block.

Using the estimated conflict resolution time and the safety restriction, Eq. (6) describes the objective function of the main-target point in dealing with the follow-up conflict. The main-target position (ptar ) is the position of EoA to the conflict end block, the main-target time (ttar ) is the estimated conflict resolution time at the conflict end block and the main-target speed (v tar ) is the maximum permitted speed at the main-target position (ptar ).

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Fig. 10. The computation of train running trajectory for preventing the follow-up conflict.

8 0 > < ptar ¼ pconfend  minfHdis g; Main-targetfc ¼ v tar ¼ maxfv ðptar Þg; > : t tar ¼ tconfResolend ;

ð6Þ

where Main-targetfc ptar p0confend Hdis

v tar

maxfv ðptar Þg ttar tconfResolend

is is is is is is is is

the the the the the the the the

main-target point of the follow-up conflict, main-target position, enter position of the conflict end block, headway in distance, main-target speed, maximum permitted speed at the main-target position, main-target time, estimated conflict resolution time for the conflict end block.

3.2.3. The flexibility of train running trajectory: sub-target points To achieve the main-target point, the trajectory can be formed with different sub-target points. The sub-target consists of different driving phases (accelerating, braking, cruising and coasting). Therefore, they can be seen as the changing points of the driving phases. A different combination of these sub-target points provides flexibility in resolving traffic conflicts. The sub-targets contain four dimensional information: sub-target distance Dsi , sub-target speed v i , sub-target time Dt i , and sub-target acceleration/deceleration ai . There are n sub-target points approaching the same main-target point. Each subtarget point is restricted by the main-target point of the crossing conflict or the follow-up conflict (Section 3.2.2). In general, the restriction for calculating sub-target points is shown in Eq. (7).

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8 Pn 0 > i¼1 Dsi ¼ jptar  pcur j > > < P n Dt ¼ t  t 0 tar i cur i¼1 ¼ ; > v n ¼ v tar ¼ maxfv ðptar Þg > > : Resfc

Sub-targets resc=fc

393

ð7Þ

where Sub-targets resc=fc Dsi Dti

is is is is is is is is is is is

vn

ptar p0cur t tar t 0cur

v tar

maxfv ðptar Þg Resfc

the the the the the the the the the the the

restriction for calculating these sub-targets in the crossing conflict or the follow-up conflict, distance of sub-target phase i, time period of sub-target phase i, target speed of last sub-target phase, main-target position, current position of the second train affected by the conflict, main-target time, which is the estimation of conflict resolution time, current time of the second train affected by the conflict, main-target speed, maximum permitted speed at the main-target position, safety restriction for the follow-up conflict (Eq. (5)).

For a better understanding of Eq. (7), we use the crossing conflict example (Fig. 9) to explain the calculation of sub-targets. In this example, the optimised trajectory consists of three phases (decelerating, cruising and accelerating) with two unknown variables v 1 and t2 marked in red colour, which can be resolved according to the sub-targets restriction, as shown in Eqs. (8)–(10).

ð8Þ

ð9Þ

) Resolv e :



v1 Dt 2

8 > < Ds1 ; v 1 ; Dt1 ; a1 ) Sub-targets ¼ Ds2 ; v 2 ; Dt2 ; a2 ; > : Ds3 ; v 3 ; Dt3 ; a3

ð10Þ

where

vi v i1 v 0cur ai

is is is is

the ending speed of sub-target phase i, the starting speed of sub-target phase i, current speed of the train affected by conflict (second train), the acceleration/deceleration of sub-target phase i.

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To reduce the workload of train dynamics calculation in traffic management, it is important to note that each sub-target phase i is assigned an assumed and constant acceleration/deceleration ai . In addition, the coasting phase is excluded in this calculation in order to reduce the computation workload as well, but it is included in a more detailed train dynamics calculation by train automation (Section 3.3). Moreover, there are only two restriction equations (see Eq. (7)) for the sum of subtarget distances (Dsi ) and the sum of sub-target time (Dt i ). Therefore, only two variables can be resolved according to these two equations. If the sub-targets consist of more than three driving phases, there will be more than two variables. In this regard, we have to assume values for those additional variables. 3.2.4. Candidates of trajectories pending evaluation There are various combinations of sub-targets, which approach the same main-target. This variation can be caused by different assumed acceleration/deceleration (ai ) in each sub-target phase or different amount of sub-target phases. Therefore, there are a number of trajectories as candidates for conflict prevention pending evaluation. Fig. 11 provides an example of these candidates through a speed-distance-time diagram. The latter four examples consume the same travel time but adjust the train speed differently leading to varying energy consumption or other traffic optimisation intentions.
Example(a) represents a non-optimised case, in which the train has to stop and wait until the conflict ahead is resolved.
Example(b) assumes that the optimised case can maintain a higher constant speed due to maximum deceleration and acceleration.
Example(c) assumes less deceleration, which leads to lower constant speed compared to Example(b).
Example(d) assumes four driving phases: constant high-speed driving, braking, constant low-speed driving and accelerating.
Example(e) assumes four driving phases but it takes braking first and keeps maximum allowed speed as the last driving phase. There is no final decision regarding which train running trajectory is the best for resolving the conflict, unless the following decision-making procedure is accomplished (Section 3.2.5). 3.2.5. Decision-making procedure to decide the best trajectory 3.2.5.1. Overview. The decision-making procedure is illustrated in Fig. 12. There are three more steps required to be carried out, as highlighted in Fig. 12. The first step is to predict and evaluate the influence of these trajectories on optimisation objectives (e.g. capacity lc; trajectory i and energy saving le; trajectory i ). The second step is to compute the weights of optimisation

Fig. 11. Examples of different train running trajectories to resolve conflict by using the same travel time.

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395

Fig. 12. Decision-making procedure to decide the best trajectory.

objectives (e.g. weight of capacity wc and weight of energy saving we ). The last step is to synthesise judgements of overall priorities and combine them to select the trajectory with the best evaluation result. 3.2.5.2. Influence of train running trajectory on capacity: lc; trajectory i . UIC (2004) proposed a 4-quadrant capacity model, consisting of four parameters: number of trains, average speed, heterogeneity and stability. Later, Rao et al. (2015) improved the UIC 4-quadrant capacity model making it a quantified and normalised model. This model indicates that the improvement in train speed, heterogeneity or stability could increase the possibility with more trains in service. Therefore, this paper provides two normalised models to evaluate the influence of train running trajectory on capacity. The first model considers stability, which represents the time needed to resolve conflict. As shown in Eq. (11), we calculate the rate of non-used track occupation time for each trajectory. This rate of non-used track occupation time determines the influence on rail network’s stability, thereby representing the influence of this trajectory on capacity, as symboled lc; trajectory i .

lc; trajectory i ¼ 1  OccRatei ¼ 1 

ttrav ellingi ; t period

ð11Þ

where t trav elling i t period OccRatei

is train’s travelling time spent in the train running trajectory i, is the time period (such as one hour), is the occupied time rate of the train running trajectory i.

However, the main-target point has guaranteed a minimum of travel time for the train to recover from the conflict, which means that each candidate trajectory consumes the same (minimum) travelling time. Therefore, this paper also suggests using another method, the evaluation of train speed, to represent the influence on capacity. As shown in Eq. (12), it normalises the deviation between the average speed in sub-targets and the optimal speed regarding minimum headway. When the target speed is close to the optimal speed, there is less headway time required and more potential to increase capacity.

lc; trajectory i ¼ 1 

jvi  v optimal j

v max

;

ð12Þ

where

vi v optimal v max

is average speed of sub-targets in train running trajectory i, is the optimal speed regarding the minimum headway of track section (Rao et al., 2015), is the maximum permitted speed.

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The value lc; trajectory i approaching 1 means that the selected trajectory can achieve a better stability or less headway time, which represents more potential to increase capacity.

3.2.5.3. Influence of train running trajectory on energy saving: le; trajectory i . The influence on energy saving could be evaluated by computing the energy consumption over the tractive force on each sub-target phase. The train running trajectory consists of n sub-target phases. As shown in Eq. (13), the overall energy consumption (Etraction; phases ) is calculated over the tractive force (F T; subTarget i ) on each sub-target phase i. The proposed normalised model for evaluating the energy saving for each trajectory is described in Eq. (14).

Etraction; phases ¼

n n n X X X F T; subTarget i  DssubTarget i ¼ aT; subTarget i  M  DsT; subTarget i þ RC; subTarget i  DsC; subTarget i ; i¼1

i¼1

le; trajectory i ¼ 1 

ð13Þ

i¼1

Etraction; phases Etraction; phases P ¼1 ; Emax; trajectory amax accel  M  ni¼1 DssubTarget i

ð14Þ

where Etraction; phases F T; subTarget i DssubTarget i aT; subTarget i M DsT; subTarget i RC; subTarget i > 0 DsC; subTarget i Emax; trajectory amax accel

is is is is is is is is is is

the the the the the the the the the the

sum of tractive energy consumption in all sub-target phases, tractive force in sub-target phase i, distance of sub-target phase i, tractive acceleration in sub-target phase i, total mass of the train, distance of sub-target phase i when it is the accelerating phase, total resistance in the cruising phase i, distance of sub-target phase i when it is in the cruising phase, maximum tractive energy consumption of the train running trajectory, theoretical maximum tractive acceleration of the train.

The value le; trajectory i approaching 1 means that the selected trajectory leads to better energy saving as it has less energy consumption in traction. The regenerative energy consumption is excluded due to the lack of train dynamics information in traffic management, but it is included when evaluating the influence of the train control command on energy saving (see Section 3.3). 3.2.5.4. Decide the best train running trajectory. The last step is to compute the overall priority for each trajectory by using the weights (wc and we ) and the evaluation of optimisation objectives (lc; trajectory i and le; trajectory i ). The calculation of weights is based on the Analytical Hierarchy Process (AHP) method, which can be found in Rao (2015). The best trajectory is the one with the highest priority value, as described in Eq. (15). Therefore, the decision-making procedure is established and the best trajectory is transmitted from traffic management to train operation.

If Pj ¼ max P i ; ¼ max flc; i¼1;...;n

i¼1;...;n

trajectory i

 wc þ le;

trajectory i

 we g;

! the traffic trajectory j is therefore decided as the best strategy to prevent unplanned train stops:

ð15Þ

3.3. The implementation of optimised train running trajectories: train automation 3.3.1. Key of train automation: train control commands When a train running trajectory is decided as the strategy to prevent potential traffic conflict, its main-target point and sub-target points will be transmitted as control targets from traffic management to train automation. The major goal of train automation is to achieve an accurate operation by minimising the deviation between those received targets and the supervised train states. It is crucial for train automation to generate a series of train control commands, which will determine the intensities of the train’s tractive force and braking force (as described in Table 3). Not only for improving the precision of train operation, these commands can also support energy saving, riding comfort and other onboard optimisation objectives. These commands can be implemented directly by ATO or they can be sent as advisory information to the train driver through DAS-O. There are three modes in braking: regenerative braking, dissipative braking, and a combination of the previous two. This paper assumes that using dissipative-braking-only mode is a bad practice when the regenerative braking capabilities of the train engine hasn’t been exploited. Therefore, this paper assumes that train drivers adopt the dissipative braking just when the imposed deceleration exceeds the regenerative capabilities of the engine. If the train has no regenerative braking

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X. Rao et al. / Transportation Research Part C 71 (2016) 382–405 Table 3 List of train control commands. Control phase

Name of train control commands

Control intensity of the tractive force: uT; i

Control intensity of the regenerative braking force: uB; i

Control intensity of the dissipative braking force: uM; i

Coasting phase Tractive phase Regenerative braking phase Dissipative braking phase Traditional braking phase

C oast Ti Bi

0 0 < uT; i  1 0

0 0 0 < uB; i  1

0 0 0

MBi

0

1

0 < uM; i  1

TBi

0

0

0 < uM; i  1

where

is control command for coasting, are different control commands represent are different control commands represent are different control commands represent are different control commands represent without regenerative braking.

C oast Ti Bi MBi TBi

different different different different

intensity intensity intensity intensity

(uT; i ) of tractive force, (uB; i ) of regenerative braking force, (uM; i ) of dissipative braking force, (uM; i ) of traditional braking force for vehicles

capabilities, then only the dissipative braking mode is applied, where the kinetic energy is converted to heat by friction in the braking linings and consequently wasted. Therefore, there are commands for vehicles with regenerative braking (including C oast ; T i ; Bi and MBi ) and for the others without regenerative braking (including C oast ; T i and TBi ). 3.3.2. Connection between train control command and predicted train states The connection between train control commands, train force (tractive force, braking force) and train states (train speed, position, running time, acceleration and deceleration) can be built at different train running phases (acceleration, braking, cruising and coasting). The train speed and the train position at next time instant are predictable by taking different train control commands, as shown by the simplified Eqs. (16) and (17). Details of these connections can be found in Rao (2015).

T i ! uT; i ! F T; i ! aaccel; i ! v iþ1 ; siþ1 ; 

ð16Þ

9 > ! F B; tot; i = ! adecel; i ! v iþ1 ; siþ1 ; MBi ! uM; i ! F B; mech; i > TBi ! uM; i ! F B; mech; i ¼ F B; tot; i ; Bi ! uB; i ! F B; elect; i



ð17Þ

where F T; i F B; tot; i F B; elect; i F B; mech; i aaccel; i adecel; i

v iþ1 siþ1

is is is is is is is is

tractive force at time step i, available braking force at time step i, electrical braking force at time step i, mechanical braking force at time step i, acceleration (> 0) at time step at time step i, deceleration (< 0) at time step at time step i, train speed at time step i þ 1, train position at time step i þ 1.

3.3.3. Decision-making procedure to decide the best train control command The decision-making procedure to decide the best train control command is illustrated in Fig. 13. Similar to the decision of best trajectory in Section 3.2.5, there are three more steps required to be carried out. The first step is to predict and evaluate the influence of train control commands on optimisation objectives, including train running accuracy (lacc; tci ), energy saving (le; tci ) and riding comfort (lrc; tci ). The second step is to compute the weights for those optimisation objectives (wacc ; wet ; wrc ). Rao (2015) has proposed three normalised models for evaluating the influence of train control commands on train running accuracy (lacc; tci ), energy saving (le; tci ) and riding comfort (lrc; tci ). The influence on train running accuracy can be evaluated by the deviation between the received control targets (Sections 3.2.2 and 3.2.3) and the predicted train states (Section 3.3.2). There are two methods to compute this deviation. The first method is to evaluate the deviation of distance and speed. This method assumes that the predicted time (t iþ1 ) equals the sub-target time. The second way is to compare the

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Fig. 13. Decision-making procedure to decide the best train control command.

deviation between the control target acceleration/deceleration (asubTarget k ) and the predicted acceleration/deceleration (ai ) according to train control command i. In this method, the running time Dt i is assumed as each time instant, such as one second. The influence on energy saving can be evaluated by calculating the tractive energy consumptions. In particular, the focus is on computing the energy consumption of the traction force (F i ) exerted by the engine over the travelled distance (from the current train position si to the predicted train position siþ1 ). Specifically, the acceleration process (positive tractive force F T; i ) costs energy, while the regenerative braking process (regenerative braking force F B; elect; i ) uses the regenerative energy, and no traction energy consumption in coasting or in dissipative braking. The influence of train riding comfort can be evaluated by the fluctuation of the acceleration/deceleration, which consists of two factors: the frequency of acceleration/deceleration transitions (f i ) and the rate of its change (Dai ). The last step is to compute the overall priority for each train control command by using the weights (wacc ; wet and wrc ) and the evaluation of optimisation objectives (lacc; tci ; le; tci and lrc; tci ). The calculation of weights is also based on the AHP method, which can be found in Rao (2015). As a result, the best train control command is the one with the highest priority value, as described in Eq. (18). In this regard, the decision-making procedure for train automation is established that the best train control command is decided and implemented on the train.

If Pj ¼ max P i ; ¼ max flacc;tci  wacc þ le;tci  wet þ lrc;tci  wrc g; i¼1;...;n

i¼1;...;n

! then the train control command j is decided to be best one and to implement:

ð18Þ

4. Case study: the importance of bidirectional communication between traffic management and train automation 4.1. Bidirectional communication between traffic management and train automation The proposed integrated optimisation model has two important highlights. The first is the decision-making procedure to decide the most attractive output from the set of optimal trajectories (Section 3.2.5) and the set of train control commands (Section 3.3.3). The second is the bidirectional communication between traffic management and train automation, as illustrated in Fig. 14. The function of traffic management delivers the control targets to train automation, while the function of train automation provides real-time feedback of train dynamics information to traffic management. The importance of this bidirectional communication was discovered during a case study, which will be introduced subsequently.

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Fig. 14. The highlights in the integrated optimisation model: the decision-making procedure and the bidirectional communication between traffic management and train automation.

4.2. Overview of the demonstrator The case study is based on a lab-demonstrator, which is programmed in JAVA. This demonstrator can simulate the track topology, train movement, the data transmission between infrastructure and train, as well as the functions of traffic management and train automation. As illustrated in Fig. 15, the track topology contains four lines merging into two, which has a total length around 90 km and the length of each track is around 1000 m. The topology is built on the doublevertex graph (Montigel, 1994). It is assumed that each track is assigned a main signal. The topology describes a compensation zone, where we pay particular attention to avoid unplanned train stops. The demonstrator can configure infrastructure layout, traffic input schedule and train characteristics by using Extensible Markup Language (XML). This makes it easier to simulate different scenarios by adapting these XML configurations. For example, we can change track length, track slope or train length, choose different locomotive types, create different input schedules, and set the weights for different optimisation objectives. In addition, this case study assumes that the simulation environment is based on the European Train Control System (ETCS) Level 2. The frequency of data transmission between the infrastructure and the train is assumed to be once per second. Moreover, this demonstrator can simulate different train types by using the static input data, such as the mass of locomotive and wagon, the number of locomotives and wagons, mass factor, horse power and the information of tractive force over train speed. This demonstrator can simulate different operational scenarios, such as crossing conflicts and follow-up conflicts. In the following section, a crossing conflict example is configured to prove the importance of bidirectional communication between traffic management and train automation. 4.3. Configure a crossing conflict scenario in the case study Fig. 15 also describes a crossing conflict example. Two trains running through the network in opposite directions conflict with each other at switch/block W64. Train ‘‘1001” (freight train with locomotive type RE-474) is the one causing conflict with slower speed (maximum speed at 140 km=h), while train ‘‘1002” (passenger train with locomotive type RE-465) is the one affected by conflict with faster speed (maximum speed at 230 km=h). In the simulation, Train ‘‘1002” is predicted to have an unplanned stop in front of block W64 and signal 61u, because it is planned to pass the line between block W64 and W44 after Train ‘‘1001”. Therefore, Train ‘‘1002” is the one to be optimised. To prove the importance of bidirectional communication between traffic management and train automation, we designed three cases in the case study:
Case 1: A non-optimised operation where traffic management will not generate train running trajectories for train automation to prevent unplanned stops.

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Fig. 15. The track topology in the demonstrator with a configured crossing conflict case.

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Fig. 16. The result of case 1: a speed  distance  time diagram of the non-optimised operation.


Case 2: An optimised operation where traffic management delivers the strategy of conflict resolution (to prevent unplanned train stops) to train automation, but train automation provides no real-time feedback of train dynamics information to traffic management.
Case 3: An optimised operation with bidirectional communication between traffic management and train automation.

4.4. Result of the case study 4.4.1. Case 1: non-optimised operation (ATO-only operation) Case 1 is a non-optimised operation by using the conventional ATO mode, which ensures that each train runs at its maximum permitted speed but it has no strategy of conflict resolution given by traffic management. The conventional ATO mode can be easily simulated by configuring the weights of train optimisation (wacc ¼ 1; wet ¼ 0; wrc ¼ 0 described in Section 3.3.3). The simulation result is in Fig. 16, which shows an unplanned stop of train ‘‘1002” in front of conflict block W64. This non-optimised result of train ‘‘1002” is used in comparison with the following Case 2 and Case 3. The mileage information can be found in the infrastructure topology design illustrated in Fig. 15.

4.4.2. Case 2: TMS-only operation Case 2 simulates the delivery of train running trajectory, as a conflict resolution (to prevent unplanned train stops) sent from traffic management to train automation. However, this case has no real-time feedback of train dynamics from train automation, such as the practical maximum train acceleration, which is usually assumed as a theoretical constant value at each sub-target phase (Section 3.2.3). The simulation result is illustrated in Fig. 17. Trajectory 51 (see Table 4) is delivered as the best theoretical resolution, which assumes that the maximum acceleration is 0.8 m/s2. However, this train is not able to accelerate as always fast as it was expected from the view of traffic management. This could happen due to the impact of several factors, such as the mass of train, the slope of track, the maximum tractive force, etc. As a result, an obvious gap between the theoretical trajectory (black dash line) from traffic management and the practical train movement (blue solid line) appears. The main-target of the Trajectory 51 cannot be achieved; therefore, the train cannot reach the main-target position at the maximum permitted speed with the estimated conflict resolution time.

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Fig. 17. The result of case 2: the operation without a real-time feedback of practical maximum acceleration.

Table 4 Trajectory variations on different sub-targets but same main-target (t: second, s: meter, v: km=h, a: m=s2 ). Trajectory

51 4

Sub-target phase 1

Sub-target phase 2

Sub-target phase 3

Evaluation

t1

v1

s1

a1

t2

v2

s2

a2

t3

v3

s3

a3

lcapacity

lenergy

96 110

108 67

70,458 70,117

0.8 0.8

337 185

108 67

63,249 68,723

0.0 0.0

369 369

200 200

61,879 61,879

0.8 0.2

0.9715 0.8263

0.8057 0.8022

4.4.3. Case 3: Bidirectional communication between TMS and ATO Case 3 simulates the bidirectional communication between traffic management and train automation. The simulation result is illustrated in Fig. 18. It introduces real-time feedback of the practical acceleration from train automation to traffic management. Traffic management changes its decision of best train running trajectory from Trajectory 51 to Trajectory 4 (see Table 4), because traffic management receives the feedback that the maximum practical acceleration at the last subtarget phase (reaccelerating phase) will only be around 0.2 m/s2. Given this real-time feedback, traffic management adapts

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Fig. 18. The result of case 3: the operation with a real-time feedback of practical maximum acceleration.

its decision and the gap between the theoretical trajectory and the practical train movement is small. Therefore, the strategy of conflict resolution (train running trajectory) from traffic management can be well executed by train automation. As shown in Table 4, Trajectory 51 and Trajectory 4 have the same main-target point (s3; t3 and v 3) for the train to prevent potential traffic conflict, but they have different sub-target phases. Trajectory 51 can achieve a higher average speed than Trajectory 4 (see Eq. (12)), but the train cannot manage the theoretical maximum acceleration (a3 ¼ 0:8) at the last sub-target phase (between mileage s2 ¼ 63249 m and s3 ¼ 61879 m). In the demonstrator, train automation can manage a more detailed train dynamics calculation compared to traffic management. The practical acceleration can be estimated for each sub-target phase according to the mass of train, the slope of track, the speed of train and the tractive force of train. When the acceleration at the last sub-target phase is estimated with the maximum value around 0.2 m/s2, we choose Trajectory 4 with theoretical acceleration a3 ¼ 0:2 m=s2 as the most attractive output. To sum up, without the strategy of conflict resolution from traffic management, the train cannot avoid unplanned stops in the conflict scenario. Without the real-time feedback of train dynamics, especially the practical maximum acceleration, traffic management’s strategy of conflict resolution might not be executed as accurately as it should be. Therefore, the bidirectional communication between traffic management and train automation is essential to achieve the optimal operation.

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5. Conclusions 5.1. Achievements For the current mainline railway, the traffic optimisation has two focuses. The first is to improve the efficiency of traffic management by providing conflict resolutions, while the second is to improve train driving behaviour by providing driver assistance or introducing train automation. This paper reviewed and classified these two focuses into different optimisation schemes. Based on this classification, this paper proposed combining the optimisation methods of traffic management and train automation into an integrated optimisation model. In the function of traffic management, the paper proposed that generating the optimal train running trajectory is regarded as a supplementary conflict resolution to train reordering or rerouting or retiming. The trajectory can improve the traffic flow by avoiding unplanned train stops. The key to generating the trajectory is to compute the main-target point. If the maintarget point is achieved, the train can pass the traffic conflict position at a maximum of allowed speed with a minimum of travel time. To achieve the main-target point, the trajectory can be formed with different sub-target points. A different combination of these sub-target points provides a freedom in preventing unplanned train stops. This paper proposes methods to evaluate each train running trajectory according to different optimisation objectives, such as increasing capacity and saving energy. A decision-making procedure is provided to synthesise all of these considerations to select the most attractive train running trajectory. The selected trajectory’s main-target point and sub-target points are sent to train automation as control targets. In the function of train automation, the paper pointed out that the key is train control command, which determines different intensities of the train’s tractive force or braking force. Similar to traffic management, a decision-making procedure is built to decide the most attractive train control command for train operation. Further, this paper shared an important finding that the bidirectional communication between traffic management and train automation is necessary to achieve the optimal operation. This is found according to a special case study (crossing conflict scenario) built in a lab-demonstrator. 5.2. Remaining questions for future study The first remaining question is how to further improve the computation of the sub-target points. This paper has described the method of computing a series of sub-target points approaching the main-target point (Section 3.2.2). It mentioned two restriction equations (Eq. (7)): the sum of sub-target distances and the sum of sub-target time. It means that only two variables can be resolved according to those two equations. If the sub-targets consist of more than three travelling phases, there will be more than two variables. 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