Modelling of the RandstadRail signalling system for supporting capacity studies; Modelleren van het RandstadRail seinsysteem voor het ondersteunen van capaciteit studies

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This report consists of 86 pages and 7 appendices. It may only be reproduced literally and as a whole. For

com-Delft University of Technology

FACULTY OF MECHANICAL, MARITIME AND MATERIALS ENGINEERING

Department of Marine and Transport Technology Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl

Specialization: Production Engineering and Logistics Report number: 2014.TEL.7905

Title: Modelling of the RandstadRail

signalling system for supporting capacity studies

Author: T. Jongerius

Title (in Dutch) Modelleren van het RandstadRail seinsysteem voor het ondersteunen van capaciteit studies

Assignment: MSc thesis

Confidential: no

Initiator (university): prof.dr.ir. G. Lodewijks

Initiator (company): ir. H. Veldhoen (HTM, Den Haag) Supervisor: dr. ir. F. Corman

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Delft University of Technology

Student: T. Jongerius Assignment type: Master Thesis

Supervisor (TUD): Dr. Ir. F. Corman Creditpoints (EC): 35 Supervisor (Company): Ir. H. Veldhoen Specialization: PEL

Report number: 2014.TEL.7905

Confidential: no

Subject: Modelling of the RandstadRail network for supporting capacity studies

HTM, a public transportation company in the city of the Hague, operates the tram and light rail (Rand-stadRail) network of the Haaglanden region. In 2016 the ‘Haags Startstation Erasmuslijn’ (HSE) pro-ject will require construction works on a part of the infrastructure of the E line, between The Hague Central Station and Rotterdam. As a consequence, the E line will have to be shortened and a choice between different solution scenarios has to be made for transporting the passengers to and from The Hague Central Station. For one scenario this requires a capacity analysis of the RandstadRail network. The scenario includes adding extra vehicles to a busy route on the network. Another example problem HTM has to deal with is the wish of the public transport company of Rotterdam (RET) to increase the frequency of the E line from six to eight vehicles per hour. Here a similar analysis is required to de-termine the consequences of this request.

These cases are an example of the many problem scenarios HTM has to deal with. Over the last years HTM and TU Delft have been developing a simulation model to support analysts in evaluating the designs and performance of different configurations of the urban tram network. However, this model does not yet include the RandstadRail network, due to the difference between the signalling systems on both networks. HTM desires to include both networks into the model to be able to evaluate the complete network as a whole. This requires a description of the signalling system logic.

The assignment is to provide a systematic description of the RandstadRail signalling system logic to support future implementation of this network into the existing HTM simulation model and to use this outcome to determine the consequences of the mentioned scenarios.

Research question:

How can the block signalling system of the RandstadRail network be described in a structured way, with the goal to support future implementation of this system into the existing HTM simulation model, and how can this be used to perform network capacity studies?

This question should be answered by performing the following steps:  Study relevant literature and create a theoretic foundation

 Analyse and describe the RandstadRail signalling system logic according to the Delft Systems Approach

 Develop a simulation model that replicates this logic and is able to calculate the RandstadRail network capacity

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Delft University of Technology

 Determine the consequences of the solution scenarios with the use of the developed simu-lation model

This report should be arranged in such a way that all data is structurally presented in graphs, tables, and lists with belonging descriptions and explanations in text.

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Summary

HTM Personenvervoer N.V. is a public transportation company that operates the tram and light rail network of The Hague. These networks are connected at The Hague Central Station, where light rail vehicles continue on the urban tram network, making it a mixed operation system. HTM frequently deals with planned changes regarding the timetable or infrastructure on these networks, for which they require a way to evaluate the consequences of the decisions that are about to be made. There-fore HTM together with the TU Delft started the development of a rail simulation model, LIBROS. It is an object-oriented discrete-event model that contains rail elements as components that can be cou-pled to form aggregated components, like crossings. However, this model does not yet contain the RandstadRail (light rail) network, which makes the model incomplete. Furthermore, few to no simula-tion models are found on the market that are able to simulate both operating principles simultaneous-ly. HTM wishes to include both networks in the LIBROS model to be able to perform network evalua-tions.

An analysis and description of the RandstadRail system is made using systems theory, in which the operational logic was described in a structure similar to the LIBROS model. System elements are iden-tified, processes are described in terms of functions and the component interactions for different con-trol scenarios are shown. This static model is translated to a simulation model, with the purpose to validate the chosen structure, to serve as a way to describe the system dynamics and to show that the model is capable of performing network evaluations for realistic cases. The simulation model is made using Delphi and TOMAS and is based on the created static model and the LIBROS structure. Input of the model consists of the infrastructure, a timetable and halting time distributions for each stop. The model then generates output in the form of pure running times between stops and stop times (halting times plus waiting times).

To validate the model, a HTM data set is used containing running times between stops from a pe-riod of two months of line 3 & 4 (Feb-Mar 2014). The normal timetable of November 2014 is used as input, with line 3 & 4 of HTM and line E of the public transportation company of Rotterdam (RET) operating on the network. Results contain average running times that show a similar pattern as the real data, but that are between 2% higher and 13% lower, with most values being slightly lower. Stops near crossings show some larger negative deviations, which are likely caused by a cumulative effect of two crossing lines that both have a lower running time. The model assumes ideal driving behaviour of drivers, which explains the lower values. Furthermore, the halting time distributions that are used are not exact fits of the real data, they have the same mean but lower positive deviations, and the real data also contains more extreme values due to the presence of external disturbances. The spread in average running time between stops that is found shows some higher spreads near

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crossings, which is logically explained by vehicles having to wait for a red signal when crossing move-ments occur.

Two practical cases are used as a case study. The first case concerns a request from RET to in-crease the frequency of line E from six to eight vehicles per hour. By using a time-distance graph two more vehicles per hour are inserted in the normal timetable. The original timetable is left intact as much as possible to preserve trip alignments and keep the results as realistic as possible. Five simula-tion runs are performed using the model. The results show comparable average running times be-tween stops, except for the stops near the merging point of line E with line 3 and 4. The increased number of crossing movements likely causes an increased waiting time for some vehicles. No propa-gation of delays to other stops was found, so an extra two vehicles per hour on line E seems to be possible considering the vehicle capacity of the network.

A second case concerns the HSE project, where a part of the line E infrastructure is unavailable for a long period of time. Vehicles of line E switch direction at an earlier stage on an intermediate buffer track. To provide sufficient passenger capacity, line 3 of HTM operates on a frequency of twelve vehi-cles per hour instead of six vehivehi-cles per hour. Passengers are transferred at the first station after line E has entered the shared network. On this small part of the infrastructure a total of 30 vehicles per hour per direction are then operated. Model results show similar increases in average running times per stop as for the previous case, but now more stops are involved. Spreads show very large increas-es at crossings and the maximum total running time deviations are significantly larger. A propagation of delays is clearly shown.

The model shows results that could be expected for the used cases and it therefore suited for comparing scenarios. Results could be improved by using iterations between runs, where a timetable is optimised in between runs using optimisation software. The accuracy of results could be increased by including stochastic disturbances and calibrating the model through applying a different driver be-haviour. The applied structure seems suitable for further developing the LIBROS model. More functio-nalities could then also be added.

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Samenvatting

HTM Personenvervoer N.V. is een openbaar vervoersbedrijf dat het tram en lightrail netwerk van Den Haag exploiteert. Deze netwerken zijn met elkaar verbonden ter hoogte van Den Haag Centraal Sta-tion, wat het een systeem maakt met een gemengd bedrijf. HTM heeft op dit netwerk op regelmatige basis te maken met geplande wijzigingen met betrekking tot de dienstregeling en de infrastructuur, waarvoor een methode nodig is om de gevolgen van beslissingen die genomen worden ten aanzien van deze wijzigingen te kunnen evalueren. Hiervoor is HTM een samenwerking met de TU Delft ge-start om het rail simulatiemodel LIBROS te ontwikkelen. Dit is een object-georiënteerd discrete-event model dat rail elementen als componenten bevat, welke gekoppeld kunnen worden om geaggregeer-de componenten zoals kruisingen te vormen. Echter is het RandstadRail (lightrail) netwerk nog niet opgenomen in dit model, waardoor het model incompleet is. Daarbij zijn er weinig tot geen simulatie-modellen op de markt te vinden welke in staat zijn om beide werkingsprincipes geïntegreerd te kun-nen simuleren. HTM wenst beide netwerken toe te voegen aan het LIBROS model om zo in staat te zijn om netwerk evaluaties uit te voeren.

Een analyse en beschrijving van het RandstadRail systeem is gemaakt met gebruik van systeem-theorie, waarin de operationele logica beschreven is in een structuur die overeenkomt met die van het LIBROS model. Systeemelementen zijn geïdentificeerd, processen zijn beschreven in termen van func-ties en de interacfunc-ties van de componenten bij verschillende beheersingsscenario’s zijn weergegeven. Dit statische model is vervolgens vertaald naar een simulatiemodel, met als doel om de gekozen struc-tuur te valideren, om als een manier te dienen om de systeemdynamica te beschrijven en om aan te tonen dat het model in staat is om netwerkevaluaties uit te voeren voor realistische scenario’s. Het simulatiemodel is gemaakt met gebruik van Delphi en TOMAS en is gebaseerd op het eerder gemaak-te statische model en de LIBROS structuur. Input van het model bestaat uit de infrastructuur, een dienstregeling en halteertijddistributies voor elke halte. Het model genereert vervolgens output in de vorm van pure rijtijden tussen haltes en stoptijden (halteertijden plus wachttijden).

Om het model te valideren is een HTM dataset gebruikt welke rijtijden tussen haltes bevat van lijn 3 en 4 over een periode van twee maanden (Feb-Mrt 2014). De reguliere dienstregeling van Novem-ber 2014 is gebruikt als input, met de operationele lijnen 3 & 4 van HTM en lijn E van het openbaar vervoersbedrijf van Rotterdam (RET). De resultaten bevatten gemiddelde rijtijden die een vergelijk-baar patroon laten zien als de werkelijke data, maar die tussen de 2% hoger en 13% lager liggen, waarbij de meeste waarden lager liggen. Haltes bij kruisingen laten een aantal grotere negatieve af-wijkingen zien, welke waarschijnlijk veroorzaakt worden door een cumulatief effect van twee kruisen-de lijnen die beikruisen-de een lagere rijtijd hebben. Het mokruisen-del gaat uit van ikruisen-deaal rijgedrag van bestuurkruisen-ders, waardoor de lagere rijtijden kunnen worden verklaard. Bovendien zijn de gebruikte

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halteertijddistribu-ties geen exacte fit van de werkelijke data, ze bevatten een gelijke mean maar lagere positieve afwij-kingen, en de werkelijke data bevatten bovendien meer extreme waarden vanwege de aanwezigheid van externe verstoringen. De spreiding die gevonden is in gemiddelde rijtijden tussen haltes toont een aantal hogere waarden nabij kruisingen, wat logisch te verklaren is doordat voertuigen moeten wach-ten voor een rood sein wanneer er kruisende bewegingen plaatsvinden.

Twee praktische cases zijn gebruikt als casestudy. De eerste case betreft een verzoek van RET om de frequentie van lijn E te verhogen van zes naar acht voertuigen per uur. Door een tijd-afstand dia-gram te gebruiken zijn twee extra voertuigen per uur ingevoegd in de reguliere dienstregeling. De originele dienstregeling is hierbij zo veel als mogelijk intact gelaten om aanwezige ritafstemmingen te behouden en daardoor de resultaten zo realistisch als mogelijk te laten zijn. Vijf simulatieruns zijn uitgevoerd met het model. De resultaten tonen vergelijkbare gemiddelde rijtijden tussen haltes, be-halve voor de haltes nabij het punt van samenvoegen van lijn E met de lijnen 3 & 4. Het verhoogde aantal kruisende bewegingen veroorzaakt zeer waarschijnlijk een verhoogde wachttijd voor sommige voertuigen. Er is geen verspreiding van vertraging door het netwerk waargenomen, waardoor twee extra voertuigen per uur op lijn E mogelijk lijkt te zijn met betrekking tot de voertuigcapaciteit van het netwerk.

Een tweede case betreft het HSE project, waarbij een deel van de infrastructuur van lijn E buiten dienst genomen is gedurende een lange periode. Voertuigen van lijn E veranderen eerder van richting op een tussengelegen bufferspoor. Om toch voldoende passagierscapaciteit te bieden opereert lijn 3 van HTM met een verhoogde frequentie van twaalf voertuigen per uur in plaats van de reguliere zes voertuigen per uur. Passagiers stappen over op de eerste halte na het punt waar lijn E het gezamen-lijke netwerk binnen rijdt. Op dit kleine gedeelte van de infrastructuur wordt dan een totaal aantal van 30 voertuigen per uur per richting geëxploiteerd. Resultaten van het model tonen vergelijkbare verho-gingen van de gemiddelde rijtijd per halte als voor de voorgaande case, maar er zijn meer haltes bij betrokken. Spreidingen tonen zeer grote stijgingen nabij kruisingen en de afwijkingen van de maxima-le totamaxima-le rijtijd zijn significant groter. Een verspreiding van vertraging door het netwerk is duidelijk waar te nemen.

Het model genereert resultaten die zijn te verwachten op basis van de gebruikte cases en is daar-door geschikt voor het vergelijken van dergelijke scenario’s. De resultaten zouden verbeterd kunnen worden door gebruikt te maken van iteraties tussen runs, waarbij een dienstregeling geoptimaliseerd wordt in de tussenstappen met gebruik van optimalisatiesoftware. De nauwkeurigheid van de resulta-ten zou verhoogd kunnen worden door stochastische effecresulta-ten te includeren en door het model te kali-breren door verschillende gedragsprofielen van bestuurders toe te passen. De toegepaste structuur lijkt geschikt voor een verdere ontwikkeling van het LIBROS model. Tevens zouden meer functionali-teiten kunnen worden toegevoegd, zoals een functionaliteit voor de dynamische herverdeling van ritten of het includeren van gedrag van passagiers.

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List of symbols

Aspect flow

Physical flow of elements that are ‘transformed’ by the system

Information flow

Flow of information required for communication and support functions, like a control function

Function

Blackbox that includes processes, or subsystems, required for transforming an aspect flow

Buffer

Element containing a queue or stock, no trans-formation takes place here

Tap

Controllable limitation of the throughput of a flow

Measurement

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Introduction

Chapter 1

General introduction

1.1

Railway companies frequently deal with complex decision making scenarios that involve many interre-lated elements and processes1_{. These scenarios often require the support of analytical computer}

methods to make decisions regarding the planning, design and operation of a railway system. Simula-tion can be a useful method to support these kind of decisions by means of replicating the behaviour of the system (Siefer, 2008).

Haagsche Tramweg Maatschappij Personenvervoer N.V. (HTM) is a public transportation company that operates passenger transportation services in the Dutch city of The Hague and the surrounding Haaglanden region. The company owns 125 trams (GTL), 72 light rail (RandstadRail) vehicles and 242 busses (HTM, 2012) and uses them to transport more than 130 milion passengers per year (HTM, 2014). It uses rail infrastructure owned by the municipality to offer rail guided services to travellers. This infrastructure globally consists of two types; a tram network and a regional light rail (Rand-stadRail) network. They meet and connect near The Hague Central Station. The former connects the city centre of The Hague with its different suburban areas and the nearby cities of Rijswijk and Delft, while the latter connects it with the more distant cities of Zoetermeer, Pijnacker and Rotterdam. Fig-ure 1.1 shows an isolated view of the RandstadRail network. The lines connecting The Hague to Zoe-termeer (line 3 & 4) are operated by the HTM whereas the line The Hague-Pijnacker-Rotterdam (E line) is operated by the public transport company of Rotterdam (RET). In section 1.3 both networks are explained in more detail.

HTM strives to provide the best possible service to its customers within the boundaries that are primarily determined by the principle transit authority, Stadsgewest Haaglanden (SGH). To realise this goal, an analysis and evaluation of the current and expected performance is required on a frequent basis. The results also need to be regularly communicated internally and with many of the concerned stakeholders. HTM and TU Delft have together developed a simulation model of the urban tram net-work of the city of The Hague, with the purpose of supporting these decision making phases. The goal of this model is to speed up difficult analyses and evaluations of the rail system, to further expand the analytical possibilities and to provide better insight and communication on the complex relations that exist in the rail system. However, the model does not yet include the regional light rail (RandstadRail)

1_{Important main processes concern e.g. planning, ‘maintenance’ and operation of vehicles, infrastructure and}

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network due to the different functioning of the more complex signalling system, compared to the tram network, on this route. HTM aims to include the RandstadRail network into the model.

HTM deals with complex problems on the RandstadRail network on a regular basis. The wish of RET to expand the line E service frequency towards The Hague or the ‘Haags Startstation Erasmuslijn’ (HSE) project, starting in 2016 (Gemeente Den Haag, 2014), are just some examples. The last prob-lem requires an analysis for determining the consequences of a number of transportation alternatives. These cases will be further explained in § 1.4, § 2.3 and Chapter 6. The addition of the RandstadRail network to the HTM simulation model would enable analytic support for similar problems and planning issues on this network. This research focusses on analysing and systematically describing the Rand-stadRail signalling system, so that as a result of this research the network can be implemented into the HTM simulation model. The proposed system structure will be tested and verified with the use of practical test cases.

Figure 1.1: RandstadRail network. Edit from urbanrail.net (2014)

Basic rail system elements

1.2

For understanding a rail system it is required to know some basic rail terminology and elements. This terminology often differs with the countries or regions it is used in, therefore the basic terminology used in this report will be defined here.

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The infrastructure that is used by HTM consists of different routes, which together form the total network. A route is a collection of consecutive tracks and nodes between a source and a destination, as it is also defined by Pachl (2008). For a simple representation of a tram network, a node is defined as a stop, as a station or as a part on the infrastructure where a vehicle can switch from one track to another, which can be through a single switch or more complex intersections. In more detailed views a node can represent sub-elements of these high-level elements. An intersection is a joining of tracks that enables multiple tracks to cross at grade, or to enter the same track from different tracks. A line is a single route on which services are provided according to a schedule. On these line routes, transit stops are present at which vehicles stop to enable passengers to board or alight the vehicles. A collec-tion of transit stops of multiple lines in the same locacollec-tion is called a transit stacollec-tion, if it includes multi-ple platform tracks per direction and if it has additional waiting and transferring facilities for passen-gers. Lines are often connected through shared stops or stations, which allows passengers to change lines during their trip.

Apart from the infrastructure that is used for operating services (main tracks), there are also infra-structure elements that are used for sorting, storing and direction switching of vehicles. Depots or shunting yards are vehicle storage facilities which often consist of several parallel dead-end tracks. Some also function as a maintenance depot. For switching the direction of a vehicle, terminal loops or tail tracks are used. The first are used for one-directional vehicles, whereas the tail tracks are dead end tracks used to switch the direction of two-directional vehicles. The infrastructure that is used for main tracks must be equipped with a signalling system. This regulates vehicle movements for improv-ing the safety of the system. Side tracks used for storimprov-ing and sortimprov-ing vehicles only require signals at the point where the vehicles enter main tracks. Outside of this area vehicles are often moved manual-ly at very low speeds. Vehicles on main tracks need to be given movement authority by the signalling system in order to continue to the next track section.

Tram vs. light rail

1.3

The tram and RandstadRail network of The Hague can be distinguished by their operating speeds. The tram infrastructure and traffic regulations allow vehicles to operate on a maximum speed of 50 km/h, while the RandstadRail network allows speeds up to 80 km/h. To be able to safely reach this speed on the RandstadRail network a dedicated infrastructure with reserved lanes is used, which means that some tracks are isolated from other traffic and a block signalling system is used to separate vehicle movements on these tracks. This is characteristic for a so-called light rail system and is very similar to the infrastructure used for national heavy rail systems. In fact, the RandstadRail network is a former heavy rail track which was called the Zoetermeer Stadslijn and has later been converted to a light rail system. Tram infrastructure differs from light rail in the fact that it uses non-dedicated tracks that share their space with other traffic. It uses the basic traffic light system, called VRI in the Netherlands, to regulate traffic priorities. Since vehicles on this network interact with other types of traffic, the

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op-erating speed is lower and vehicles are much more susceptible to delays. Not every intersection is protected through the VRI system, therefore tram drivers regularly have to interpret situations on sight. Another difference is in the stopping regime; tram lines only stop at stopping locations where passengers request to board or alight the vehicle. On the contrary, RandstadRail stops at every stop-ping location, regardless of whether passengers need to get on or off. Furthermore, HTM trams are one-directional vehicles, whereas RandstadRail vehicles can drive in both directions. This influences on which parts of the infrastructure they are able to switch direction.

In the case of HTM and RET the RandstadRail vehicles run a light rail regime when travelling be-tween Zoetermeer or Rotterdam and The Hague Central Station (for line 3 & 4 this is up to the stop ‘Beatrixkwartier’). From there the HTM vehicles of line 3 and 4 continue their trip on a mixed tram/light rail infrastructure, between the stops Beatrixkwartier and Grote Markt, that also uses a block signalling system, but with different operating principles. After leaving this area they enter the shared tram network towards their end destination on the other side of The Hague, during which they operate according to the tram network protocol. The opposite order holds for the opposite direction of travel. The different signalling systems require these RandstadRail vehicles to be able to switch be-tween two types of operation.

The E line of RET enters the network from the direction of Rotterdam and then uses the same in-frastructure as line 3 and 4 of HTM between Nootdorp and The Hague Laan van NOI. From here the E line separates from line 3 and 4 and continues on its own infrastructure towards a dedicated end stop at The Hague Central Station, as shown in Figure 1.2. During undisturbed operation, the track section that limits the capacity of the whole RandstadRail network is generally assumed to be the part where the line 3, 4 and E share the same infrastructure. Here the total number of vehicles per hour using the infrastructure is the largest. This mainly depends on the amount of vehicles that can be processed by the block signalling system. This will be explained further in § 2.4.2.

Figure 1.2: E-line (blue) ending at The Hague Central Station. Zoomed in from Figure 1.1. Edit from urbanrail.net (2014)

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Example problems as case studies

1.4

For different reasons, the services that are offered on the network constantly change. Often aspects like service frequencies, routes and departure times are adjusted in advance when these changes are more or less planned and cause disturbed operations for a longer period of time. The main reasons for HTM to change its planned timetable are to change the offered service level or the scheduling of planned works. An example of both scenarios will be used in this research as a practical case for showing the added value of using simulation at HTM, as well as for testing the flexibility of the model.

At this moment RET is operating line E with a maximum frequency of six vehicles per hour for both directions. To fulfil the increasing customer demand they propose to increase the frequency of the E line to eight vehicles per hour during peak hours. Line 3 and 4 of HTM now operate services of, respectively, six and twelve vehicles per hour in each direction on this shared infrastructure. This would require this part of the infrastructure to process a total of twenty-six vehicles per hour for each direction, instead of the regular twenty-four vehicles per hour. The capacity of the network is not ex-actly known, but it is generally assumed to be operating near its maximum capacity due to the physi-cal limitations of the signalling system. Furthermore, whether this increase is possible without incur-ring too much delays that directly result from the timetable also depends on the timetable that is used. Here a simulation of the scenario could show what the consequences of increasing the line E frequency are.

The HSE case is one of many projects HTM is involved in that require an insight into the conse-quences of making temporary and permanent changes to the line routes or infrastructure. In the cur-rent situation the E line of RET uses two of the twelve heavy rail tracks of The Hague Central Station as a start and end stop of the line. The Dutch National Railways (NS) indicated some time ago that they would need all twelve tracks for heavy rail transportation in the future, which meant that an al-ternative should be found for the E line. This eventually resulted in the creation of plans for the con-struction of a dedicated terminal for this line (Gemeente Den Haag, 2014). These plans include that construction works will be conducted and that the dedicated part of the track for the E line near The Hague Central Station will be unavailable for at least six months in 2016. During this time the E line will be shortened and its end station will be a preceding station on the line. Consequently, RET asked HTM if it is willing and able to transport the passengers of RET to and from The Hague Central Station on the remaining route. A solution scenario is still being developed for this case by HTM, RET, SGH and the municipality of Zoetermeer, which includes an exchange of passengers between RET and HTM. Transporting the RET passengers by light rail is the most obvious solution, but would very likely mean that extra rail vehicles need to be used on the shared route with line 3 & 4. It is therefore un-sure if the HSE transportation scenarios can be executed without disturbing the operations. Among the alternative scenarios that have been considered are scenarios to transfer these passengers to the intersecting tramline 19 or to transport them by bus, however, these scenarios were found to include practical impossibilities and are not taken into further consideration at this moment. For the HTM to

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determine what the consequences of this scenario are, a capacity analysis of the network needs to be conducted.

Simulation at HTM

1.5

To analyse cases like the ones mentioned in § 1.4 it is increasingly more common to use the support of software tools. It is often hard to assess the consequences of changes in a rail network due to the high amount of dependencies. When these are modelled, it becomes easier to visualise and under-stand these consequences in a quick way. Especially the influence of stochastic occurrences like halt-ing times and disturbances on a rail system is hard to analyse manually or through analytical models and often requires the use of more advanced tools. Modelling and simulation is a suitable method for studying the behaviour of such a system in high detail (Siefer, 2008).

HTM and the Systems Engineering department at the faculty of Technology, Policy and Manage-ment of the TU Delft have cooperated over the past years to develop a simulation model that allows analysts and designers to evaluate their choices regarding the design of the rail system (Kanacilo & Verbraeck, 2005; Huang, 2013). It consists of a library of rail components that is based on the Dis-tributed Simulation Object Language (DSOL) suite (Jacobs, 2005). This resulted in a model that de-scribes the tram network in high detail and allows the simulation of individual vehicles on this network as a result of the inserted timetable. Objects at the level of e.g. sensors and traffic lights, including their behaviour, are used in the model. Some objects can be combined into coupled models, which are modular compositions at a higher hierarchical level. In an object-oriented way the infrastructure and signalling system are modelled and they interact with vehicles through a discrete event-messaging system. These events communicate the state change of an object with other objects that depend on this state. These events result in changes in vehicle motions, which are determined through solving differential equations. The model can be used for a variety of analyses, like determining the capacity of the infrastructure, calculating running times between stops, testing infrastructure designs, detecting timetable conflicts, determining delays resulting from the timetable or the operation, etcetera.

Currently, this model is still in the development phase and is not yet used by employees of the company, since it still lacks a user interface and usable output. These are now being developed by an external software company, which will also perform the final delivery and maintenance of the model for the HTM. Another problem concerning the model is the fact that the RandstadRail network is not yet included in this model. This is partly due to the difference in complexity of the operating logic of the two signalling systems, where the block signalling system of RandstadRail has a higher complexity than the tram system. This is caused by the overlapping control of blocks by control units. HTM wants to expand the current simulation model so that it includes the RandstadRail network, in order to be able to analyse this network and its interaction with the tram network. It could then be used for sup-port in problem solving, e.g. for problems similar to the HSE case. The software company is, however, not familiar enough with the logic of the block signalling system to be able to include it in the model.

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Research objective and approach

1.6

So far the motivation of this research can be derived from the previous sections. A descriptive analysis of the RandstadRail infrastructure and structure of the signalling system is required in order for the software company that maintains the HTM simulation model to be able to complete it. To guarantee a valid and working model that is easy for them to maintain in the future it is preferable that they will also perform the final implementation of the RandstadRail network into this model. This will guarantee their familiarity with the structure and logic of the complete model. In addition, for the scope of this research it would be too extensive to get acquainted with the source code of the existing simulation model in order to implement the RandstadRail system directly into the model. Therefore, a goal of this research will be to provide a way to clearly formulate the logic behind the signalling system, so that the external company can further develop the model based on this representation. In order to clearly formulate the structure of this system, so that it can be interpreted unambiguously, it would be a good idea to represent it in a structured model. This static model should create a clear overview of the RandstadRail signalling system structure, which can then serve as a basis for further development of a dynamic simulation model.

Inclusion of the RandstadRail network into the HTM simulation model allows designers and ana-lysts at HTM to analyse the entire network, including the influence of both networks on each other, making it an integrated model. Having both networks in one model, instead of using separate models, also adds to the user-friendliness and to the consistency of use and quality of output of the model. The last is especially important, since the effects on one network can have an influence on the other and vice versa.

After describing the operational logic of the RandstadRail infrastructure, the result will have to be validated. In addition, the practical cases can be used to show how this descriptive static model can be applied for performing dynamic calculations. For these purposes a dynamic model will have to be developed that is able to replicate the system’s behaviour and can produce relevant output, as well as determine the consequences for these cases in terms of vehicle capacity of the network. Based on the preceding observations, the following main research question can be defined:

How can the block signalling system of the RandstadRail network be described in a structured way, with the goal to support future implementation of this system into the existing HTM simulation model, and how can this be used to perform network capacity studies?

To answer the main research question in a structured way, it is decomposed into the following sub-questions:

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How can the working of the block signalling system of the RandstadRail network be presented in a structured way to make it easily translatable to the HTM simulation model structure?

How can the RandstadRail network capacity be calculated, using the static model as a basis? What can be concluded about the practical cases when applying the resulting model?

For providing an answer to the last three questions, the development of a separate simulation model as a part of this research is considered to be a suitable method. It provides a quantitative validation method for the structure of the static model as well as a tool for analysing the capacity of the net-work. Furthermore it improves the understanding of the system by being able to see its behaviour in a dynamic environment, which can also be supportive for the software company during implementation of the system into the existing simulation model. To reproduce the logic of the RandstadRail system in a simulation model, first an analysis of the signalling system should be made. As said before, the translation of the outcome of the analysis into a static descriptive model could be a good way to pro-vide a structured and clear description of the rail system, which can then be used for the development of both simulation models.

A suitable method for systematic analysis and modelling is the ‘Delft Systems Approach’ (DSA) (Veeke, Ottjes & Lodewijks, 2008), which will be used in this research for representing the signalling system. According to Veeke & Ottjes (1999) the approach has a process-oriented and hierarchical structure, which allows for a natural way of communication and a balanced model with a clear structure. Both characteristics are of importance for reaching the goal of this research, since they help in getting a quick understanding of the system. The hierarchical structure corresponds to the structure of the existing simulation model, which makes a translation more straightforward. Chapter 3 will explain this in more detail. Veeke & Ottjes also propose the use of the simulation package TOMAS2_for

simulating such a system, since this tool also uses a process-approach for modelling a system. It therefore enables to use a similar structure as for a descriptive model, which makes the translation an easier and more manageable process. This ‘toolbox’ for Delphi will be used in this research to create a simulation model of the RandstadRail network. It will then be validated using empirical data, to check if the behaviour that is simulated by the model corresponds to reality. After validation the model will be used for studying the practical cases.

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Thesis outline

1.7

The research questions stated in the previous section will be answered in the report. First an introduc-tion to the background that is used for this research is made and a problem statement is formulated in Chapter 2. Here the characteristics of rail systems in general are discussed, as well as an explana-tion of the RandstadRail system, the cases that are used in the report are introduced and a general review of railway simulation is presented. The first research question will be answered by this chapter. Chapter 3 contains the performed analysis and the systematic description of the RandstadRail system, this will provide the framework for further analysis and will answer the second research question. The third research question will be answered by describing the created simulation model in Chapter 4, after which the model will be validated in Chapter 5. In Chapter 6 the model is used to determine the consequences of the choices made in two practical case studies. Chapter 7 will be used to draw the final conclusions and discuss the outcome of this research.

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Background & problem statement

Chapter 2

This chapter aims to clarify the current problem situation at HTM, for which a solution needs to be found, and to create a context for supporting further analysis. From Chapter 1 it became clear that HTM is looking for a way to incorporate the RandstadRail network into the existing HTM simulation model, in order to make it complete and produce a reliable and accurate output. It can then be used for calculating the capacity of both networks, however, the model is intended for a broader range of applications and the need of HTM to include the RandstadRail network goes beyond the need for per-forming capacity studies. Before going into detail on the problem description and the use of simula-tion, the definition of capacity is first described in § 2.1 to define what needs to be analysed. To get a view on the different planning and design stages in a railway system that require (computerised) ana-lytical support, these are described in § 2.2 for general railway operation. Before continuing with the analysis of the signalling system in Chapter 3, first the HSE case and the influence of the design of the RandstadRail infrastructure on its capacity will be explained in more detail in § 2.3 and § 2.4. To un-derstand how simulation can contribute in a railway system and to get an extended view on the ap-proaches that are generally used in rail simulation, § 2.5 discusses the advantages, disadvantages and general modelling methods found in literature. In addition, examples of existing railway simulation applications are given in § 2.6. The intended use and structure of the HTM model in specific is de-scribed in §2.7.

Definition of capacity

2.1

HTM requires to know the capacity of its network to be able to make decisions regarding the use of it. Capacity, however, is a complex and ambiguous concept. It is therefore necessary to understand what capacity is. The International Union of Railroads says the following about capacity (UIC, 2004): Capacity as such does not exist. Railway infrastructure capacity depends on the way it is utilised. The basic parameters underpinning capacity are the infrastructure characteristics themselves and the in-clude the signalling system, the transport schedule and the imposed punctuality level.

They state that capacity consists of a balance of interdependencies between the number of trains, the average speed, the stability and the heterogeneity of services. This balance is graphically displayed in Figure 2.1.

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Figure 2.1: Railway capacity balance (UIC, 2004)

This figure also shows some differences between mixed-train operation, as is customary for heavy rail transportation, and metro operation, which in this case is similar to the HTM RandstadRail operation. For metro operation the number of trains and the stability is rather high, since there is often only one train type running the same kind of service (homogeneous) and the average speed is much lower than that of heavy rail trains, so vehicles can drive at a closer range. The capacity is indicated in the figure by the length of the lines connecting the axis. In addition, Landex (2009) adds capacity consumption as a fifth measurement. He argues that a high capacity consumption leads to a high risk of knock-on delays for the following trains. However, this can also be seen as part of the stability.

To determine the capacity of a rail system, it needs to be determined within what limits the system can perform at an acceptable level. Choosing a too high value for one of the four parameters should result in a decrease of one of the other parameters if the maximum capacity is reached. A way to determine the theoretic maximum capacity on the RandstadRail network would be to introduce as many vehicles as possible in a homogeneous way, without causing delays. In practice, the actual timetable will play an important role in deciding where to insert extra vehicles. Also the resulting quali-ty, in terms of frequency and delays, that is delivered to the customer needs to be considered ac-ceptable.

Railway system in general

2.2 Configuring resources

2.2.1

Railway companies continuously need to improve their quality and quantity of operations to deal with an increasing transportation demand due to increasing mobility, or are forced to operate more effi-cient to maintain the current service level as a result of economic decline. Expanding the infrastruc-ture to cope with growth in demand can be too costly, while increasing the number of vehicles is also

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a big investment and could go at the cost of punctuality due to a high infrastructure occupation. It is therefore important to find an optimal configuration of resources for the operational process, in order to obtain the maximum service level with the available resources.

Marinov et al. (2012) state there are two types of resources that influence the processing capacity of the components of a railway system. The first are static resources, which are all infrastructure components, such as tracks, lines, signals, platforms, junctions, switches etc. The second include dy-namic resources, like passengers, locomotives, train sets, maintenance machines, but also staff, plans and schedules. These resources need to be used in a coordinated way to guarantee a certain perfor-mance level. Through improving the planning processes of these resources, the coordination can be improved. The topic concerning research on optimisation of railway operations that is most found in literature is the aspect of timetabling. This plays a central role in combining infrastructure, vehicles, personnel and passengers with the goal to provide the transportation demand that is required. Creat-ing the most optimal timetable is a big challenge, which is dependable on the plannCreat-ing and realisation of these resources.

Planning phases

2.2.2

The planning of a railway system can roughly be divided in long-term, medium-term and short-term planning tasks (Pachl, 2008; Radtke, 2008; Siefer, 2008; Vromans, 2005). Long-term planning con-sists of measuring and predicting the demand for transportation, from which the infrastructure lay-out and train paths (lines) are created. The expansion of infrastructure needs to be aligned with the ex-pected demand for transportation and the required lines. The frequency of trips on the lines roughly determines the required capacity of the infrastructure. Also the approximately required amount of vehicles for operation can be determined from these plans. During this planning phase relatively few information is available, so the amount of assumptions that are made about e.g. running times and schedules is high. To support the long-term planning process, simulation could be used for determin-ing routes of train paths or testdetermin-ing the infrastructure design on operational performance.

Medium-term planning concerns a time window of approximately one year. This is where the drafts that were created in the long-term planning process are translated into a timetable. Running times are determined through test runs or recently realised trip data and from these the departure and arrival times at stations can be calculated. Also a vehicle maintenance schedule is created or adjusted by the maintenance department. While constructing the timetable, a great number of facets have to be taken into account. The connection of different lines at stops and stations should be tuned to make sure long passenger waiting times are prevented while transferring. Conflicts between vehicles at stops and intersections or simultaneous use of tracks have to be prevented by shifting trip times or implement-ing buffer times at stops or a certain headway between vehicles. The last represents the time be-tween each consecutive vehicle. A homogeneous supply of services over time is pursued when creat-ing the timetable, in order to offer travellers the comfort of regular arrivals at any time. The precedcreat-ing is a process of constant iteration, e.g. by improving the connectivity at one stop, a conflict could arise

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on another part of the line. The trips that are finally created in the timetable are then filled with crew duties. These are duties that are created according to the constraints of the collective labour agree-ments of the company. The total process of creating the timetable and crew duties is a complex task that has to deal with a great number of constraints. Many analytical tools therefore exist to support railway planners in the different steps of timetabling. With the help of these optimisation tools a theo-retic timetable can be created that complies to all the rules that were set. However, these tools often do not show how the created timetable performs in real operation, under the influence of mostly sto-chastic effects. This is where simulation is able to help, by providing a way for testing the timetable in an operational scenario. When running times are modelled through defining the acceleration charac-teristics of the vehicles, it becomes possible to determine running times on new routes or new parts of infrastructure.

When the creation of a ‘framework’ is done, the short-term planning phase starts. Short-term planning is done from once a year up to tasks that are planned on a daily basis. They include the as-signing of personnel to the created crew duties, the assignment of vehicles to trips in the timetable and the daily rescheduling of disturbed operations by the traffic control centre. Especially the last problem receives much attention in recent research on railway scheduling problems (Marinov, Sahin, Ricci & Vasic-Franklin, 2012). Both planned and unplanned disturbances occur during operation, caused by e.g. maintenance works, weather conditions or accidents. These disturbances cause delays in operation, which require action to bring the system back to normal operation. When vehicles break down, or need to be rerouted due to the unavailability of infrastructure, it could happen that the vehi-cle schedules are deranged. Especially when a vehivehi-cle was planned for maintenance at a specific loca-tion this can be highly undesirable. These situaloca-tions require difficult rescheduling acloca-tions from traffic controllers. This includes evaluating different scenarios within a short time frame to find the best solu-tion. Even today this is often done manually based on experience of the traffic controllers. Here, com-puter support can be very helpful in evaluating the different solutions and selecting the best actions.

HSE case

2.3

As was mentioned in § 1.4 the construction works of the HSE project will cause the E line to be short-ened for approximately half a year in 2016, due to the unavailability of the dedicated track between The Hague Central Station and Den Haag Laan van NOI (Figure 1.1). At the moment of writing this report, multiple solution scenarios for transporting the E line passengers back and forth to The Hague Central Station are still being discussed by HTM, RET, SGH and the municipality of Zoetermeer. These solution scenarios are required to offer an acceptable transportation alternative for these passengers. ‘Acceptable’ is a loosely defined term that consists of a combination of different requirements, which are discussed by the four stakeholders mentioned above. For example, the total extra travel time or number of extra transfers for passengers should be as low as possible, the costs of the measure may not be too high and the solution should be acceptable for all stakeholders. One of these scenarios

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involves transporting the E line passengers with HTM services, by increasing the amount of vehicles of line 3 (for a more detailed schematic map of the network, see Appendix B). This extra capacity can then be used to transport the passengers of the E line. This will require transferring the passengers at a stop on a shared part of the infrastructure, somewhere between the stops Den Haag Laan van NOI and Leidschenveen. The last offers a nearby buffer track, called Pijlkruidveld, that allows vehicles to switch direction outside of the normal operation, so with minimum disruption for other services. The insertion of extra vehicles will result in a more compact timetable in which the interval between vehi-cles will be smaller on a short part of the infrastructure. Furthermore it will need to fit as good as possible within the current timetable. The question that arises is if this is possible within the current infrastructure layout. It is required to observe that this scenario requires the use of additional vehicles to provide extra passenger capacity. HTM should therefore be able to supply these extra vehicles to be able to implement this scenario. At the moment of writing there are no extra vehicles available, but there are six coupled vehicles that run in a coupled service that could be uncoupled during this sce-nario to be made available during this time period. The number of passengers that have to be trans-ported is not yet known to HTM, so the exact capacity that needs to be offered to transport every passenger is also unknown. Since the E line runs at a frequency of six vehicles per hour, these addi-tional six vehicles of HTM should be enough in terms of passenger capacity.

Figure 2.2: Zoetermeer part of the RandstadRail network. Zoomed in on Figure 1.1.

RandstadRail infrastructure capacity

2.4

In § 1.3 the difference between the tram and the RandstadRail network was briefly discussed. This section will describe what aspects of the RandstadRail infrastructure influence the network capacity.

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Lines in operation

2.4.1

On the HTM part of the RandstadRail network, the infrastructure mainly consists of one route, but in Zoetermeer it splits in a route that continues in the same direction (line 4) and a route that circles around a number of districts in the city (line 3), as can be seen in Figure 1.1 and Figure 2.2. Note, however, that these figures only show the routes of the lines that are operated, not the actual layout of the infrastructure itself. Although these don’t differ much, the figures might give the idea that cer-tain vehicle movements are not possible, while in reality they are possible. In the timetable that is currently operated by the HTM, line 3 operates approximately every 10 minutes in both directions3_,

but during peak hours the number of trips is doubled on a part of the route west from The Hague Central Station (on the tram network) as an extra trip is inserted after every regular trip. Line 4 also operates approximately every 10 minutes in both directions and the number of trips is doubled for a part of the day on the RandstadRail network and a part of the tram network, but here extended peak hours are used. A part of the RandstadRail infrastructure is shared with the E line, which the E line vehicles enter and leave through their own infrastructure, as can also be seen in the mentioned fig-ures. The E line also operates with a 10 minute interval for most of the day, but in the evening, after peak hours, it switches to a half hour interval4_{. When looking at the occupation of the infrastructure of}

the complete HTM RandstadRail network over a day, it is expected that the maximum occupation will occur during peak hours on the part where line 3, line 4 and the E line are joined together. This is also what is generally assumed to be the ‘capacity bottleneck’ of the RandstadRail system by employees of HTM.

Block signalling system

2.4.2

The network uses a block signalling system for safety and is not influenced by other traffic, which together enables the network to operate at a higher speed than the tram network. The signalling sys-tem has the aim to protect against the collision of two rail vehicles or of a rail vehicle with other traffic at a level crossing. It also intervenes when a vehicle drives at such high speeds that the vehicle could derail (van Amstel & Gerritsen, 2006). This is done through the use of block sections.

A block signalling system is based on the fact that rail vehicles have a large braking distance, which makes it impossible to stop in time when driving at high speeds if the driver has to spot the vehicle in front of him on sight (Pachl, 2008). Vehicles are therefore separated by blocks, which are controlled by signals. A block is an area that can generally contain one vehicle and usually has approx-imately the size of the braking distance of this vehicle at the maximum allowed speed. A signal gives information on the movement authority of a vehicle for the next block. It will indicate a red signal if

3_{http://www.htm.nl/reisinformatie (retrieved 20-5-2014)}

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the next block already contains a vehicle and will only clear if the block is empty and it is safe for the next vehicle to enter. In addition to a red signal the RandstadRail signalling system generally uses a yellow and green signal. Yellow indicates that it is safe to drive to the next block, but the next signal is red and the speed needs to be reduced to be able to stop for this signal. A green signal indicates that it is safe to drive to the next block at the allowed speed. With the use of these signals it is possible for a driver to react in time to make the vehicle stop at the required position.

Since every block can contain only one vehicle, these blocks also greatly influence the capacity of the network. Theoretically, if the blocks are made smaller, the capacity rises and vice versa. The logic and communication that control the signals also influence the flow of vehicles. Especially at intersec-tions it often happens that two vehicles want to enter a block at the same time. The way these situa-tions are handled also influences the capacity of the network.

To make sure that vehicles comply to the signals and do not accidentally continue at too high speeds or ignore the signals the RandstadRail network uses an automated braking system (van Amstel & Gerritsen, 2006). This system has a maximum speed profile that varies throughout the block ac-cording to which a vehicle is automatically slowed down if it exceeds this speed. This only happens at a speed of 10 km/h or higher. This way human errors at high speeds are corrected to maintain a safe operation.

Railway simulation theory

2.5

The previous sections were used to explain general planning and design problems as well as the HSE problem. The next sections will be used to go into more detail on rail simulation in general and the HTM simulation model. This section starts with discussing the advantages and disadvantages of using rail simulation and explaining general rail simulation theory.

Advantages and disadvantages

2.5.1

Simulation creates an environment in which important properties of a system and external influences on this system are replicated and can be changed to see how the system reacts. For railway systems, a railway simulation model of the system can be a great design and analysis tool. According to Siefer (2008), ‘in this laboratory, infrastructure and timetables can be changed and modified in different ways. The virtual laboratory has no limitations and is much more cost efficient than a physical experi-mental model’. This emphasizes the general usefulness of using rail simulation. Part of the limitations of a physical model is the fact that railway timetables often have a high density, which makes it very difficult to experiment in real operation without causing delays. Simulation therefore makes it possible to perform analyses that would otherwise require too much sacrifice.

The scenarios that need to be analysed mainly consist of a combination of trains, infrastructure, timetables and personnel. Due to the high amount of changing variables in these scenarios it is often not an option to perform calculations by hand. Computer simulation enables to perform these

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calcula-tions in a short amount of time. It is therefore also much faster than experimenting in real time. Keen and Sol (2008) state that simulation can often produce surprising results that are sometimes counter-intuitive to decision makers. They say the reason for this is that ‘the human intuition cannot predict the collective dynamics of systems containing thousands of parameters’. They have the opinion that simulation is not yet fully accepted as a decision enhancement tool, but that it is essential to use such models to be able to make key decisions about future scenarios.

Vromans (2005) compares rail simulation to the much applied analytical methods to describe its advantages and disadvantages. He mentions that simulation models often include a bigger part of the network (usually the entire network), as opposed to an isolated part, and have a higher level of detail. Analytical models generally have a more abstract or focussed nature. He also mentions that simulation models have the possibility to use any distribution for any process or input, whereas analytical models are often based on restrictive forms of input distributions. This is especially useful for introducing sto-chastic variables, like disturbances. Also the output format that is generated by the model differs. Where analytical models are often focussed on one or a few types of output, simulation models repli-cate the entire process and are therefore able to generate almost any type of output. The possible output formats depend on the amount of detail that the model contains. Vromans also adds the possi-bility to include animation as a benefit. Animation helps to better understand the processes and re-sults of the model.

Simulation also has some disadvantages that need to be taken into account. First of all, to create a detailed simulation model, a high amount of data is required. It then requires expert knowledge on both model development as well as rail systems to develop and maintain a model from these data (Thompson, 2001; Keen & Sol, 2008). The data and knowledge that is needed has to be acquired and time needs to be invested for development. This can be an obstacle for deciding to develop such a model.

The preceding factors also affect the costs for model development. Additional costs might need to be made for providing the right hardware infrastructure, like a computer server, and for a possible system for collecting missing data. This can increase the initial costs of the model to a high level. Of-ten these costs are compensated by the future benefits of the model, but they need to be taken into account before starting the development phase.

The use of distributions in a simulation model allows to see how the system reacts to fluctuating input variables, but these distributions often also include some assumptions. Especially disturbances are usually unpredictable, but are often modelled through the use of distributions. A high number of assumptions can create a high level of uncertainty in the model. It is therefore advisable to use empir-ical data for these situations if this is possible.

Simulation is a great tool for replicating the behaviour of a system for different scenarios, but it will not provide solutions for occurring problems. Pure simulation sticks to evaluation of the system and shows how the system performs. For further improvement of the system, manual adjustments or

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ad-ditional optimisation tools are required. Some commercial simulation tools already include such opti-misation tools in the model, but these are based on separate algorithms.

Infrastructure modelling

2.5.2

The classification of rail simulation models is generally done in a number of classes. The first classifi-cation concerns the level of detail that is used in the model. Rail infrastructure modelling is usually done through structures derived from graph theory (Radtke, 2008). This splits up the infrastructure model in nodes and links, where nodes often represent an arbitrary location in the network (stop, station, junction, etcetera) and links are the connections between these nodes. Such a structure makes the model modular and flexible. The same representation can be used on different hierarchical levels. The content of these nodes and links depends on the level of detail in the model. Often the nodes are positioned at points in the network where changes in one or more properties (for example the speed limit) or physical directions take place. Figure 2.3 shows such a node-link representation. The level of detail of the infrastructure often depends on the purpose of the model. When it is used for long-term planning tasks, like route determination or average running time calculation, a more abstract model often suffices. This limits the amount of data and calculation capacity needed to run the model and keeps the model redundancy free. Such a model is called a macroscopic level model and is usually limited to contain routes and stops or stations (Radtke, 2008). For more accurate anal-yses, like short-term planning tasks, a model needs to consist of more detailed infrastructure.

Figure 2.3: Node-link representation of infrastructure (Radtke, 2008)

Such a model includes detailed elements like signalling system components, individual switches and tracks and their speed limits. A mesoscopic model generally contains elements with a detail level that is between a macro- and microscopic level.

To illustrate the main difference between macroscopic and microscopic infrastructure models, Radtke (2008) gives an example of a running time calculation. Figure 2.4shows a section of rail infra-structure modelled in a macroscopic and microscopic way, including the corresponding speed limits. The macroscopic model uses a speed limit that is an average of the microscopic speeds over the dif-ferent lengths (96.51 km/h). Radtke performed running time calculations on both models and showed

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a difference in running times between +6% and -20%. Due to this inaccuracy macroscopic models are not suited for performing detailed and accurate tasks. This shows that the scale of the model should be chosen to fit the purposes of the model.

Figure 2.4: Difference between microscopic and macroscopic railway modelling (Radtke, 2008)

Processing techniques

2.5.3

The techniques that are used for executing processes in simulation modelling differ to some extent. This is due to the development of different scientific theories, of which often a specific processing technique is preferred depending on the nature of the system that needs to be modelled. Zeigler et al. (2000) call these modelling formalisms and mention the following types:

 Differential Equation System Specifications (DESS)  Discrete Time Systems Specification (DTSS)  Discrete Event System Specifications (DEVS)

In literature these are also often classified as continuous or discrete, where the DESS formalism is a continuous formalism. Continuous formalisms are traditionally used to model systems that progress continuously over time. It is especially suited for modelling systems that are well-represented by dif-ferential equations, like vehicle motions, and need continuous updating of their state. Due to continu-ously performing calculations this formalism requires a high computer capacity. Discrete methods only execute processes at fixed moments in time. These formalisms can be used when the system is dis-crete by nature, or when required accuracy of the model allows to determine the states of its objects at discrete moments in time. Important in using a discrete formalism is to make sure the chosen in-tervals at which the state of an object is determined produce an accurate representation of the real behaviour of the system. According to Zeigler et al. it is increasing common practice to use a com-bined discrete and continuous model, where the system is divided in sub-systems that can use differ-ent formalisms, depending on their nature. The discrete evdiffer-ent formalism is a variant that uses the