Cerreto, Fabrizio

Rettidigheden af togtrafik på jernbanenet afhænger af flere faktorer som kanrelateres til planlægningsfasen eller med driften. I planlægningsfasen bliver robustekøreplaner designet med fokus på at begrænse dannelsen af primære togforsinkelser samtpå at absorbere dem for at hurtigt vende tilbage til normal drift ved at reducere opformeringaf sekundære forsinkelser af andre tog. Primære togforsinkelser i togtrafikken kan ogsåreduceres ved at forbedre de bagvedliggende driftsprocesser. At forstå hvordanforsinkelser opstår og opformeres er centralt i forhold til at forbedre design af robustekøreplaner og korrigerende produktionsprocesser i jernbanetrafikken.Dette studie undersøger de fænomener, der er forbundet med forsinkelser ijernbanedrift, både fra en teoretisk og empirisk vinkel. Den teoretiske struktur afforsinkelser bliver undersøgt grundigt ved hjælp af analytiske modeller. Effekterne afvalgte beslutninger i køreplanerne vurderes med simuleringsmodeller. Endeliggennemføres empiriske studier af forsinkelsesårsager for at identificere tilbagevendendeforsinkelser i togdriften.I den første del af afhandlingen undersøges almindeligt anvendte indikatorer forkøreplansstabilitet og robusthed for at forstå hvordan de er påvirket af trafikvolumen,heterogenitet af køreplaner og forskellige infrastrukturlayout. Den typiske fokus påtrafikheterogenitet og linjeudnyttelse af ex-ante analytiske målinger sammenlignes medmålinger baseret på driftssimulering. Driftssimulering efterligner driften afjernbanetrafikken og skaffer meget detaljeret indsigt herom, dog på bekostning af højerekrav til beregningsmæssige ressourcer. Studiet anvender mikrosimulering afjernbanedriften og finder ud, at den aggregerede linjeforsinkelse, afviklingstid oggennemsnitlige togforsinkelse er egnede indikatorer for driftssikkerhed. Det bliversammenlignet med standard indirekte målinger primært baseret på linjekapacitet ogudnyttelse eller planlagte buffere mellem vognløb og deres fordeling. Den massiveberegning, der kræves til mikrosimulering, gør dog metoden uegnet til online anvendelsertil beslutningsstøtte såvel som til rekursive anvendelser i f.eks. de heuristiskeoptimeringsmodeller, der typisk bruges til køreplanoptimering. Afhandlingen undersøgerderfor også metoder til at mindske mængden af simulation ved anvendelse af de sammemålinger af robusthed under evaluering.Som konklusion er mikrosimulering en særdeles detaljeret metode til atmodellere jernbanedrift, men det er også en ressourcekrævende proces. For at mindskeberegningsbehovet præsenteres derefter i den anden del af afhandlingen en analytiskmodel til beregning af forsinkelsesopformering med en lukket formel, som tillader hurtigberegning af indikatorerne for driftssikkerhed. Analytiske modeller er typisk megethurtigere end mikrosimulering og er derfor mere egnet til at indgå i optimeringsmodeller.Det er også tilfældet med den i studiet udviklede model. Den matematiske model skaberindsigt i forholdet mellem primære forsinkelser og den totale forsinkelse dannet påjernbanelinjer. Modellen beregner de individuelle forsinkelser af hver eneste tog ved hverstation. Forholdet mellem primære forsinkelser og aggregerede linjeforsinkelser bliver visti en sammensat polynom som spænder fra første til tredje grad ifølgeforsinkelsesgenopretning. Køreplan parametre kan så justeres med denne model for atberegne effekten af forskellige værdier af køretidstilskud og togfølgetids buffere.Modellen udvikles først til homogen trafik på enkeltsegmenter af jernbaner og bliverderefter integreret med stokastisk simulation og udvidet til heterogen trafik samt til atomfatte forsinkelsesgenereringsprocessen. Fordelinger af afgangstid og varighed afbegivenheder kombineres med køreplansstruktur for at modellereforsinkelsesgenereringen forårsaget af begivenheder, som for eksempel en midlertidigsporblokering eller en fejl ved signalerne. I den stokastiske model bliver den aggregeredeforsinkelse beregnet som konsekvens af en begivenhed, der påvirker et specifik tog, og detvægtede gennemsnit benyttes derefter til at beregne den totale forsinkelsesfunktionforbundet til hele køreplanen.Studiet analyserer i den tredje del empiriske data fra jernbanedrift for at uddrageoplysninger til parametrisering af modelleringen og for at kunne identificere systematiskeforsinkelse, der kræver specifikke modforanstaltninger. Fordelinger af realiseredekøretider studeres for at forstå togenes reelle maximale ydeevne og de korteste muligekøretider på en given strækning. På denne måde kan det faktiske slæk i køreplanenberegnes som støtte til robusthedsanalyser. Big-data teknikker anvendes til analyser afempiriske data for at identificere tilbagevendende forsinkelsesmønstre, som kan forbindesmed specifikke serviceegenskaber, som f.eks. tidsfaktorer og ydeevne af det rullendemateriel. Tidsstempler fra banedriften arrangeres i forsinkelsesprofiler af individuellevognløb, hvilke så grupperes ved hjælp af cluster teknikker i grupper af vognløb medsammenlignelige forsinkelsesmønstre. K-means clustering anvendes i mange forskelligefelter og værdsættes for metodens enkelhed og hurtighed. De resulterende klasser afforsinkelsesprofiler forbindes til individuelle vognløbs egenskaber, så specifikke ogfokuserede korrigerende foranstaltninger kan designeres til jernbanedriften og køreplaner.Alt i alt gør den udviklede viden det muligt at planlægge robuste køreplaner ogat undersøge effekter af valgte parametre allerede i planlægningsfasen. Studiet bidrager tillitteraturen med en analytisk model for forsinkelse udbredelse med anvendelse afdataanalyser for realiseret drift og dækker ydermere metoder for driftsikkerhedsvurdering.Den totale forsinkelse genereret på en banelinje i forhold til primære forsinkelservises at være den mest sensitive indikator for robusthed ved ændringer af trafikvolumenog infrastrukturforbedring. En analytisk metode udvikles til at beregne dette mål udenmikrosimulering. Denne metode gør analyser hurtigere og gør det muligt at inkluderesådanne mål i online anvendelser og optimeringsmodeller. Derudover tillader depræsenterede empiriske analyser identifikation af tilbagevendende forsinkelsesmønstre ijernbanedrift, hvilket støtter designet af specifikke korrigerende foranstaltninger afdriftsmæssige processer.Punctuality of railway networks depends on several factors, associated with the planning phase or the operation phase. In the planning phase, robust timetables are designed to withstand the variability in operation and to contain the generation of primary delays. Also, railway planners seek timetable stability to absorb primary delays reducing the propagation into secondary delays and return quickly to the unperturbed condition. Besides, primary delays that occur in the operations phase can be reduced by improving the industrial processes behind the railway services. Understanding how delays generate and propagate is central to the efficient design of robust timetables and corrective measures of service production processes. The purpose of this study is the examination of the phenomena related to delays in railways, from both theoretical and empirical perspectives. The theoretical structure of delays is examined in analytical models. The effects of selected timetabling decisions are investigated in simulation models. Empirical studies on delay records from the realized operation are provided to identify recurrent patterns in the delay generation and recovery. In the first section, the study evaluates commonly used indicators for timetable stability and robustness and compares their sensitivity to changes in traffic volume, heterogeneity, and the infrastructure layout. The comparison includes analytical measuresbased on the timetable structure and measures based on simulation of operation under known perturbations. On the one hand, ex-ante analytical measures focus typically on traffic heterogeneity and line exploitation, often considering individual characteristics of the timetable only separately. For instance, delay recovery is usually modeled through either running time supplements or headway buffers between trains. On the other hand, simulation of operation mimics the behavior of railway systems and provides a more detailed insight. Simulation tools allow different types of measurements, such as the individual train delays recorded at different timing points, which can be evaluated in different methods. The accuracy of simulation comes, though, at the price of higher demand for computational time and resources. In this section, aggregate delay as a function of primary delays is measured in a microsimulation environment, and it is escribed as a valid indicator of timetable reliability. However, the extensive calculation performed in microsimulation makes this method unsuitable for applications where the velocity of calculation counts. For instance, online applications for decision support tools need fast responses, in a few seconds, and heuristic optimization algorithms often require recursive calculations, so the overall response times dilate quickly. In this thesis, methods to reduce the amount of simulation are also investigated, based on the same robustness measures under evaluation. The first section of this thesis identifies a valid measure of timetable robustness in the aggregate line delay related to known incidents. One of the major obstacles to theapplication of this type of measure in real-time traffic management and optimization is its dependence on simulation, which is a time-consuming process. The following section presents alternative methods that combine analytical and simulation models to estimate the aggregate line delay as a function of primary delays with reduced resources requirement, paving the way to applications that require prompt responses. In the second section, an analytical model is presented to describe the delay propagation in a closed form function, allowing quick calculation of the reliability indicators identified in the previous section, including aggregate line delay. Analytical models are typically much faster than microsimulation and are therefore more suitable for optimization environments and online decision support tools. The mathematical model provides insight into the relationship between primary delays and the consequent total disturbance on railway lines. This relationship is described by a composite polynomial, which spans from first to third degree, depending on the magnitude of primary delay relative to the size of the study domain. Timetable design parameters can be adjusted in this model, and different settings can be quickly compared. The robustness given by different values of running time supplements, headway buffers, and punctuality threshold can be assessed. The model is initially formulated for homogeneous traffic on railway lines. It is later integrated with stochastic simulation to support heterogeneous traffic and to include the delay generation process. This process consists of three parts. The first part, the incident simulation, mimics events that block the railway, such a temporary track blockage, or signal failure, described by the distributions of initial time and duration. In the second part, the model generates primary delays combining the incident with the timetable structure. Lastly, the primary delay is propagated to the subsequent trains and the downstream stations. In the stochastic simulation model for heterogeneous traffic, the total delay is estimated as a consequence of an incident that affects an individual train service, and a weighted average is then used to derive the total delay function associated to the whole timetable. In addition to the aggregate line delay, the model provides the individual delays of every train recorded at each station and can be extended, therefore, to implement several metrics. Both the analytical and simulation models presented in the previous sections rely on simplifying assumptions. One of the most influential assumptions, yet one of the most frequent, is that trains always use all the slack available in the timetable to recover from delays, in the absence of further circulation conflicts. In reality, delay recovery is a stochastic process itself, and it is ruled by several factors, driving behavior, rolling stock performance, and passenger comfort among others. Furthermore, possible recovery depends on the allocation of timetable slack along the path. In the timetabling phase, railway planners typically allocate the slack according to general rules from practice. Investigation of recurrent patterns in delay development and recovery in railway operation can improve this process, giving the opportunity to tailor the slack according to specificcharacteristics of individual train services. The whole railway operation can also be improved identifying the factors that cause recurrent delays so that individual critical processed can be fixed, and specific delay mitigation measures can be designed. In the third section, this study lastly analyses empirical records from railway operation to extract information for modeling and to identify systematic delays that require specific countermeasures. Distributions of realized running times are studied to understand the real maximum performance of trains and the minimum feasible running time on a line section. The actual use of running time supplement to recover from delays highlights points of lack or excess of timetable slack. In this way, the real potential delay recovery available in the timetable can be determined to support robustness analyses of the timetable. Big data techniques are successively applied to empirical records to identify recurrent delay patterns to be associated with specific service characteristics, such as time factors and rolling stock performances. Timestamps from railway operation are arranged in delay profiles of individual service runs, which are then classified in clusters of services that develop their delay in similar ways. The method identifies locations where the delay changes recurrently in the same way, which may suggest changes in the schedules, or in the processes linked to the railway operation. The K-means clustering method finds application in very different fields, and it is generally appreciated for its simplicity and velocity. The resulting classes of delay profiles are eventually linked to the characteristics of individual trains, so that specific and focused corrective measures can be designed for the railway service production processes. In summary, based on the knowledge developed in this study, it is possible to design robust timetables and to investigate the influence of selected parameters already in the planning phase. The study contributes the literature with an analytical delay propagation model, with the application of data analysis of the realized operation, and covers, besides, methods for appraisal of service reliability. The total delay generated on a railway line as a function of primary delays is identified as the indicator that is most sensitive to variations in traffic volume and infrastructure improvements. Methods to estimate this measure without using microsimulation are proposed, making analyses quicker, and opening the possibilities to include such statistics in online applications and optimization models. Additionally, the empirical analyses presented permit the identification of recurrent delay patterns in railway operation, supporting the design of dedicated corrective measures of productive processes

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Analytical, Big Data and Simulation Models of Railway Delays

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Analytical, Big Data and Simulation Models of Railway Delays

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