Robustness and Recoverability in Transport Logistics

Abstract Transport is the foundation of any economy: it boosts economic growth, creates wealth, enhances trade, geographical accessibility and the mobility of people. Transport is also a key ingredient for a high quality of life, making places accessible and bringing people together. The future prosperity of our world will depend on the ability of all of its regions to remain fully and competitively integrated in the world economy. Efficient transport is vital in making this happen. Operations research can help in efficiently planning the design and operating transport systems. Planning and operational processes are fields that are rich in combinatorial optimization problems. These problems can be analyzed and solved through the application of mathematical models and optimization techniques, which may lead to an improvement in the performance of the transport system, as well as to a reduction in the time required for solving these problems. The latter aspect is important, because it increases the flexibility of the system: the system can adapt in a faster way to changes in the environment (i.e.: weather conditions, crew illness, failures, etc.). These disturbing changes (called disruptions) often enforce the schedule to be adapted. The direct consequences are delays and cancellations, implying many schedule adjustments and huge costs. Consequently, robust schedules and recovery plans must be developed in order to fight against disruptions. This dissertation makes contributions to two different fields: rail and air applications. Robust planning and recovery methods are presented. In the field of railway transport we develop several mathematical models which answer to RENFE’s (the major railway operator in Spain) needs: 1. We study the rolling stock assignment problem: here, we introduce some robust aspects in order to ameliorate some operations which are likely to fail. Once the rolling stock assignment is known, we propose a robust routing model which aims at identifying the train units’ sequences while minimizing the expected delays and human resources needed to perform the sequences. 2. It is widely accepted that the sequential solving approach produces solutions that are not global optima. Therefore, we develop an integrated and robust model to determine the train schedule and rolling stock assignment. We also propose an integrated model to study the rolling stock circulations. Circulations are determined by the rolling stock assignment and routing of the train units. 3. Although our aim is to develop robust plans, disruptions will be likely to occur and recovery methods will be needed. Therefore, we propose a recovery method which aims to recover the train schedule and rolling stock assignment in an integrated fashion all while considering the passenger demand. In the field of air transport we develop several mathematical models which answer to IBERIA’s (the major airline in Spain) needs: 1. We look at the airline-scheduling problem and develop an integrated approach that optimizes schedule design, fleet assignment and passenger use so as to reduce costs and create fewer incompatibilities between decisions. Robust itineraries are created to ameliorate misconnected passengers. 2. Air transport operators are continuously facing competition from other air operators and different modes of transport (e.g., High Speed Rail). Consequently, airline profitability is critically influenced by the airline’s ability to estimate passenger demands and construct profitable flight schedules. We consider multi-modal competition including airline and rail, and develop a new approach that estimates the demand associated with a given schedule; and generates airline schedules and fleet assignments using an integrated schedule design and fleet assignment optimization model that captures the impacts of schedule decisions on passenger demand.

Changes in the external costs of freight surface transport in Spain

This paper studies the external costs of surface freight transport in Spain and finds that a reduction occurred over the past 15 years. The analysis yields two conclusions: trucks have experienced a reduction in external costs, and rail has lower externalities. The external costs of road freight transport decrease between 1993 and 2007 (44%). The external costs of rail freight increase by 12%. During this period, the external costs of road freight related to climate increase by 16%, oppositely than those from air pollution and accidents (51 and 44%). The external costs of rail related to pollutant emissions and climate increase by 4% and 43%. Oppositely, the external costs related to accidents decrease by 27%. Road freight generates eight times the external costs of rail, 2.35 Euro cents per tonne kilometre in 2005 (5.6% accidents, 74.7% air pollution and 19.7% climate) vs. 0.28 (13.4% accidents, 53.9% air pollution and 32.7% climate).

Robust rolling stock under uncertain demand in rapid transit networks

This paper focuses on the railway rolling stock circulation problem in rapid transit networks where the known demand and train schedule must be met by a given fleet. In rapid transit networks the frequencies are high and distances are relatively short. Although the distances are not very large, service times are high due to the large number of intermediate stops required to allow proper passenger flow. The previous circumstances and the reduced capacity of the depot stations and that the rolling stock is shared between the different lines, force the introduction of empty trains and a careful control on shunting operation. In practice the future demand is generally unknown and the decisions must be based on uncertain forecast. We have developed a stochastic rolling stock formulation of the problem. The computational experiments were developed using a commercial line of the Madrid suburban rail network operated by RENFE (The main Spanish operator of suburban trains of passengers). Comparing the results obtained by deterministic scenarios and stochastic approach some useful conclusions may be obtained.

Estudio geotécnico para la cimentación del terraplén de acceso a un paso superior. Línea de alta velocidad Madrid-Castilla la Mancha-Comunidad Valenciana-Región de Murcia

Este proyecto aborda el estudio geotécnico para la cimentación del terraplén de acceso a un paso superior sobre el tramo Albatera-Elche, incluido en la Línea de Alta Velocidad Madrid-Castilla La Mancha-Comunidad Valenciana-Región de Murcia. Con el fin de identificar y clasificar los materiales del terreno de cimentación, se analiza el marco geológico regional y local del área de estudio. En el proyecto se presentan los resultados obtenidos en la campaña de reconocimiento de campo y en los ensayos realizados en laboratorio, a partir de los cuales se realiza la caracterización geotécnica de los materiales y se determinan sus parámetros geotécnicos. Asimismo, se considera la singular problemática geotécnica de la zona de estudio, por lo que se analiza la estabilidad global del terraplén, los tiempos de consolidación del terreno y se realiza una estimación de asientos. De acuerdo a todos los cálculos y consideraciones realizadas, se determinan los tratamientos de mejora y refuerzo del terreno de cimentación. Por último, se evalúan los costes derivados de la campaña de reconocimiento geotécnico y de la redacción del presente estudio. ABSTRACT This project is a geotechnical report for the foundation of the access embankment to an overpass in the railway section Albatera-Elche, included in the High Speed Rail line Madrid-Castilla La Mancha-Comunidad Valenciana-Región de Murcia. In order to identify and classify the foundation soil materials, the regional and local geological frame of the study area is analyzed. The results of the field survey and laboratory tests performed are displayed in the project, from which the geotechnical characterization of materials is made and geotechnical parameters have been determined. It is also considered the special geotechnical problems in the study area, so the overall stability of the embankment and ground consolidation times are analyzed, as well as an estimate of ground settlement is also made. According to all calculations and considerations made, treatments to improve and strengthen the foundation soil are determined. Finally, the costs of the geotechnical campaign and the elaboration of this report are evaluated.

A 2D computational parametric analysis of the sheltering effect of fences on a railway vehicle standing on a bridge and experiencing crosswinds

In a crosswind scenario, the risk of high-speed trains overturning increases when they run on viaducts since the aerodynamic loads are higher than on the ground. In order to increase safety, vehicles are sheltered by fences that are installed on the viaduct to reduce the loads experienced by the train. Windbreaks can be designed to have different heights, and with or without eaves on the top. In this paper, a parametric study with a total of 12 fence designs was carried out using a two-dimensional model of a train standing on a viaduct. To asses the relative effectiveness of sheltering devices, tests were done in a wind tunnel with a scaled model at a Reynolds number of 1 × 105, and the train’s aerodynamic coefficients were measured. Experimental results were compared with those predicted by Unsteady Reynolds-averaged Navier-Stokes (URANS) simulations of flow, showing that a computational model is able to satisfactorily predict the trend of the aerodynamic coefficients. In a second set of tests, the Reynolds number was increased to 12 × 106 (at a free flow air velocity of 30 m/s) in order to simulate strong wind conditions. The aerodynamic coefficients showed a similar trend for both Reynolds numbers; however, their numerical value changed enough to indicate that simulations at the lower Reynolds number do not provide all required information. Furthermore, the variation of coefficients in the simulations allowed an explanation of how fences modified the flow around the vehicle to be proposed. This made it clear why increasing fence height reduced all the coefficients but adding an eave had an effect mainly on the lift force coefficient. Finally, by analysing the time signals it was possible to clarify the influence of the Reynolds number on the peak-to-peak amplitude, the time period and the Strouhal number.

Characterisation of laser hybrid welded dissimilar joints

The investigation addresses the over-all performance of dissimilar joints of low carbon steel and stainless steel thin sheets achieved by laser hybrid welding. First, the technological de-velopment of dissimilar laser hybrid welding of thin sheets is briefly pre-sented. Joint characterisation by means of macro and microstructural examination and hardness tests is fur-ther described. Microhardness testing was used as an alternative and effi-cient mean of assessing the changes in mechanical properties of difficult to characterize areas, like HAZ and fu-sion zone of these thin sheets Laser-GMA dissimilar welded joints. The overall tensile performance of the joint is discussed together with the weld metal strength overmatching. The ten-sile tests results indicate that in case of transversally loaded joints, the po-sitive difference in yield strength between the weld metal and the base materials (overmatching welds) may reduce the weight of the structure, without diminishing its strength.

Entorno de simulación para verificación y validación de equipamiento CBTC

Debido a sus características de seguridad, los sistemas de señalización ferroviarios requieren una gran cantidad de pruebas para su verificación y validación durante las diferentes etapas de su ciclo de vida, y en particular durante la instalación y puesta en marcha de una nueva línea o rehabilitación de una línea existente, siendo esta última aún más complicada debido a los cortos períodos de tiempo disponibles durante la noche para los trabajos. Este proyecto tiene como objetivo desarrollar una herramienta para reducir los esfuerzos antes mencionados mediante la simulación de los diferentes subsistemas de una línea equipada con sistema CBTC, el cumplimiento de las interfaces entre los subsistemas y el uso dentro de la simulación de equipos reales. Con estas premisas se desarrolló un entorno de pruebas para equipos y datos de señalización para líneas equipadas con el sistema CBTC. Los objetivos del proyecto que fueron establecidos en el inicio del desarrollo y han sido cumplidos con el desarrollo que se presenta en este artículo son los siguientes: • Poder realizar ensayos reales de equipos CBTC y su integración: equipos embarcados, equipos de control de área, etc. • Poder realizar ensayos reales con otros elementos de señalización y su integración: enclavamientos y ATS. • Poder realizar validación de datos vía CBTC. Para lograr estos objetivos se han desarrollado diversas aplicaciones de simulación, de las cuales, los más importantes son las siguientes: infraestructura, trenes automáticos, simulación de sistemas de tren, herramienta de gestión de los escenarios de simulación, etc Este sistema ha sido desarrollado y está añadiendo actualmente nuevos módulos y funcionalidades para las empresas del Grupo Invensys: Westinghouse Rail Systems en el Reino Unido y Dimetronic Signals en España, y está en uso en las nuevas líneas CBTC bajo su responsabilidad.

Explointing FPGA block memories for protected cryptographic implementations

Modern Field Programmable Gate Arrays (FPGAs) are power packed with features to facilitate designers. Availability of features like huge block memory (BRAM), Digital Signal Processing (DSP) cores, embedded CPU makes the design strategy of FPGAs quite different from ASICs. FPGA are also widely used in security-critical application where protection against known attacks is of prime importance. We focus ourselves on physical attacks which target physical implementations. To design countermeasures against such attacks, the strategy for FPGA designers should also be different from that in ASIC. The available features should be exploited to design compact and strong countermeasures. In this paper, we propose methods to exploit the BRAMs in FPGAs for designing compact countermeasures. BRAM can be used to optimize intrinsic countermeasures like masking and dual-rail logic, which otherwise have significant overhead (at least 2X). The optimizations are applied on a real AES-128 co-processor and tested for area overhead and resistance on Xilinx Virtex-5 chips. The presented masking countermeasure has an overhead of only 16% when applied on AES. Moreover Dual-rail Precharge Logic (DPL) countermeasure has been optimized to pack the whole sequential part in the BRAM, hence enhancing the security. Proper robustness evaluations are conducted to analyze the optimization for area and security.

Dynamic & Cyclic behaviour of ballast in the long term as determined in Cedex's track box

The 6 cylinder servo-hydraulic loading system of CEDEX's track box (250 kN, 50 Hz) has been recently implemented with a new piezoelectric loading system (±20 kN, 300 Hz) allowing the incorporation of low amplitude high frequency dynamic load time histories to the high amplitude low frequency quasi-static load time histories used so far in the CEDEX's track box to assess the inelastic long term behavior of ballast under mixed traffic in conventional and high- speed lines. This presentation will discuss the results obtained in the first long-duration test performed at CEDEX's track box using simultaneously both loading systems, to simulate the pass-by of 6000 freight vehicles (1M of 225 kN axle loads) travelling at a speed of 120 km/h over a line with vertical irregularities corresponding to a medium quality lin3e level. The superstructure of the track tested at full scale consisted of E 60 rails, stiff rail pads (mayor que 450 kN/mm), B90.2 sleepers with USP 0.10 N/mm and a 0.35 m thick ballast layer of ADIF first class. A shear wave velocity of 250 m/s can be assumed for the different layers of the track sub-base. The ballast long-term settlements will be compared with those obtained in a previous long-duration quasi- static test performed in the same track, for the RIVAS [EU co-funded] project, in which no dynamic loads where considered. Also, the results provided by a high diameter cyclic triaxial cell with ballast tested in full size will be commented. Finally, the progress made at CEDEX's Geotechnical Laboratory to reproduce numerically the long term behavior of ballast will be discussed.

Languages for safety-certification related propertis

The Safety Certification of Software-Intensive Systems with Reusable Components project, in short SafeCer (www.safecer.eu),is targeting increased efficiency and reduced time-to-market by composable safety certification of safety- relevant embedded systems. The industrial domains targeted are within automotive and construction equipment, avionics, and rail. Some of the companies involved are: Volvo Tech- nology, Thales, TTTech, and Intecs among others. SafeCer includes more than 30 partners in six different countries and has a budget of e25.7 millions. A primary objective is to provide support for system safety arguments based on arguments and properties of system components as well as to provide support for generation of corresponding evidence in a similar compositional way. By providing support for efficient reuse of certification and stronger links between certification and development, compo- nent reuse will be facilitated, and by providing support for reuse across domains the amount of components available for reuse will increase dramatically. The resulting efficiency and reduced time to market will, together with increased quality and reduced risk, increase competitiveness and pave the way for a cross-domain market for software components qualified for certification.

Effects of traffic loads on reinforced concrete railroad culverts

In the context of the present conference paper culverts are defined as an opening or conduit passing through an embankment usually for the purpose of conveying water or providing safe pedestrian and animal crossings under rail infrastructure. The clear opening of culverts may reach values of up to 12m however, values around 3m are encountered much more frequently. Depending on the topography, the number of culverts is about 10 times that of bridges. In spite of this, their dynamic behavior has received far less attention than that of bridges. The fundamental frequency of culverts is considerably higher than that of bridges even in the case of short span bridges. As the operational speed of modern high-speed passenger rail systems rises, higher frequencies are excited and thus more energy is encountered in frequency bands where the fundamental frequency of box culverts is located. Many research efforts have been spent on the subject of ballast instability due to bridge resonance, since it was first observed when high-speed trains were introduced to the Paris/Lyon rail line. To prevent this phenomenon from occurring, design codes establish a limit value for the vertical deck acceleration. Obviously one needs some sort of numerical model in order to estimate this acceleration level and at that point things get quite complicated. Not only acceleration but also displacement values are of interest e.g. to estimate the impact factor. According to design manuals the structural design should consider the depth of cover, trench width and condition, bedding type, backfill material, and compaction. The same applies to the numerical model however, the question is: What type of model is appropriate for this job? A 3D model including the embankment and an important part of the soil underneath the culvert is computationally very expensive and hard to justify taking into account the associated costs. Consequently, there is a clear need for simplified models and design rules in order to achieve reasonable costs. This paper will describe the results obtained from a 2D finite element model which has been calibrated by means of a 3D model and experimental data obtained at culverts that belong to the high-speed railway line that links the two towns of Segovia and Valladolid in Spain

Diseño acústico y electroacústico de Waipahu Transit Center en Honolulú, Hawái

El objetivo de este Proyecto Fin de Grado es el diseño de megafonía y PAGA (Public Address /General Alarm) de la estación de tren Waipahu Transit Center en la ciudad de Honolulú, Hawái. Esta estación forma parte de una nueva línea de tren que está en proceso de construcción actualmente llamada Honolulu Rail Transit. Inicialmente la línea de tren constará de 21 estaciones, en las que prácticamente todas están diseñadas como pasos elevados usando como referencia las autopistas que cruzan la isla. Se tiene prevista su fecha de finalización en el año 2019, aunque las primeras estaciones se inaugurarán en 2017. Se trata en primer lugar un estudio acústico del recinto a sonorizar, eligiendo los equipos necesarios: conmutadores, altavoces, amplificadores, procesador, equipo de control y micrófonos. Este primer estudio sirve para obtener una aproximación de equipos necesarios, así como la posible situación de estos dentro de la estación. Tras esto, se procede a la simulación de la estación mediante el programa de simulación acústica y electroacústica EASE 4.4. Para ello, se diseña la estación en un modelo 3D, en el que cada superficie se asocia a su material correspondiente. Para facilitar el diseño y el cómputo de las simulaciones se divide la estación en 3 partes por separado. Cada una corresponde a un nivel de la estación: Ground level, el nivel inferior que contiene la entrada; Concourse Level, pasillo que comunica los dos andenes; y Platform Level, en el que realizarán las paradas los trenes. Una vez realizado el diseño se procede al posicionamiento de altavoces en los diferentes niveles de la estación. Debido al clima existente en la isla, el cual ronda los 20°C a lo largo de todo el año, no es necesaria la instalación de sistemas de aire acondicionado o calefacción, por lo que la estación no está totalmente cerrada. Esto supone un problema al realizar las simulaciones en EASE, ya que al tratarse de un recinto abierto se deberán hallar parámetros como el tiempo de reverberación o el volumen equivalente por otros medios. Para ello, se utilizará el método Ray Tracing, mediante el cual se halla el tiempo de reverberación por la respuesta al impulso de la sala; y a continuación se calcula un volumen equivalente del recinto mediante la fórmula de Eyring. Con estos datos, se puede proceder a calcular los parámetros necesarios: nivel de presión sonora directo, nivel de presión sonora total y STI (Speech Transmission Index). Para obtener este último será necesario ecualizar antes en cada uno de los niveles de la estación. Una vez hechas las simulaciones, se comprueba que el nivel de presión sonora y los valores de inteligibilidad son acordes con los requisitos dados por el cliente. Tras esto, se procede a realizar los bucles de altavoces y el cálculo de amplificadores necesarios. Se estudia la situación de los micrófonos, que servirán para poder variar la potencia emitida por los altavoces dependiendo del nivel de ruido en la estación. Una vez obtenidos todos los equipos necesarios en la estación, se hace el conexionado entre éstos, tanto de una forma simplificada en la que se pueden ver los bucles de altavoces en cada nivel de la estación, como de una forma más detallada en la que se muestran las conexiones entre cada equipo del rack. Finalmente, se realiza el etiquetado de los equipos y un presupuesto estimado con los costes del diseño del sistema PAGA. ABSTRACT. The aim of this Final Degree Project is the design of the PAGA (Public Address / General Alarm) system in the train station Waipahu Transit Center in the city of Honolulu, Hawaii. This station is part of a new rail line that is currently under construction, called Honolulu Rail Transit. Initially, the rail line will have 21 stations, in which almost all are designed elevated using the highways that cross the island as reference. At first, it is treated an acoustic study in the areas to cover, choosing the equipment needed: switches, loudspeakers, amplifiers, DPS, control station and microphones. This first study helps to obtain an approximation of the equipments needed, as well as their placement inside the station. Thereafter, it is proceeded to do the simulation of the station through the acoustics and electroacoustics simulation software EASE 4.4. In order to do that, it is made the 3D design of the station, in which each surface is associated with its material. In order to ease the design and calculation of the simulations, the station has been divided in 3 zones. Each one corresponds with one level of the station: Ground Level, the lower level that has the entrance; Concourse Level, a corridor that links the two platforms; and Platform Level, where the trains will stop. Once the design is made, it is proceeded to place the speakers in the different levels of the station. Due to the weather in the island, which is about 20°C throughout the year, it is not necessary the installation of air conditioning or heating systems, so the station is not totally closed. This cause a problem when making the simulations in EASE, as the project is open, and it will be necessary to calculate parameters like the reverberation time or the equivalent volume by other methods. In order to do that, it will be used the Ray Tracing method, by which the reverberation time is calculated by the impulse response; and then it is calculated the equivalent volume of the area with the Eyring equation. With this information, it can be proceeded to calculate the parameters needed: direct sound pressure level, total sound pressure level and STI (Speech Transmission Index). In order to obtain the STI, it will be needed to equalize before in each of the station’s levels. Once the simulations are done, it is checked that the sound pressure level and the intelligibility values agree with the requirements given by the client. After that, it is proceeded to perform the speaker’s loops and the calculation of the amplifiers needed. It is studied the placement of the microphones, which will help to vary the power emitted by the speakers depending on the background noise level in the station. Once obtained all the necessary equipment in the station, it is done the connection diagram, both a simplified diagram in which there can be seen the speaker’s loops in each level of the station, or a more detailed diagram in which it is shown the wiring between each equipment of the rack. At last, it is done the labeling of the equipments and an estimated budget with the expenses for the PAGA design.

Recovery of Disruptions in Rapid Transit Networks

This paper studies the disruption management problem of rapid transit rail networks. Besides optimizing the timetable and the rolling stock schedules, we explicitly deal with the effects of the disruption on the passenger demand. We propose a two-step approach that combines an integrated optimization model (for the timetable and rolling stock) with a model for the passengers’ behavior. We report our computational tests on realistic problem instances of the Spanish rail operator RENFE. The proposed approach is able to find solutions with a very good balance between various managerial goals within a few minutes. Se estudia la gestión de las incidencias en redes de metro y cercanías. Se optimizan los horarios y la asignación del material rodante, teniendo en cuenta el comportamiento de los pasajeros. Se reallizan pruebas en varias líneas de la red de cercanías de Madrid, con resultados satisfactorios.

Nonlinear models for lateral dynamics of railway vehicles on bridges subject to wind action

The study of lateral dynamics of running trains on bridges is of importance mainly for the safety of the traffic, and may be relevant for laterally compliant bridges. These studies require threedimensional coupled vehicle-bridge models, wheree consideration of wheel to rail contact is a key aspect. Furthermore, an adequate evaluation of safety of rail traffic requires nonlinear models. A nonlinear coupled model is proposed here for vehicle-structure vertical and lateral dynamics. Vehicles are considered as fully three-dimensional multibody systems including gyroscopic terms and large rotation effects. The bridge structure is modeled by means of finite elements which may be of beam, shell or continuum type and may include geometric or material nonlinearities. The track geometry includes distributed track alignment irregularities. Both subsystems (bridge and vehicles) are described with coordinates in absolute reference frames, as opposed to alternative approaches which describe the multibody system with coordinates relative to the base bridge motion. The wheelrail contact employed is a semi-Hertzian model based on realistic wheel-rail profiles. It allows a detailed geometrical description of the contact patch under each wheel including multiple-point contact, flange contact and uplift. Normal and tangential stresses in each contact are integrated at each time-step to obtain the resultant contact forces. The models have been implemented within an existing finite element analysis software with multibody capabilities, Abaqus (Simulia Ltd., 2010). Further details of the model are presented in Antolín et al. (2012). Representative applications are presented for railway vehicles under lateral wind action on laterally compliant viaducts, showing the relevance of the nonlinear wheel-rail contact model as well as the interaction between bridge and vehicle.

Analysis of the railway track as a spatially periodic structure

This article presents a new and computationally efficient method of analysis of a railway track modelled as a continuous beam of 2N spans supported by elastic vertical springs. The main feature of this method is its important reduction in computational effort with respect to standard matrix methods of structural analysis. In this article, the whole structure is considered to be a repetition of a single one. The analysis presented is applied to a simple railway track model, i.e. to a repetitive beam supported on vertical springs (sleepers). The proposed method of analysis is based on the general theory of spatially periodic structures. The main feature of this theory is the possibility to apply Discrete Fourier Transform (DFT) in order to reduce a large system of q(2N + 1) linear stiffness equilibrium equations to a set of 2N + 1 uncoupled systems of q equations each. In this way, a dramatic reduction of the computational effort of solving the large system of equations is achieved. This fact is particularly important in the analysis of railway track structures, in which N is a very large number (around several thousands), and q = 2, the vertical displacement and rotation, is very small. The proposed method allows us to easily obtain the exact solution given by Samartín [1], i.e. the continuous beam railway track response. The comparison between the proposed method and other methods of analysis of railway tracks, such as Lorente de Nó and Zimmermann-Timoshenko, clearly shows the accuracy of the obtained results for the proposed method, even for low values of N. In addition, identical results between the proposed and the Lorente methods have been found, although the proposed method seems to be of simpler application and computationally more efficient than the Lorente one. Small but significative differences occur between these two methods and the one developed by Zimmermann-Timoshenko. This article also presents a detailed sensitivity analysis of the vertical displacement of the sleepers. Although standard matrix methods of structural analysis can handle this railway model, one of the objectives of this article is to show the efficiency of DFT method with respect to standard matrix structural analysis. A comparative analysis between standard matrix structural analysis and the proposed method (DFT), in terms of computational time, input, output and also software programming, will be carried out. Finally, a URL link to a MatLab computer program list, based on the proposed method, is given