19International Journal of Civil Engineering. Vol.8, No. 1, March 2010

1. Introduction

So far, railway timetables are based ondeterministic running, dwell and headway timesbetween stations. These times are mostly scaledin minutes and refer to a virtual stopping point atthe stations. Small variations of the service timesare compensated by standard running time anddwell time supplements, as well as margins(buffer times) between the train paths. Thedetermination of supplements and buffer times inpractice, however, is mainly based on rules ofthumb, sometimes validated by simulation, andonly seldom verified by means of statisticalanalysis of real-world operations data.

Stochastic analytical approaches, like queuingmodels [1, 2, 3, 4, 5] assume the train intervalsand the service times to be independent randomvariables, which is questionable in case ofperiodic timetables with high frequencies. Thevariation of inter-arrival times and minimalheadway times is modelled mostly on the basis ofassumed, not validated random distributions forinter-arrival and service times. The estimatedwaiting time of a timetable is a function of the

track occupancy and the coefficients of variationof the scheduled headway and service times ofindividual lines and/or stations, which cannot beeasily extrapolated to multi-channel servicesystems and complex networks. Scheduledwaiting times generated by stochastic variables ofthe timetable are clearly distinguished fromestimated original and consecutive delays duringoperations.

Combinatorial optimisation models are usedmore and more for strategic line planning in largecomplex networks, timetable design, rollingstock and crew scheduling [6, 7, 8]. The modelsaim at solving the formulated (timetable)problem for a certain objective function underpredefined constraints to optimality and, thus,generating an optimal design for the individualdeparture and arrival times in a network. They arecomputed via (Mixed) Integer LinearProgramming ((M)ILP) by means general-purpose solver or by using Lagrangian relaxationand heuristic methods. In general, optimisationmodels apply deterministic variables forsearching the optimal value of the objectivefunction, like minimisation of overall runningtimes in networks, at given constraints likeminimal headway and transfer times betweentrains. The first known stochastic optimisationapproach for estimation of the robustness ofrailway timetables is presented by Vromans [9].

Railway Network Timetabling and Dynamic TrafficManagement

I. A. Hansen*

Received: September 2009 Accepted: February 2010

Abstract: The paper discusses the current state of research concerning railway network timetabling and trafficmanagement. Timetable effectiveness is governed by frequency, regularity, accurate running, recovery and layovertimes, as well as minimal headway, buffer times and waiting times. Analytic (queuing) models and stochastic micro-simulation are predominantly used for estimation of waiting times and capacity consumption anlong corridors and instations, while combinatorial models and stability analysis are suitable for network timetable optimisation. Efficienttraffic management can be achieved by real-time monitoring, fusion, analysis and rescheduling of railway traffic incase of disturbances. Real-time simulation, optimisation and impact evaluation of dispatching measures can improvethe effectiveness of rescheduling and traffic management. The display of dynamic signal and track occupancy data indriver cabins, as RouteLint developed by ProRail, can support anticipative actions of the driver in order to reduceknock-on delays and increase throughput.

Keywords: timetabling, attratciveness, waiting times, punctuality, conflict detection, traffic management,

* Corresponding author. Email: I.A.hansen@tudelft.nl

Professor, Department of Transport & Planning,Delft University of Technology.

20 International Journal of Civil Engineerng. Vol. 8, No. 1, March 2010

Micro-simulation models, like STRESI [10],RailSys [11], OpenTrack [12] or ATTPS [13] areused to estimate the effect of exogenous randomprimary delays on track occupation andconsecutive delays of hindered trains. Theinduced primary delays are drawn from assumedor empirical distributions for a given timetable,track infrastructure and signal system. Kaminski[14] introduced a heuristic limit for the buffertime distribution at bottlenecks in order tocompensate for 80 % of the primary delays.Carey & Carville [15] presented a heuristicapproach for solving conflicts between trainpaths and routes and simulation of random delaysin order to test the reliability and robustness oftimetable options.

This paper will first describe the principles ofscheduling and periodic railway networktimetables focusing on the estimation of capacityconsumption and the optimisation of timetableparameters. Then, the requirements andcharacteristics of advanced information anddecision support systems for dynamic railwaytraffic management are presented in order toevaluate their impact on train drivers’,dispatchers’ and network performance. The paperconcludes with remaining issues for furtherresearch and development.

2. Timetabling

Railway schedules are necessary for thecoordination of resources in different planningand production stages in order to match transportdemand and capacity and to inform stakeholdersand customers. Timetables must assure that theexpected transport demand can be realisedaccording to the requirements of passengers,shippers, train operating companies,infrastructure manager and public authoritieseffectively and efficiently. Effectively means ahigh quantity and quality of availableinfrastructure, rolling stock, personnel, transportand traffic services, while efficiently requires amaximum output with the least possible input.

The principal goal of railway transport is toattract a maximum number of customers and loadon planned or existing lines with a minimum ofinvestment cost, personnel, equipment, energy

consumption, operating and maintenance costs.The acceptance by passengers, shippers andpublic authorities depends in a competitivemarket on performance criteria as speed,frequency, comfort, reliability, punctuality, safetyand price of services [16, 17].

The effectiveness of a timetable can beexpressed by indicators as:

• Number of trains, passengers and load pertime period,

• Amount of passenger-kilometre and ton-kilometre per time period,

• Operating and circulating speed of trains,• Headways and buffer times,• Scheduled waiting times,• Time and effort for modification and updating

(reschedule).

Distinction is made between non-periodic andperiodic timetables. The latter are more and moreinternational standard, because cyclic(‘clockfaced’) timetables are easy to rememberfor passengers and easier to handle for railwaypersonnel. The scheduled intervals between thetrains of the same line of a cyclic timetable areregular over the (daily) service period, but maybe increased to an integer multiple of the base

Fig. 1. Periodic timetables (source: Liebchen [18])

21I. A. Hansen

interval or decreased by an integer divisor e.g.during peak periods. The trains from bothdirections of a line then meet each other twiceduring one interval creating a symmetry axis ofthe train graph if the running times per directionare not (much) different. A symmetric cyclictimetable (Fig. 1) exists if the symmetry axes ofall lines are identical e.g. situated at every fullhour. Integrated cyclic timetables in networks arecharacterised by scheduled transfer connectionsbetween different lines at (major) railway stations(‘hubs’), where the trains meet each other atregular intervals (at least hourly).

The quality of timetable design for a giventraffic demand, rail infrastructure and train mixdepends mainly on:

• Frequency• Regularity• Precise and realistic running an dwell times• Sufficient but not too large recovery times• Exact minimal headway times between

different pairs of trains,• Estimated waiting time.

2.1. Frequency

The higher the train frequency the moreattractive it is for the customers, but the higherare the operating costs. Depending on the tripdistance, transport demand, car ownership andcompetition with other modes in the area served,an average frequency of e.g. 6(12) times/(peak)hour and direction can be considered as excellentfor heavily loaded national (regional) passengerrailway lines, while 2(4) times/hour issatisfactory for less loaded lines and time periods(Tab. 1). Only in densely populated metropolitan

areas higher frequencies than 12 times per hourper track might be needed. A passenger trainfrequency of less than once per hour frequencyper direction must be considered as poor.

For freight trains a frequency of twice a dayper direction is good, while less than once a day(week) per direction for regional (international)lines may be considered by shippers as ratherinappropriate.

2.2. Regularity

A high level of regularity of scheduled servicesis very important for high frequent passengerlines in order to avoid hinder due to overloadedplatforms and trains. Irregularity of a timetablecan be easily computed through the standarddeviation of the scheduled intervals betweentrains at stations in a network. The smaller thestandard deviation, the higher is the regularity ofthe planned train services. The regularity of linesor certain stations in a network may be weighteddifferently according to their importance.Regularity of train operations is generally morecritical than that of schedules.

2.3. Running and Recovery Times

Deterministic running times at a scale ofminutes are standard in most railway timetables.Only very densely occupied railway lines in somecountries as Japan or metro lines, so far, applymore accurate scheduled running times scaled at10 to 15 seconds. A major reason is the inabilityof train drivers to perform better without moreprecise on-board information and advancedsupport. Another reason is the common practiceto add certain running time supplements to the

Passenger train lines/h dir Local Regional (Inter-) National

Freight train lines/d dir Regional (Inter-)

NationalA Excellent 12 6 3 4 4 2 4 B Good 6 3 1 2 2 1 2 CSatisfactory

4 2 0.5 1 1 0.5 1

D Poor 2 1 0.25 0.5 0.5 0.5

Table 1. Quality levels of train frequencies

22 International Journal of Civil Engineerng. Vol. 8, No. 1, March 2010

nominal ‘technical’ running times in order toenable easy recovery from small delays withouthinder for other trains. Many railways apply astandard running time supplement of 7%, asrecommended by UIC, which is meant to coverrunning times up to 93% of the right tail of anormal distribution. In fact, the scheduledrunning times and required supplements can beestimated much more accurate, provided detailedstatistical analysis is made of empirical trackoccupation and release data (see chapter 3.1).

Empirical distributions of exact running timescan be easily derived from track occupation andrelease data which are recorded and savedautomatically by the existing signalling andsafety system.

As these data only contain the passing timesper train number at main signals and these aredistant from the stopping points at platforms theadditional deceleration and acceleration timerespectively from and to the last (first) mainsignal needs to be estimated taking into accountthe remaining distance between the last/firstmeasuring point and the stop location, as well asthe train characteristics (length, weight, power,standard deceleration/acceleration rate). At TUDelft the tools called TNV-Prepare and TNV-Filter [20] have been developed by which therecorded passing times at signals and insulationjoints of any train can be filtered and the realrunning times and delays per train series becomputed automatically according to their route,

type and period of the day. The true minimal running times per link can be

revealed at a precision of seconds by selectingonly those trains that were delayed at thepreceding departure station and experienced nohinder. The percentile of running times at acertain level of probability can be estimated bystatistical analysis of the precise running timesper train line.

The running times depend on the alignment,number of dwell times at intermediate stops,type, length and weight of rolling stock operatedas on the behaviour of the train drivers andweather conditions. The running timedistributions per train line can be used forestimation of the amount of recovery time insteadof using a standard supplement.

2.4. Minimal Headway and Buffer Times

In practice, timetable designers mostly applystandard mean minimal headway times (2 to 5min) between train paths depending on the typeof conflict and train sequence. The existing buffertimes in a conventional graphical timetable whichindicate only the train paths and headway times ata scale of minutes cannot be determinedsufficiently, because these do not indicate theprecise start and end of the capacity consumptionaccording to the prevailing signalling an safetysystem.

Fig. 2. Frequency of running time peak factors ofpassenger trains [19] Fig. 3. Blocking time diagram [21]

23I. A. Hansen

The minimal time headway between two trainson a railway route is governed by blocking timesof trains and its speed differences [21, 22]. Theblocking time diagram of a train (Fig. 3)represents the time instances that a train needs torun safely without hinder at design speed over asequence of track sections. The scheduled trainpaths virtual as well as the track occupancy timesare represented in a time-distance diagram andindicate clearly the remaining buffer times. Anyoverlap between the blocking times of differenttrains clearly indicates a timetable conflict, whichneeds interaction in order to avoid a decelerationor stop of the following train.

The blocking times depend not only on thesignal spacing and train length, but also on theactual train speed and deceleration rate. If themovement authority for the train at sight distanceof the distant signal is given late because ofinsufficient headway to the preceding train, thefollowing train would be deceleratedautomatically, which means an increase of theblocking time.

Furthermore, the scheduled dwell times areoften exceeded during operations, which lead toan increase of the blocking time of the routesserving the platform tracks. The quality oftimetable design would be enhancedconsiderably if the estimated blocking timesreflect well the variation of train speed and dwelltimes in practical operations.

So far, the blocking times in timetables areassumed to be deterministic and estimated with aprecision of seconds. The arrival and departuretimes of trains and the headway times betweentrains in most railway timetables, however, aredetermined currently with a precision of minutesdue to rounding-up of the estimated runningtimes and easy comprehension by the passengers.

This practice includes hidden scheduled waitingtimes, which could be exploited if thedetermination of the arrival, departure andheadway times (for in-company planning andoperation purposes) was done at a higherprecision in steps of 5 to 10 sec (according tocurrent practice in Japanese railways).

For capacity estimation of heavily occupiedroutes in bottlenecks the track infrastructureneeds to be subdivided in individual route nodes:the smallest track elements that can be used byone train at a time (Fig. 4). The variations of timeheadway and train speed at heavily occupiedjunctions may lead to knock-on delays andqueuing of trains before network bottlenecks. Onthe routes approaching to level crossings close tomain stations we observed a significant drop ofthe mean train speed by a bout 20 to 50 % withregard to design speed which means a clearreduction of infrastructure performance. Thismeans the scheduled speed and headway timesshould correspond better to real operations andthe train drivers need to be supported by dynamicspeed advices in order to avoid hinder to and by

Fig. 4. Division of an interlocking arrangement into routenodes [21]

Fig. 5. Distribution of blocking times of Intercity trainsapproaching to the Dutch station The Hague HS [27]

Table 2. Recommended capacity consumption by UICnorm 406 [22]

24 International Journal of Civil Engineerng. Vol. 8, No. 1, March 2010

other trains at junctions. In fact, the blockingtimes are stochastic and not deterministic, and soare the remaining buffer times (Fig. 5).

The total track occupancy and the remainingtimetable slack of a given line is estimated finallyby means of a virtual compression of theblocking time graphs according to UIC norm406, which recommends maximal trackoccupancy rates of e.g. 75 % during peak hoursand 60 % a day for lines used in mixed traffic(Tab. 2).

2.5. Waiting Times

Every timetable comprises scheduled waitingtimes and generates, in practical operations, non-scheduled waiting times (delays). Scheduledwaiting times result from differences between thescheduled and desired running, headway,departure/arrival times by train operatingcompanies, as well as timetable constraints. Thescheduled waiting times depend on the marketdemand, track possession times due tomaintenance and synchronisation conflictsbetween train graphs at railway nodes andbottlenecks, whereas non-scheduled waitingtimes can emerge from technical failures of trackinfrastructure or rolling stock, accidents, andtrain delays. The amount of scheduled waitingtimes can be used as indicator of timetablequality. The total waiting time during a timeperiod, in general, increases exponentially withthe number of trains operated. The researchchallenge is to determine the optimal trackoccupancy at a desired level of service.

Schwanhäusser [1] developed already in 1974a stochastic approach for the estimation of themean queue length as function of the distributionof primary delays, buffer time, mean headway,train sequence and priority by a queuing model oftype M/D/1. This led e.g. to an estimated meanbuffer time of 1 min in case of a minimalheadway of 2 min and all trains delayed (p. 59).As the assumed Poisson distribution of trainarrivals has been questioned later on, queuingmodels of the type G/G/1 and M/G/1 have beendeveloped by Wakob [2] and Hertel [3]respectively.

Hertel presented, too, an analytical approach

for the waiting time (Fig. 6) as function of trafficflow, relative waiting time sensitivity (partialderivative of mean waiting time to trackoccupancy) and maximal traffic ‘energy’ (definedas product of train intensity and speed).According to Hertel the recommended area oftrain intensity as function of waiting timesensitivity and traffic ‘energy’ of a track operatedin one direction would be about 150 to 200 trainsper day, while the waiting time per train mayincrease up to 10 min.

Kaminski [12] analysed the timetable andcompared the estimated waiting times by micro-simulation with the recorded train delays of alarge network (>2000 km) in Germany and founda good fit of the buffer times with a negative-exponential distribution.

He estimated the impact of buffer time lengthcorresponding to 80 % of the train delays

recorded at a number of stations by multiplesimulation, while maintaining the train orders.The mean consecutive delay per delayed trainwas estimated at about 30 sec.

The expected total waiting times of railwaylines and networks are estimated in severalEuropean countries by means of micro-simulation tools like STRESI [8], RailSys [9] orOpenTrack [10] that draw and insert samples ofrandom primary delays from predefineddistributions to a timetable. The virtual hinderbetween trains, which is simulated throughmodification of the scheduled blocking timegraphs (bending of train paths, increasing ofdwell times, change of train order and routing),while its impact is estimated by the distributionof delays, the kind and percentage of hindered

Fig. 6. Waiting time as function of traffic flow, relativesensitivity of waiting time and traffic ‘energy’[3]

25I. A. Hansen

trains and the punctuality level. The timetable slack of interconnected lines in

networks with periodic timetable depends notonly on the buffer times of the individual lines,but also on the buffer times between thescheduled train arrivals and departures at thetransfer stations. The following constraints forthe design of an integrated network timetablehold:

• The round trip time of a line must be integermultiple of the headway,

• The travel time between the nodes (sum of therunning and dwell times) must be an integermultiple of half of the cycle time (mostly 60min),

• The scheduled arrival and departure times ofinterconnected lines at the nodes must overlapsufficiently,

• The sum of the travel times on a circuitbetween three nodes must be an integermultiple of the cycle time and of the timeheadway.

As such constraints lead in large networks withmany nodes and lines to a great complexity ofperiodic timetables, combinatorial operationsresearch methods like MILP were developed inorder to search for the optimal solution of a giventimetable [6, 7]. The network timetable problem,however, is known to be NP-complete andrequires the development of intelligentalgorithms to find a solution within a reasonablecomputation time – if existing under givenconstraints – and/or to relax some constraints.Predefined constraints like minimal headway andtransfer times, however, don’t guarantee thetimetable feasibility in complex junctions and,therefore, need to be proven by a detailedanalysis of blocking times and/or micro-simulation.

The existing buffer times and its distribution inperiodic timetables of large networks can becalculated analytically by means of the (max, +)algebra approach, which transforms the networktimetable and constraints into an extensive set ofsimple recursive linear equations [23]. Thistechnique enables to identify the critical circuitswithin a large complex railway network and to

calculate the minimal cycle time of the wholetimetable and the existing timetable slack. Thebasic periodic network timetable of the DutchRailways can be automatically transformed bythe tool PETER [24] into a (max,+) state matrixof the travel times, minimal headway times andtransfer times in order to identify the criticalcircuits, to calculate the stability margin and toperform a delay propagation and recovery timeanalysis. The impact of an increase or decrease oftravel times and buffer times on the timetableslack and on the location of the critical circuit ofperiodic network timetable can be estimatedrapidly, as well as the propagation of train delaysin the network (Fig. 7). a

3. Dynamic Traffic Management

3.1. Performance of Train Operations

The operations performance can be assessedby means of different analytical approaches andmicro-simulation. A high level of performance,of course, requires that the basic timetable isfeasible, a high availability of infrastructure,experienced personnel and a low failure rate ofrolling stock.

Schwanhäusser [1] defined in 1974 thesmoothness of operation as the share ofunscheduled waiting trains at any location inorder to proceed. He developed an analytical

Fig. 7. Recovery time sensitivity of initial delay ofIntercity train Delft to The Hague on the Dutch railway

network [24]

26 International Journal of Civil Engineerng. Vol. 8, No. 1, March 2010

approach for estimating consecutive delays incase of hinder based on queuing theory. Theadmitted level of hinder during operations wasdetermined empirically by certain maximalqueue lengths and described by a simpleexponential equation as function of the share ofpassenger trains:

LW =

LW : queue length

: coefficients

pP : probability of passenger trains

LW = 0.257. (calibrated function for

Deutsche Bahn AG).

Three different levels of quality of operations(0.5 = very good, 1.0 = satisfactory, 1.5 =unsatisfactory) are defined as ratio of theestimated queue length divided by the maximumadmitted queue length. The amount of dailyknock-on delays at stations that are tolerated byDeutsche Bahn is determined at 130 min up to300 min depending on the share of passengertrains. The estimation of scheduled andunscheduled waiting times as a measure ofoperations quality of a given timetable,infrastructure and signalling system isimplemented in the software tool ANKEdeveloped at RWTH Aachen [25].

Detailed statistical analysis of train delays atseveral major Dutch stations [26] confirmed thattrain departure delays can best be described bynegative-exponential or Weibull distributions,while the lognormal distribution fits better toinitial and arrival delays of all trains, becausetrains may arrive early due to running timemargins, whereas early departures are notpermitted.

The impact of primary and consecutive traindelays on the robustness of train services instation areas is estimated according to Yuan [27]by means of coupling the (conditional)probabilities and distributions of sequencing traindelays at arrival, departure, and of thecorresponding running and route release times.The survival probability of knock-on delays at aroute node for a given delay of the precedingtrain is shown in Fig. 9.

The propagation of delays in large networks ofinterconnected lines can be modelled also bymicro-simulation. Watson [28] compared thecharacteristics of current commercial simulationtools and concluded that ‘signal berth’ level toolsare necessary for stochastic simulation.Simulation tools mostly require interaction of theuser in case of conflicts between blocking timegraphs or the application of a predefinedautomatic conflict resolution strategy. In order toevaluate the different dispatching measurementson the stability margin and the location ofnetwork bottlenecks in case of disturbancedifferent options can be computed. The analysisof individual link and train dependent recoverytimes would allow a variety of experiments toestimate the robustness of different re-schedulingoptions (re-timing, re-ordering, re-routing). The

pPe 3.1�

���

pPe ��� ��

Fig. 8. Density distributions of train delay, arrival anddwell time distributions of individual lines at the Dutch

station The Hague HS [26]

27I. A. Hansen

effectiveness of different conflict resolutionstrategies can be evaluated on the basis of theamount of disturbance (primary delay, knock-ondelays, punctuality) and fading-out time.However, the available micro-simulation toolsneed to be coupled to accurate on-line traindetection, speed and delay monitoring systems inorder to be used real-time for conflict detection,delay prediction and dynamic traffic managementsupport.

3.2. Automatic Monitoring of Initial and Knock-on

Delays

Actual passenger train delays monitored topassengers waiting at stations and to dispatchersby means of displays are based on standard traindescriber systems and track occupation andrelease data, which has been compared withscheduled arrival, departure times at previouslocations. These records do not distinguishbetween initial and knock-on delays, whichshould be considered by infrastructure managersand train operating companies in order to identifythe cause and responsible party and to take themost effective measures to reschedule the trafficin case of larger delays.

A software tool called TNV-Conflict [29] hasbeen developed recently by TU Delft thatidentifies automatically all signalled headwayand route conflicts including the critical tracksections, involved train numbers, and the amount

of initial and, separately, consecutive delay at aprecision of less than 5 seconds. The output of thetool containing chronological infrastructure andtrain description messages can be used offline foranalysis of timetable, infrastructure use and trainperformance, as well as online input for decisionsupport systems of dispatchers. The comparisonof measured track occupation and blocking timesof the train graphs with the scheduled onesclearly indicate the difference of individual trainprocess times (Fig. 10).

The aqcuired information include the locationsand number of route conflicts, their effect oncapacity consumption and punctuality, theassignment of knock-on delays to conflictingtrains in a non-discriminatory way, and theidentification of structural route conflicts fromtimetable flaws (e.g. infeasible minimumheadways, late trains due to precedingbottlenecks, and early trains due to excessiverunning time supplements). The tool providesessential information to improve capacityallocation and to construct reliable train paths.Furthermore, data on actual train length, speed,headway, dwell time at platform and precisedelay is collected that is needed for adaptingrapidly the timetable and adjusting real-time theprediction of downstream arrival, departuretimes.

Fig. 9. Knock-on delay survival probability for anorthbound departing train as function of frequency of

trains passing a critical level crossing at the Dutch stationThe Hague HS [27]

Fig. 10. Example of conflicting train graphs between alocal and an Intercity train south of Rotterdam generated

by TNV-Conflict [29]

28 International Journal of Civil Engineerng. Vol. 8, No. 1, March 2010

3.3 Real-Time Rescheduling

Regulation of railway traffic aims at ensuringsafe, seamless and as much as possible punctualtrain operations. Due to the strict time limits forcomputing a new timetable in presence ofdisturbances, train dispatchers usually performmanually only a few timetable modifications (i.e.adjust train routes, orders and speeds), while theefficiency of the chosen measures is oftenunknown. Some computerized dispatchingsupport systems have been developed, so far,which can provide good solutions for smallinstances and simple perturbations. Recentreviews on the related literature can be found e.g.in Törnquist & Persson [30]. However, mostexisting dispatching systems operate based onlocal information and decisions are taken locally,"on the spot and now". These systems are able toprovide viable solutions only if few trains aredelayed and the chosen traffic control actions areoften sub-optimal. They cannot deal with heavydisturbances in larger networks as the actual traindelay propagation is simply extrapolated anddoes insufficiently take into account the traindynamics and signalling constraints. Therefore,extensive control actions are necessary to obtainglobally feasible solutions.

Advanced real-time traffic managementsystems should take into account the wholetraffic in a larger area, detecting future conflictsamong train movements (that have direct impacton the level of punctuality), automatically

calculating optimal traffic flow and suggestingpossible change of orders or routes to thedispatcher, as well as displaying advisory speedsto the train drivers. Efficient traffic managementsupport systems must be able to simulate theeffects of different dispatching measures andsupport traffic controllers by frequently updatingthe actual timetable and ranking the dispatchingoptions according to their expected performance.

The recently developed advanced real-timerescheduling tool ROMA (Railway trafficOptimization by Means of Alternative graphs)estimates the future evolution of the railway trafficconsidering actual train positions, signalling andsafety operating rules and conditions, as well asdynamic train characteristics (fig. 11). ROMAcomputes a dispatching solution that minimizestrain delays and their propagation by pro-activelydetecting train conflicts by means of blocking timegraphs and solving headway and route conflicts byiterative adjustment of train speeds and/orreordering and rerouting of trains within shortcomputation times [31, 32, 33]. The effectivenessof extensive rerouting strategies is explored byincorporating the search for new routes in a tabusearch scheme, in order to escape from localminimal [32].

The investigated dispatching area comprisesthe 50 km long line from Utrecht to Den Boschoffering a number of possibilities of trainreordering and local rerouting (Figure 12). Foreach train a default route and a set of localrerouting options are given.

Infeasible

Schedule

Train

(Re)Scheduling

Train

Rerouting

Rerouting

Alternatives?

Timetable

Infrastructure Data

Train Data

Passable Routes

Feasible

Schedule

Possible

Improvements

No Rerouting or

Time Limit Reached Optimal Orders

Optimal Routes

New Routes

Fig. 11. Architecture of the real-time railway traffic optimization module

29I. A. Hansen

During peak hours, 26 passengers and freighttrains in both directions are scheduled each hourfor the area around Geldermalsen and up to 40trains at Den Bosch station. The minimum timefor passenger connections varies from two to fiveminutes, depending on the distance between thearrival platforms. 32 instances with differenttimetable perturbations have been simulated andtested during a simulation period of one hour. Thetest results are listed in Table 3.

The automatic route setting represents the basecase of current rail operations. The second and thirdlines refer to the average results by using theadvanced scheduling algorithm (BB) and thererouting optimization algorithm (TS),respectively. Each column of this table shows theaverage results on the 16 timetable perturbations.The fifth column presents the percentage of trainroutes that have been changed by the real-timerailway traffic optimization module starting fromthe set of default routes given by the disruptionrecovery module. The last column indicates thepercentage of train orders that have been changedwith respect to the timetable. The computationresults show the effectiveness of using real-timerailway traffic optimization algorithms with respect

to simple and local dispatching procedures.

3.4. Advanced Driver Assistance

Apart from advanced rescheduling systems,new ICT-tools for the support of train drivers inorder to anticipate hinder from other trains havebeen developed recently. Currently, train driversreceive only movement authorities and speedlimit information in signal-controlled networkpassing at trackside discrete signal locationsand/or by on-board automatic train controldisplays. In general, drivers are not informedabout their train delay, except when comparing

Utrecht Lunetten

HoutenCulemborg

Utre

cht

HoutenCastellum Geldermalsen

Dordrecht

Nijmegen

ZaltbommelDen BoschGeldermalsen Yard

Den Bosch

ZaltbommelGel

derm

alse

n Betuweroute Oss

Eindhoven

Den Bosch Yard

Tilburg

Zaltbommel(freight only)

Fig. 12. Railway dispatching area between Utrecht and Den Bosch

Table 3. Performance of the ROMA configurations in case of timetable perturbations [32]

Roma Configurations Max Cons Delay

Avg Cons Delay

Total CompTime

% TrainRoute Changed

% TrainOrders Changed

Automatic route setting (ARI) 342.0 38.7 4.8 - 12.3Scheduling Algorithm (BB) 246.4 27.8 3.9 - 16.9Rerouting Algorithm (TS) 238.7 24.6 127.9 15.5 12.2

/ Lecture RouteLint and MATRICS May 19 2009

RouteLint: anticipation is key

ZWD-25030 +1DDR-11930 -2

KFHAZ-KRBRD-2

KJRTLB-22228 -5

RTST-KG

RTZ-2RTST-KF608 -3

10:31Treinnummer Vertraging

Train itinerary

My train

Routesetting

Delay (minutes)

Route settingsteps

Leaving the planned itinerary Routesetting

other trainsTrains in front Delay

Train behind

Fig. 13. Hand-held signal and track occupancy

information RouteLint

30 International Journal of Civil Engineerng. Vol. 8, No. 1, March 2010

the actual time with the scheduled times atstations on their own or if traffic controllerscontact them via train radio.

Continuous update of information aboutchanges of actual signal aspects and route releasecan be transmitted via radio to on-board hand-held PADs (Fig. 13). The Dutch infrastructuremanager ProRail has developed and demonstratedthe effectiveness of transmitting such actual datato train drivers that enabled to start coasting ordecelerating even before they come close to adanger signal in order to follow more closely theirscheduled path or to avoid a train stop on the opentrack because of a still occupied track and routesection further ahead. The dynamic on-boardinformation system called ‘RouteLint’ [34] mayreduce energy consumption of Intercity andfreight trains by about 5% (Fig. 14).

A further development step consists in theapplication of head-up displays of downstreaminformation on the windscreen. Such, drivingtrains on ‘electronic sight’ would become reality.

4. Conclusion

The current methods and tools for railwaytimetable design enable a high precision of theestimated travel times, headway times and timemargins in order to achieve high-quality, conflict-free timetables of lines and networks. Queuingmodels and micro-simulation tools have beenapplied successfully to improve the timetable

quality and to estimate the propagation of stochastictrain delays. The key for high-quality timetabling isa precise estimation of blocking times based onrealistic running, dwell and headway times takinginto account the signal spacing and train processingat critical route nodes and platform tracks.Statistical analysis of empirical track occupationand release data in major Dutch stations hasrevealed that the trains often leave later and operateat speeds less than scheduled due to hinder by othertrains, late route clearance, excess dwell times aswell as drivers’ and conductors’ behaviour.Deterministic models for stability analysis andoptimisation of network timetables like max-plusalgebra technique or linear programming still needto incorporate the impact of dispatching measureson perturbed train traffic.

Queuing and simulation models for theestimation of unscheduled delays in daily trafficstill reflect insufficiently the impact of speedvariations and behaviour of railway staff. A newprobabilistic model of TU Delft enables anestimation of the survival rate of knock-on delaysat platform tracks and junctions based onempirical distributions of running and releasetimes of the involved train pairs. The maximalnumber of trains and amount of consecutivedelays at a given initial delay and required levelof punctuality can be computed.

Efficient traffic management support systemsneed to compile actual monitoring data on trainpositions, headways and detect automaticallyconflicts between trains in advance in order tosupport dispatchers by regularly the actualtimetable, incorporate standard conflictresolution measures and simulate their effects.Simple headway conflicts between only twotrains might be solved automatically, whereasroute conflicts in heavily occupied networks andcomplex stations require accurate real-timesimulation and optimisation of dispatchingoptions according to their expected performance.The effectiveness of different measures may beevaluated and ranked on the basis of the totalamount of consecutive delays, links and stationsaffected and the time to fade out. More detailed,accurate and continuous traffic information withregard to actual deviation from the train schedule,location of trains ahead and occupation and

Fig. 14. Plot of train performance with(out) dynamic on-board information system RouteLint [34]

31I. A. Hansen

release of block and route sections can help traindrivers to anticipate and solve conflicts better.

More research is still necessary to developmore powerful analytical, simulation andoptimisation models of train rescheduling incomplex networks in order to improve thereliability, efficiency and robustness of railwayoperations.

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