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1 Modelling and Analysis of Railway Network Control Logic using Coloured Petri Nets a dissertation submitted to the School of Mathematics University of South Australia for the degree of doctor of philosophy in Mathematics By Chris W. Janczura BAppSc(Hons) School of Mathematics and Institute for Telecommunications Research August 1998 Supervised by Professor Jonathan Billington

2 Contents 1 Introduction Background The Beginnings Scope Research Aims The Approach Case Study Structure of the Thesis Rail Transportation Railways and Signalling a Historical Perspective Background Information on Railways Evolution of railways The modular high-speed train Railway Transportation in Australia Situation of railways in Australia Railways in Adelaide and South Australia Advantages of Railways Formal Methods in Rail Railway Networks and Coloured Petri Nets Coloured Petri Nets Background ii

3 3.2 Coloured Petri Nets Analysis of Coloured Petri Nets Reachability analysis Invariant analysis Reduction analysis Analysis technique of choice Graphical Notation A simple CPN example Coloured Petri net components Reachability graph Strongly connected component graph Computer Support for CPNs Brief history of Design/CPN Choice of Design/CPN Components of the Design/CPN tool Occurrence Graph tool functions Initial CPN Specication of a Railway Network Description of the Railway Network Requirements Safety Requirement Operational Requirement 1: Absence of deadlock Operational Requirement 2: Overtaking Operational Requirement 3: Trapping in the loop Operational Requirement 4: Correct usage of the loop A CPN Model of the Railway Network Level of abstraction Description of the CPN model Implementation of requirements iii

4 4.3.4 Execution of the model The ML Version of the CPN Model Notation and Denitions Markings Atomic multisets Legal initial markings Set of legal markings Set of sequences of transition occurrences from a legal marking Progress Property Analysis of the CPN Model with One Express and One Normal Train Analysis of the CPN model of Figure Safety Requirement Operational Requirement Operational Requirement Operational Requirement Operational Requirement Extension of Results to any Legal Initial Marking Safety Requirement Operational Requirement Operational Requirement Operational Requirement Operational Requirement Analysis of the Network with Feasible Numbers of Trains Introduction General Notation Numbers of trains considered Legal initial markings Set of legal markings iv

5 6.2.4 Set of sequences of transition occurrences from a legal marking Set of sequences of markings from a legal marking Set of all reachable markings General Approach Discussion of the Requirements Follower Marking Results Follower marking of a legal initial marking Follower marking notation Safety Requirement Operational Requirement Investigation of the Deadlock Property Introduction Network with Normal Trains Only One normal train Two normal trains Three normal trains Four normal trains Five normal trains Network with Express Trains Only One Normal Train and One Express Train One Normal Train and Two Express Trains One Normal Train and Three Express Trains One Normal Train and Four Express Trains Two Normal Trains and One Express Train Two Normal Trains and Two Express Trains Three Normal Trains and One Express Train Four Normal Trains and One Express Train Three Normal Trains and Two Express Trains v

6 Verication of operational requirement 1 for two arbitrary legal initial congurations Consecutive and separated express trains Generalization of operational requirement 1 to any legal initial marking Associated results Two Normal Trains and Three Express Trains Verication of operational requirement 1 for an arbitrary legal initial conguration Consecutive and separated express trains Generalization of operational requirement 1 to any legal initial marking Associated results Congurations with Six Trains Six express trains Six normal trains Five express trains and one normal train Five normal trains and one express train Four express trains and two normal trains Four normal trains and two express trains Three express trains and three normal trains Summary Investigation of the Overtaking Property Introduction Discussion of Overtaking Associated Notation Set of overtaking markings Participating express train Set of ready to overtake markings Number of ready to overtake markings Generic overtaking sequence vi

7 8.3.6 Set of overtaking sequences Set of overtaking complete markings Discussion of the overtaking sequence An Approach to Verifying the Overtaking Requirement Verication of Operational Requirement One normal train and two express trains One normal train and three express trains One normal train and four express trains One normal train and ve express trains Investigation of the no Trapping Property Introduction Possible Trapping Behaviours An Approach to Verifying Operational Requirement Congurations in which a Normal Train is not Trapped One or two normal trains only One normal train and one express train Deadlocked congurations with six trains Congurations in which a Normal Train may ormay not be Trapped Three normal trains Four normal trains Five normal trains One normal train and two express trains Congurations in which a Normal Train is always Trapped One normal train and three express trains One normal train and four express trains Six normal trains One normal train and ve express trains Summary of Results vii

8 1 Revised Specication of the Railway Network Introduction Approaches for Eliminating Deadlocks Some possibilities Suitability of approaches and justication of a chosen approach Modied Coloured Petri Net Model Results Identical to those for the Original CPN Follower of a Legal Initial Marking in the Modied CPN Safety Requirement Operational Requirement Analysis of the Deadlock Property and Discussion of Overtaking and no Trapping Properties Introduction Two Normal Trains and One Express Train Two Normal Trains and Two Express Trains Three Normal Trains and One Express Train Four Normal Trains and One Express Train Three Normal Trains and Two Express Trains Verication of operational requirement 1 for an arbitrary legal initial conguration Consecutive and separated express trains Generalization of operational requirement 1 to any legal initial marking Associated result Two Normal Trains and Three Express Trains Verication of operational requirement 1 for an arbitrary legal initial conguration Consecutive and separated express trains Generalization of operational requirement 1 to any legal initial marking Associated result viii

9 11.8 Discussion of the Remaining Two Requirements Operational Requirement Operational Requirement Summary Conclusions Contributions of the Dissertation Future Work Further investigation of the modied CPN model Possible generalizations for the same topology Levels of abstraction Dierent topologies Analysis techniques Proof techniques References 25 A Denition of Coloured Petri Nets and Related Concepts 215 A.1 Background A.2 Sets and Multisets A.2.1 Sets A.2.2 Multisets A.3 Concepts from Algebraic Specication A.3.1 Many sorted signature with variables A.3.2 Natural and Boolean signature A.3.3 Many sorted algebra A.3.4 Set and multiset of terms A.3.5 Assignment and evaluation A.4 Denition of CPNs A.4.1 Marking ix

10 A.4.2 Set of occurrence modes A.4.3 Set of transition modes A.4.4 Enabling condition A.4.5 Occurrence rule A.4.6 Set of reachable markings A.5 Reachability Graph A.6 Strongly Connected Component Graph A.7 Input and Output Places A.8 Notation A.9 Notion of Sequences A.9.1 Sequences A.9.2 Element ofa sequence A.9.3 Set of nite sequences A.9.4 Set of innite sequences A.9.5 Length of a sequence A.9.6 Empty sequence A.9.7 Representing sequences A.9.8 Concatenation of sequences A.9.9 Prex of a sequence x

11 List of Figures 1.1 Single track topology Double track topology A coloured Petri net example Reachability Graph of a CPN example Strongly Connected Component Graph A simple railway network The coloured Petri net of the railway network The CPN ML version of the CPN model of the railway network RG generated for the marking M Reachability Graph generated from M 2 L The RG M a with deadlock M d1 (node 9) The RG M b with deadlock M d2 (node 48) The RG M c with deadlock M d1 (node 63) The RG M a with deadlock M d (node 9) The RG M b with deadlock M d (node 49) The RG M c with deadlock M d (node 58) Reachability Graph generated from M 2 L Reachability Graph generated from M 2 L Reachability Graph generated from M 1 specied in Table Reachability Graph generated from M 1 specied in Table Reachability Graph generated from M 2 specied in Table xi

12 7.13 Reachability Graph generated from M 3 specied in Table Reachability Graph generated from M 4 specied in Table SCC Graph corresponding to RG M, M 2 L SCC Graph corresponding to RG M, M 2 L RG generated for the marking M dened by Equation The modied CPN model of the railway network The Reachability Graph generated from M a 2 L The Reachability Graph generated from M b 2 L The Reachability Graph generated from M c 2 L The Reachability Graph generated from M a 2 L The Reachability Graph generated from M b 2 L The Reachability Graph generated from M c 2 L xii

13 List of Tables 3.1 Statistics and the list of deadlocks of RG M of Figure SCCG M statistics for Figure Satisfaction of safety requirement for Figure Existence of marking M, with M(loop) =fnormalg in SCC Notational dierences between the CPN model and the ML version Statistics and the list of deadlocks of RG M for Figure List of all 36 markings of RG M Satisfaction of safety requirement for Figure List of markings M ro for the CPN of Figure SCCG M statistics for Figure Satisfaction of the 4th operational requirement for Figure List of markings of RG M, M 2 L Statistics and the list of deadlocks of RG M M 2 L Statistics and the list of deadlocks of RG M M 2 L Statistics and the list of deadlocks of RG M M 2 L Statistics and the list of deadlocks of RG M M 2 L Statistics and the list of deadlocks of RG M M 2 L Statistics and the list of deadlocks of RG M M 2 L Statistics and the list of deadlocks of RG M M 2 L Statistics and the list of deadlocks of RG M M 2 L Statistics and the list of deadlocks of RG M M 2 L xiii

14 7.11 Home properties of the CPN with M 2 L Statistics and the list of deadlocks of RG M M 2 L Home properties of the CPN with M 2 L Statistics and the list of deadlocks of RG M M 2 L Home properties of the CPN with M 2 L Statistics and the list of deadlocks of RG M M 2 L Home properties of the CPN with M 2 L Statistics and the list of deadlocks of RG M for M dened by Equation Statistics and the list of deadlocks of RG M for M dened by Equation RG M a statistics for M a dened by Equation RG M b statistics for M b dened by Equation The 48 markings of RG M b RG M c statistics for M c dened by Equation The 12 non-consecutive markings from RG M c Checking if the marking of node 1 from Table 7.24 belongs to [M b i List of dead markings with the marking information for all 3 RGs List of home nodes for all three RGs Statistics and the list of deadlocks of RG M for M dened in Equation RG M a statistics for M a dened by Equation RG M b statistics for M b dened by Equation The 18 non-consecutive markings from RG M b RG M c statistics for M c dened by Equation The 12 non-consecutive markings from RG M c List of dead markings with the marking information for all 3 RGs List of home nodes for all three RGs List of 6 markings of RG M M 2 L List of 7 markings of RG M with M (M j ) dened by Equation Statistics and the list of deadlocks of RG M with M (M j ) dened by Equation xiv

15 7.39 Four legal initial markings at which t5 is enabled Statistics and the lists of deadlocks for all four RGs Marking information for each of the four dead nodes Checking if marking M 2 belongs to RG M Four legal initial markings at which t5 is enabled Statistics and the lists of deadlocks for all four RGs Marking information for each of the four dead nodes Checking if marking M 2 belongs to RG M Checking if the follower M of M 2 belongs to RG M Six legal initial markings at which t5 is enabled Statistics and the lists of deadlocks for all six RGs Marking information for each of the six dead nodes Checking if M 2 belongs to RG M Checking if M 5 belongs to RG M SCCG M statistics, M 2 L SCCG M statistics, M 2 L Checking if all markings in SCC1, SCC2, SCC3, SCC4, SCC6, SCC7 and SCC8 are overtaking markings Absence of overtaking markings in SCC List of nodes in SCC2, SCC3, SCC4, SCC6, SCC7 and SCC8 in Figure The set of markings, RO 3 1 contained in SCC2, SCC3, SCC4, SCC6, SCC7 and SCC SCCG M statistics, M 2 L Checking if all markings in SCC1, SCC2, SCC1, SCC21, SCC3 and SCC31 are overtaking markings Absence of overtaking markings in SCC List of nodes in SCC31, SCC3, SCC28 and SCC27 in Figure The set of markings, RO 4 1, contained in SCC31, SCC3, SCC28 and SCC27149 xv

16 9.1 Marking information for an innite sequence of markings at which t7 isnot enabled in the network with four normal trains Marking information for an innite sequence of markings at which t7 isnot enabled in the network with ve normal trains Marking information for an innite sequence of markings at which t7 isnot enabled in the network with one normal and two express trains Summary of results for the network with up to ve trains for any legal initial marking Statistics and the list of deadlocks of RG M M 2 L Statistics and the list of deadlocks of RG M M 2 L Statistics and the list of deadlocks of RG M M 2 L Statistics and the list of deadlocks of RG M M 2 L Statistics and the list of deadlocks of RG M for M dened by Equation RG M a statistics for M a dened by Equation RG M b statistics for M b dened by Equation The 48 non-consecutive markings of RG M b RG M c statistics for M c dened by Equation The 12 non-consecutive markings from RG M c List of dead markings for all three RGs Statistics and the list of deadlocks of RG M for M dened by Equation RG M a statistics for M a dened by Equation RG M b statistics for M b dened by Equation The 18 non-consecutive markings from RG M b RG M c statistics for M c dened by Equation The 12 non-consecutive markings from RG M c List of dead markings for all three RGs xvi

17 Summary This dissertation documents the process of modelling and analysis of a railway network using coloured Petri nets (CPNs). The railway network under consideration is a small, representative network consisting of a circular main track of six sections and one passing loop. The network caters for two types of trains (express and normal) which move in one direction. The CPN model captures the control logic of the railway network which allows an express train to overtake a normal train using the passing loop. The network is considered at a high level of abstraction where only functional properties are captured. Other important issues, such as timing, scheduling and performance, are abstracted out and are not pursued in the thesis. The properties of interest are: a safety property, which states that each section is occupied by exactly one train or it is empty and four operational properties: 1. The network does not deadlock. 2. Express trains must be able to overtake normal trains using the passing loop. 3. A normal train is never trapped in the loop. 4. Express trains must never use the loop. After a general introduction to railways and coloured Petri nets, the CPN model of the railway network is obtained and described. The model is analysed for all legal initial markings to determine if the properties are satised. (An initial marking is legal if each section contains one train or is empty (safety property), and the passing loop does not contain an express train (operational property 4).) The verication process involves hand proofs assisted by automated reachability analysis. Verication is based on interrogating the complete state space of the system and is supported by a software package called Design/CPN. The following results have been obtained and are considered the major contributions of the thesis: 1. Investigation of the original design for one express and one normal train, for a particular legal initial marking, showed that all the requirements are satised. 2. An approach to generalize the results obtained for one legal initial marking to the set of all legal initial markings has been developed. 3. Using this approach itisproved that all ve requirements are satised in the model with any legal initial marking involving one express and one normal train. xvii

18 4. Generalization of the model to cater for all feasible congurations with the total number of trains between one and six inclusive has revealed that: The safety property is satised and express trains never enter the loop. The networks with express trains only or normal trains only with the total number of trains between one and ve inclusive are deadlock-free. Similarly, the networks with one normal and up to four express trains are deadlock-free. Congurations involving at least one express and at least two normal trains can or will deadlock. (In most cases the network deadlocks in one way, but it is also possible to have multiple deadlocks.) Nearly all congurations with six trains positioned initially on the main track (with the loop empty) are deadlocked in the initial marking. Exceptions arise for a particular class of congurations. The overtaking property is met in the network with express or normal trains only, in the network with one normal and up to four express trains, and for certain legal initial markings, also in the network with one normal and ve express trains. (Trivially) Reaching any deadlocked conguration prevents further train movement and hence overtaking is not possible. (For the network with six express or six normal trains the overtaking property is satised, because it does not arise.) A normal train is not trapped in the loop in the network with up to two trains, in the network with express trains only, and in any deadlocked conguration with six trains on the main track. There are four main groups of congurations for which a normal train becomes trapped in the loop: { Deadlocked congurations (which involve a normal train in the loop). { Three, four or ve normal trains only. { One normal train and two, three or four express trains. { Special cases of deadlock-free congurations involving 6 trains with at least one normal train. 5. The original CPN has been modied in order to eliminate deadlock. Study of the modied model, with the number of trains between one and six inclusive, has shown that: The safety property is satised and express trains never enter the loop. xviii

19 The deadlock has been eliminated from all of the train congurations with less than six trains for which it was discovered in earlier analysis. As expected, for congurations involving six trains, the modication did not remove deadlock. With respect to the remaining two operational properties, for the network with at least one express train and at least two normal trains with the total number of trains less than six, it has been conjectured that, the removal of deadlock: { has led to the satisfaction of operational requirement 2 at previously deadlocked markings, { has not led to the satisfaction of operational requirement 3. In the concluding chapter, the thesis describes signicant areas of future work. It is hoped that the work presented in this thesis is setting the foundations for the development of a CPN based methodology for railway network control logic design. xix

20 Declaration I declare that this thesis does not incorporate without acknowledgment any material previously submitted for a degree or diploma in any university and that to the best of knowledge it does not contain any materials previously published or written by another person except where due reference is made in the text.... Chris W. Janczura BAppSc(Hons) August 1998 xx

21 Acknowledgements There are number of people to whom I would like to express my personal gratitude. First of all I would like to thank my PhD supervisor Professor Jonathan Billington for introducing me to the area of Petri nets. I am grateful to Professor Billington for his guidance, inspiration, useful suggestions and valuable feedback concerning both the technical aspects of the thesis and the use of English. Without his enthusiasm and patience this work would not have been possible. Iwould like tothankmy associate supervisor Mr Basil Benjamin for introducing me to the eld of railway transportation, continuous support and guidance throughout the years. Iwould also like to express my gratitude to the School of Mathematics at the University of South Australia for providing me with much needed nancial assistance: by giving me the opportunity to conduct paid tutorials and by providing a scholarship. My special thanks go to the Head of the School of Mathematics, Mr Len Colgan, and Dr Adrian Vladco for their help and support. I am particularly indebted to Dr Tony Bedford, Chief of Communications Division at Defence Science and Technology Organization (DSTO), Dr Warren Marwood, Head of Information Access Group, Dr Chris Woodru, Head of Intelligent Networks Group, and Mr Ian Coat and Dr Michael Webb my work supervisors for giving me the opportunity to complete the thesis while working at DSTO. I thank them for their understanding, support and trust. I wish to thank Professor Kurt Jensen and Dr Sren Christensen of the University of Aarhus, Denmark for their comments and suggestions concerning the Design/CPN model investigated in the thesis and the use of the Design/CPN tool. Finally, Iwould like tothank my wife Marie for her unconditional love which allowed me to carry on and succeed. xxi

22 Chapter 1 Introduction 1.1 Background The specication, analysis and implementation of railway control logic has been an important activity ever since trains and railways were invented centuries ago [84, 49, 7]. This is because failure of control logic can lead to railway accidents and loss of human life [83]. At the present time, this activity is perhaps more important than ever because railway networks are often large, the speed of trains and trac density is increasing, and activities within networks are taking place concurrently and at geographically dierent locations [3, 81, 54]. As a result, the overall complexity of railway systems increases, and hence greater demands are placed on the control logic of these systems. Thus, it is important that the control logic is rigorously specied and then veried to ensure that any errors or omissions are detected before implementation. Given this inherent complexity, the design of modern railway networks is a non-trivial undertaking. The design of railway networks can be aided by rigorous mathematical techniques. In this thesis we employ the theory of coloured Petri nets [61, 11, 62] to formulate and verify certain properties of a small railway network. 1.2 The Beginnings My interest in railway networks began during my Honours degree candidature in 1992, within the Scheduling and Control Group [16] (SCG) at the University of South Australia, Australia. My Honours degree supervisor, Mr Basil Benjamin, introduced me to some problems and research areas which were investigated by the group. 1

23 During my Ph.D candidature I continued to attend SCG meetings. During one such meeting, an interesting application of a railway network suitable for my Ph.D study was jointly proposed by Mr Benjamin and Prof. Ian Milroy (of the University of South Australia). The railway network was believed to be representative of a general class of networks. It consisted of six sections, and a passing loop with two types of trains: express and normal. Subsequently, I decided to use this network to illustrate the approach taken in the thesis. Together with my Ph.D supervisor we specied the structure and the properties of the network. The network was then modelled as a coloured Petri net (CPN) and veried to satisfy the properties. The thesis provides a detailed account of this study. 1.3 Scope Development of a design methodology to cover all aspects of railway system design is an immense research undertaking. In order for this thesis to have a manageable size and to be completed within a reasonable time period, the scope of the investigation had to be reduced to cover a class of railway networks having certain characteristics only. In particular, we investigate railway networks with two types of trains (express and normal), which move in a clockwise direction on a single circular track. The track has one passing loop to allow express trains to overtake normal trains. The railway networks are considered at a high level of abstraction where only functional behavior is investigated. At that level, we formulate and analyse a safety property and certain operational properties the network should satisfy. 1.4 Research Aims The principal objective of this thesis is to make a contribution towards the development of a coloured Petri net based methodology to aid the design of railway networks. In order to realize this objective, the following aims are identied: To develop the CPN specication of a railway network case study. To formulate the safety property and certain operational properties the network should satisfy. To verify the properties for the network with one express and one normal train. To investigate these properties for the network with all feasible initial congurations of trains. 2

24 Consequently, to illustrate that CPN theory and associated analysis techniques can be applied in the domain of railway networks design. (This is a relatively new domain for CPNs.) In essence, these aims constitute the statement of the problem that is addressed in the thesis. 1.5 The Approach In this thesis, we employ coloured Petri nets to model and analyze railway networks. Our approach consists of the following steps: 1. Determine the set of properties that the railway network should obey. 2. Model the network at an appropriate level of abstraction which just captures its control logic. 3. Analyse the model to determine if the control logic satises the set of properties. The verication process involves hand proofs assisted byreachability analysis. Some proofs are based on interrogation of the complete state space of the system and employ the notion of strongly connected components (SCC) of the reachability graph (RG) [62]. The modelling and analysis is supported by a coloured Petri net software package called Design/CPN [29]. 1.6 Case Study In this thesis we consider a single case study that of a metropolitan railway system. As mentioned in Section 1.2, this particular conguration of the railwaynetwork was proposed by Mr Benjamin and Prof. Milroy as being a suitable application relevant to the South Australian Transport Authority (TransAdelaide). In general, most railway networks have one of two topologies: a single track with passing loops to allow for two directional movement (as shown in Figure 1.1) or two tracks (one for each direction of movement) with passing loops to allow express trains to overtake normal trains (as shown in Figure 1.2). (We note that in both Figure 1.1 and 1.2, the ends of railwaytracks are represented by the shaded rectangles. The black rectangles, on the other hand are used to divide the track into sections. The arrows indicate possible directions of the train movement.) In the rst case the passing loops can also be used 3

25 for overtaking. Railway networks which are a combination of both topologies are also common. Descriptions of dierent track topologies and signalling systems can be found in [84]. < < > > Figure 1.1: Single track topology > > < < Figure 1.2: Double track topology We investigate the second case. Because trains switch from one track to the other at the end of the line, the two tracks are eectively a circular track with passing loops (see Figure 1.2). This allows us to consider trains to travel in one direction only along a circular track. In our case study, we only consider a single passing loop. Initially, we consider one express and one normal train in the network. 1.7 Structure of the Thesis The remaining part of the thesis is structured as follows. Chapter 2 introduces the reader to the rail transportation area. It begins with a historical overview of railways and signalling systems. This is followed by an outline of the current situation. Chapter 2 concludes with a discussion of the recent applications of formal methods, including Petri nets, to the design of railway networks. Chapter 3 explains the mathematical background and the notation used in the thesis. It contains an introduction to coloured Petri nets, a brief description of analysis techniques associated with CPNs, and a short description of the computer tool, Design/CPN, supporting CPN system modelling and analysis. For ease of reference, the denition of CPNs and related concepts are placed in the Appendix. 4

26 Chapters 4 to 11 deal with modelling and analysis of the case study. The railway network and its CPN model are presented and described in Chapter 4. Chapter 5 contains the results of the analysis of the network with one express and one normal train. The investigation of the network with dierent numbers of trains begins in Chapter 6 where the safety and operational requirement four (the absence of an express train in the loop) are studied. The next three Chapters 7, 8 and 9 deal with the remaining three operational requirements: deadlock-freeness, overtaking and no trapping of a normal train in the loop. Analysis conducted in Chapter 7 has proved that, given certain numbers and types of trains, the network can deadlock. The deadlock is eliminated by modifying the CPN model of the network. The new model together with the verication of the safety requirement and operational requirement four is presented in Chapter 1. The absence of deadlock property for the modied model is investigated in Chapter 11. Some conjectures regarding the overtaking and no trapping properties are also included in Chapter 11. Chapter 12 contains a summary of the contribution of the thesis and outlines possible future work. 5

27 Chapter 2 Rail Transportation The aim of this chapter is to place the work presented in the remaining part of the thesis in perspective, by familiarizing the reader with railway transportation and by providing some exposure to recent scientic developments in the design of railway systems. The chapter begins with a historical account of railways and signalling systems. Then some background information on the current situation of railways worldwide, with a special emphasis on railways in Australia, is presented. Subsequently, the advantages of railways are listed. This is followed by a description of several applications of formal methods to the design of railway systems. In the nal section, we focus on applications of Petri nets and coloured Petri nets to the modelling and analysis of railway systems. 2.1 Railways and Signalling a Historical Perspective Signalling provides a valuable means for the control of trac and for its safe and ecient movement. Signals oer the most positive form of control of all devices (excluding railway crossing gates) [89]. In rail operations, signalling systems are designed to accomplish three major functions: dispatching of trains, collision avoidance and safeguarding the movement of trains at junctions [84, 7]. The rst two functions are related since the ability to maintain the separation between trains allows the operator to schedule short headways (the distance between two consecutive trains on the same track) and to operate safely in trac that mixes passenger and freight trains. One of the major components of signalling systems are interlocking systems. Railway interlocking systems control points and signals so that no train collisions or derailments occur. Development and implementation of the rst signalling systems began soon after the invention of the rst railways in the rst half of the 19th century. 6

28 In the remaining part of this section we provide a short description of the early days of railways and the beginnings of signalling systems. This topic, together with the description and discussion of some historical railway accidents, is given excellent coverage in [83]. The material presented here is largely based on [83]. Railways rst appeared at the beginning of the 19th century in British mines. In the early days of steam railways, the most important objective was to move the train. Once moving, in order to ensure safe speeds the train was often preceded by a man carrying a red ag and sitting on a walking horse. The importance of speeds at which trains can travel has soon increased. For instance, the requirements for speed and weight haulage were specied at the Rainhill (England) competition which took place in However, another important issue, that is how to stop the train, was still not considered for some time. The importance of this issue was demonstrated at the same competition. The lack of braking power resulted in a tragic accident, when a man crossing a railway line was run over by a train. The locomotive driver could see the man long before but had no means of stopping the train in time. It seems that in those early years, signicant engineering eort was directed towards increasing the tractive capacity and the speed of locomotives. Whereas limited consideration was given to the lack of braking power. By the middle of the 184's trains were traveling at relatively high-speeds of approximately 95 km/h. Another major limitation of the early railways were very primitive arrangements for signalling. Originally almost all signalling was performed by ex-military men called policemen. These men, to whom we refer as the operators, were stationed at intervals along the line, and conveyed the stop, caution and go signals to train drivers by means of hand signals. They stood in certain positions according to the message they had to convey to the driver. These arrangements had obvious shortcomings because the complete responsibility and consequently the reliability of systems was placed on humans. Potential problems and the actual catastrophes resulting from this type of signalling are described in [83]. The next step in enhancing signalling systems was to provide the operators with better means of signalling such as hand semaphores or the Great Western discs and crossbars. The design and operating principles of semaphores were not entirely safe. Following the old hand signals the semaphores were arranged to show three indications stop, caution and all right (or all clear). The corresponding arm positions were horizontal, inclined down and vertically down. The danger of displaying the potentially very dangerous all clear signal when the semaphore was broken (i.e. hanging vertically down) was neglected. A similar lack of appreciation of the possible dangers was demonstrated in the design of night indicators. At night, white lightwas used to indicate all clear. Quite possibly a light 7

29 external to the railway could have been taken as the all clear signal by the approaching train. Dangerous operating practice was also revealed in the way the headway between successive trains was regulated. This was done purely on a time basis (also known as open block), i.e. when a train had passed an operator for a certain time, the caution signal was given to the next approaching train, and after a longer time had elapsed, the operator was instructed to issue all clear to the approaching train. The type of train (i.e. normal or express) or the order in which they passed the operator seemed to be not important. It is easy to imagine that the open block arrangement was potentially very dangerous. Once a train disappeared from the operator's sight, it could be slowed down or come to a complete halt as a result of some mechanical failure. Such failures were not uncommon in the early days of railways. Since the operator had no way of knowing about the failure, after a certain time elapsed, the all clear signal was issued to the next approaching train. At this point, the only way of avoiding a collision was for the driver of the moving train to sight the stationary train in time to stop. Perhaps the most important achievement in the evolution of railway signalling systems was the replacement of the open block system with the space interval block system. The principle of space interval block is to allow a train to proceed if and only if the other train had reached a certain xed point ahead. Initially, the electric telegraph was used to communicate between the two ends of a block section. Year 1841 marks the beginning of the space interval block system being used in practice. The system was implemented in two long tunnels: Clay Cross and the Clayton Tunnel. In principle, the space interval block system guaranteed safety. No collisions were possible as long as at least one section in frontofevery train was kept clear. However, implementing this principle in practice required some sort of communications protocol which specied how the information regarding the status of sections is to be processed and interpreted by train drivers and line operators. These specications were often in the form of a set of oral or written informal instructions used by the operators. Further, these fragmentary specications were conveyed by rather primitive means of communication (hand signals, signs, early telegraph). Needless to say, the completeness of such specications was never veried. The rst signalling systems were rather simple as they dealt with a small number of trains and sections, slowly moving trac and a low number of other network components such as crossings and tunnels. The possible dangers of inadequate specication was largely not realized. The history reports on a number of near accidents or accidents which resulted from inadequate specication of signalling systems. One such early disaster occurred in the Clayton Tunnel after 2 years of successful operation. The accident, in which 21 people were killed and 176 were injured, was caused by an inadequate set of instructions given 8

30 to the operators and lack of adequate communication means. An excellent description of this accident is presented in [49]. Today there are dierent signalling systems in use around the world. The principles of most of them have been developed in the rst half of the 2th century and have changed little since then [84]. It appears that one of the most popular systems is the British system called MAS (multiple aspect colour light signalling) adopted in The elements of the system which may be 2, 3 or 4 aspect, according to trac needs, are described in detail in [84]. In brief, the number of aspects corresponds to the number of colours used in the lamps operating in the signalling system. Two aspect is the simplest, and it consists of 2 aspect Red/Green stop signals [84]. For higher trac densities (more trains per hour) more advance warnings about change or a possible change of the signal ahead of a train are necessary, and hence 3 aspect (Green, Yellow, Red) or 4 aspect (Green, Yellow, double Yellow, Red) systems are used. (For example, the yellow colour is used to indicate to the driver that the next signal may bered, and hence caution needs to be taken). It is worth noting that although the early limitations of signalling and associated communication systems have now been eliminated, the problems with establishing unambiguous rules of communication to maintain safety are still present [49]. Railway accidents, fortunately seldom, still take place. Last year, for example, in Spain as a result of train derailment 21 people died and 11 were injured [3]. More recently, ingermany, more than 1 people died and 3 were injured when a fast train (traveling at approximately 2 km/h) derailed and hit a bridge [2]. 2.2 Background Information on Railways Railways form an important part of transportation systems [91, 71]. It is widely acknowledged that fundamental innovations in the development of transportation included the discovery of the wheel, the railway and the aeroplane [91]. Today, railways are experiencing a period of moderate growth, which combined with their constantly improving safety record, makes them a very attractive option compared with other modes of transport [81, 4, 91, 54]. In this thesis, we limit ourselves to providing only a brief discussion of railways and the associated scientic developments. The interested reader may consult the literature [81, 82, 91, 51, 54] and follow links provided on internet sites [19, 4, 18, 11] for a more detailed treatment. 9

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