Contributions to trajectory prediction theory and its application to arrival management for air traffic control

La gestión del tráfico aéreo (Air Traffic Management, ATM) está experimentando un cambio de paradigma hacia las denominadas operaciones basadas trayectoria. Bajo dicho paradigma se modifica el papel de los controladores de tráfico aéreo desde una operativa basada su intervención táctica continuada hacia una labor de supervisión a más largo plazo. Esto se apoya en la creciente confianza en las soluciones aportadas por las herramientas automatizadas de soporte a la decisión más modernas. Para dar soporte a este concepto, se precisa una importante inversión para el desarrollo, junto con la adquisición de nuevos equipos en tierra y embarcados, que permitan la sincronización precisa de la visión de la trayectoria, basada en el intercambio de información entre ambos actores. Durante los últimos 30 a 40 años las aerolíneas han generado uno de los menores retornos de la inversión de entre todas las industrias. Sin beneficios tangibles, la industria aérea tiene dificultades para atraer el capital requerido para su modernización, lo que retrasa la implantación de dichas mejoras. Esta tesis tiene como objetivo responder a la pregunta de si las capacidades actualmente instaladas en las aeronaves comerciales se pueden aplicar para lograr la sincronización de la trayectoria con el nivel de calidad requerido. Además, se analiza en ella si, conjuntamente con mejoras en las herramientas de predicción trayectorias instaladas en tierra en para facilitar la gestión de las arribadas, dichas capacidades permiten obtener los beneficios esperados en el marco de las operaciones basadas en trayectoria. Esto podría proporcionar un incentivo para futuras actualizaciones de la aviónica que podrían llevar a mejoras adicionales. El concepto operacional propuesto en esta tesis tiene como objetivo permitir que los aviones sean pilotados de una manera consistente con las técnicas actuales de vuelo optimizado. Se permite a las aeronaves que desciendan en el denominado “modo de ángulo de descenso gestionado” (path-managed mode), que es el preferido por la mayoría de las compañías aéreas, debido a que conlleva un reducido consumo de combustible. El problema de este modo es que en él no se controla de forma activa el tiempo de llegada al punto de interés. En nuestro concepto operacional, la incertidumbre temporal se gestiona en mediante de la medición del tiempo en puntos estratégicamente escogidos a lo largo de la trayectoria de la aeronave, y permitiendo la modificación por el control de tierra de la velocidad de la aeronave. Aunque la base del concepto es la gestión de las ordenes de velocidad que se proporcionan al piloto, para ser capaces de operar con los niveles de equipamiento típicos actualmente, dicho concepto también constituye un marco en el que la aviónica más avanzada (por ejemplo, que permita el control por el FMS del tiempo de llegada) puede integrarse de forma natural, una vez que esta tecnología este instalada. Además de gestionar la incertidumbre temporal a través de la medición en múltiples puntos, se intenta reducir dicha incertidumbre al mínimo mediante la mejora de las herramienta de predicción de la trayectoria en tierra. En esta tesis se presenta una novedosa descomposición del proceso de predicción de trayectorias en dos etapas. Dicha descomposición permite integrar adecuadamente los datos de la trayectoria de referencia calculada por el Flight Management System (FMS), disponibles usando Futuro Sistema de Navegación Aérea (FANS), en el sistema de predicción de trayectorias en tierra. FANS es un equipo presente en los aviones comerciales de fuselaje ancho actualmente en la producción, e incluso algunos aviones de fuselaje estrecho pueden tener instalada avionica FANS. Además de informar automáticamente de la posición de la aeronave, FANS permite proporcionar (parte de) la trayectoria de referencia en poder de los FMS, pero la explotación de esta capacidad para la mejora de la predicción de trayectorias no se ha estudiado en profundidad en el pasado. La predicción en dos etapas proporciona una solución adecuada al problema de sincronización de trayectorias aire-tierra dado que permite la sincronización de las dimensiones controladas por el sistema de guiado utilizando la información de la trayectoria de referencia proporcionada mediante FANS, y también facilita la mejora en la predicción de las dimensiones abiertas restantes usado un modelo del guiado que explota los modelos meteorológicos mejorados disponibles en tierra. Este proceso de predicción de la trayectoria de dos etapas se aplicó a una muestra de 438 vuelos reales que realizaron un descenso continuo (sin intervención del controlador) con destino Melbourne. Dichos vuelos son de aeronaves del modelo Boeing 737-800, si bien la metodología descrita es extrapolable a otros tipos de aeronave. El método propuesto de predicción de trayectorias permite una mejora en la desviación estándar del error de la estimación del tiempo de llegada al punto de interés, que es un 30% menor que la que obtiene el FMS. Dicha trayectoria prevista mejorada se puede utilizar para establecer la secuencia de arribadas y para la asignación de las franjas horarias para cada aterrizaje (slots). Sobre la base del slot asignado, se determina un perfil de velocidades que permita cumplir con dicho slot con un impacto mínimo en la eficiencia del vuelo. En la tesis se propone un nuevo algoritmo que determina las velocidades requeridas sin necesidad de un proceso iterativo de búsqueda sobre el sistema de predicción de trayectorias. El algoritmo se basa en una parametrización inteligente del proceso de predicción de la trayectoria, que permite relacionar el tiempo estimado de llegada con una función polinómica. Resolviendo dicho polinomio para el tiempo de llegada deseado, se obtiene de forma natural el perfil de velocidades optimo para cumplir con dicho tiempo de llegada sin comprometer la eficiencia. El diseño de los sistemas de gestión de arribadas propuesto en esta tesis aprovecha la aviónica y los sistemas de comunicación instalados de un modo mucho más eficiente, proporcionando valor añadido para la industria. Por tanto, la solución es compatible con la transición hacia los sistemas de aviónica avanzados que están desarrollándose actualmente. Los beneficios que se obtengan a lo largo de dicha transición son un incentivo para inversiones subsiguientes en la aviónica y en los sistemas de control de tráfico en tierra. ABSTRACT Air traffic management (ATM) is undergoing a paradigm shift towards trajectory based operations where the role of an air traffic controller evolves from that of continuous intervention towards supervision, as decision making is improved based on increased confidence in the solutions provided by advanced automation. To support this concept, significant investment for the development and acquisition of new equipment is required on the ground as well as in the air, to facilitate the high degree of trajectory synchronisation and information exchange required. Over the past 30-40 years the airline industry has generated one of the lowest returns on invested capital among all industries. Without tangible benefits realised, the airline industry may find it difficult to attract the required investment capital and delay acquiring equipment needed to realise the concept of trajectory based operations. In response to these challenges facing the modernisation of ATM, this thesis aims to answer the question whether existing aircraft capabilities can be applied to achieve sufficient trajectory synchronisation and improvements to ground-based trajectory prediction in support of the arrival management process, to realise some of the benefits envisioned under trajectory based operations, and to provide an incentive for further avionics upgrades. The proposed operational concept aims to permit aircraft to operate in a manner consistent with current optimal aircraft operating techniques. It allows aircraft to descend in the fuel efficient path managed mode as preferred by a majority of airlines, with arrival time not actively controlled by the airborne automation. The temporal uncertainty is managed through metering at strategically chosen points along the aircraft’s trajectory with primary use of speed advisories. While the focus is on speed advisories to support all aircraft and different levels of equipage, the concept also constitutes a framework in which advanced avionics as airborne time-of-arrival control can be integrated once this technology is widely available. In addition to managing temporal uncertainty through metering at multiple points, this temporal uncertainty is minimised by improving the supporting trajectory prediction capability. A novel two-stage trajectory prediction process is presented to adequately integrate aircraft trajectory data available through Future Air Navigation Systems (FANS) into the ground-based trajectory predictor. FANS is standard equipment on any wide-body aircraft in production today, and some single-aisle aircraft are easily capable of being fitted with FANS. In addition to automatic position reporting, FANS provides the ability to provide (part of) the reference trajectory held by the aircraft’s Flight Management System (FMS), but this capability has yet been widely overlooked. The two-stage process provides a ‘best of both world’s’ solution to the air-ground synchronisation problem by synchronising with the FMS reference trajectory those dimensions controlled by the guidance mode, and improving on the prediction of the remaining open dimensions by exploiting the high resolution meteorological forecast available to a ground-based system. The two-stage trajectory prediction process was applied to a sample of 438 FANS-equipped Boeing 737-800 flights into Melbourne conducting a continuous descent free from ATC intervention, and can be extrapolated to other types of aircraft. Trajectories predicted through the two-stage approach provided estimated time of arrivals with a 30% reduction in standard deviation of the error compared to estimated time of arrival calculated by the FMS. This improved predicted trajectory can subsequently be used to set the sequence and allocate landing slots. Based on the allocated landing slot, the proposed system calculates a speed schedule for the aircraft to meet this landing slot at minimal flight efficiency impact. A novel algorithm is presented that determines this speed schedule without requiring an iterative process in which multiple calls to a trajectory predictor need to be made. The algorithm is based on parameterisation of the trajectory prediction process, allowing the estimate time of arrival to be represented by a polynomial function of the speed schedule, providing an analytical solution to the speed schedule required to meet a set arrival time. The arrival management solution proposed in this thesis leverages the use of existing avionics and communications systems resulting in new value for industry for current investment. The solution therefore supports a transition concept from mixed equipage towards advanced avionics currently under development. Benefits realised under this transition may provide an incentive for ongoing investment in avionics.

Estrategia de desarrollo de negocio para el producto Atos RTTF (Real Time Traffic Forecast)

El objetivo del presente proyecto de fin de máster es desplegar la estrategia de negocio completa, desde las declaraciones y premisas hasta la implantación y ejecución, para una solución novedosa de la compañía AtoS. Esta solución se denomina RTTF (Real Time Traffic Forecast), y sus objetivos principales, a alto nivel, son los siguientes: a) Conseguir unas mejores ciudades en la que vivir y trabajar. b) Realizar una gestión de tráfico proactiva para un uso de recursos de las ciudades optimizado. Nuestro planteamiento en este trabajo es, basado en las el módulo de estrategia del máster, diseñar un plan de negocio para desarrollar y potenciar la anterior solución. Para ello también necesitaremos herramientas de otros módulos del máster, como el de marketing, operaciones, o finanzas. Para ello, comenzaremos analizando el entorno desde el punto de vista de la posible receptividad al producto, así como de los posibles competidores, con objeto de posicionar de manera inicial nuestra solución, y reflexionar sobre si ese posicionamiento es el adecuado. Añadiendo también el estudio interno de la compañía y de la propia solución sobre la que versa el proyecto. El principal entregable del presente trabajo será un plan de negocio, con fechas, objetivos y un listado de clientes por orden de prioridad, con el objetivo final de desarrollar la solución.

Experimental analysis of energy savings and hygrothermal conditions improvement by means of air curtaines in stores with intensive pedestrian traffic

Current worldwide building legislation requirements aim to the design and construction of technical services that reduce energy consumption and improve indoor hygrothermal conditions. The retail sector in Spain, with a lot of outdated technical systems, demands energy conservation measures in order to reduce the increasingly electrical consumption for cooling. Climatic separation with modern air curtains and advanced hygrothermal control systems enables energy savings and can keep suitable indoor air temperature and humidity of stores with intense pedestrian traffic, especially when located in hot humid climates. As stated in the article, the energy savings in commercial buildings with these systems exceeds 30%

A survey of feature selection in Internet traffic characterization

In the last decade, the research community has focused on new classification methods that rely on statistical characteristics of Internet traffic, instead of pre-viously popular port-number-based or payload-based methods, which are under even bigger constrictions. Some research works based on statistical characteristics generated large fea-ture sets of Internet traffic; however, nowadays it?s impossible to handle hun-dreds of features in big data scenarios, only leading to unacceptable processing time and misleading classification results due to redundant and correlative data. As a consequence, a feature selection procedure is essential in the process of Internet traffic characterization. In this paper a survey of feature selection methods is presented: feature selection frameworks are introduced, and differ-ent categories of methods are briefly explained and compared; several proposals on feature selection in Internet traffic characterization are shown; finally, future application of feature selection to a concrete project is proposed.

Investigations on the distribution of air transport traffic and CO2 emissions within the European Union

This study analyses the structure of air traffic and its distribution among the different countries in the European Union, as well as traffic with an origin or destination in non-EU countries. Data sources are Eurostat statistics and actual flight information from EUROCONTROL. Relevant variables such as the number of flights, passengers or cargo tonnes and production indicators (RPKs) are used together with fuel consumption and CO2 emissions data. The segmentation of air traffic in terms of distance permits an assessment of air transport competition with surface transport modes. The results show a clear concentration of traffic in the five larger countries (France, Germany, Italy, Spain and UK), in terms of RPKs. In terms of distance the segment between 500 and 1000 km in the EU, has more flights, passengers, RTKs and CO2 emissions than larger distances. On the environmental side, the distribution of CO2 emissions within the EU Member States is presented, together with fuel efficiency parameters. In general, a direct relationship between RPKs and CO2 emissions is observed for all countries and all distance bands. Consideration is given to the uptake of alternative fuels. Segmenting CO2 emissions per distance band and aircraft type reveals which flights contribute the most the overall EU CO2 emissions. Finally, projections for future CO2 emissions are estimated, according to three different air traffic growth and biofuel introduction scenarios.

Dynamic behaviour of underspanned suspension road bridges under traffic loads

Underspanned suspension bridges are structures with important economical and aesthetic advantages, due to their high structural efficiency. However, road bridges of this typology are still uncommon because of limited knowledge about this structural system. In particular, there remains some uncertainty over the dynamic behaviour of these bridges, due to their extreme lightness. The vibrations produced by vehicles crossing the viaduct are one of the main concerns. In this work, traffic-induced dynamic effects on this kind of viaduct are addressed by means of vehicle-bridge dynamic interaction models. A finite element method is used for the structure, and multibody dynamic models for the vehicles, while interaction is represented by means of the penalty method. Road roughness is included in this model in such a way that the fact that profiles under left and right tyres are different, but not independent, is taken into account. In addition, free software {PRPgenerator) to generate these profiles is presented in this paper. The structural dynamic sensitivity of underspanned suspension bridges was found to be considerable, as well as the dynamic amplification factors and deck accelerations. It was also found that vehicle speed has a relevant influence on the results. In addition, the impact of bridge deformation on vehicle vibration was addressed, and the effect on the comfort of vehicle users was shown to be negligible.

Using aircraft as wind sensors for estimating accurate wind fields for air traffic management applications

A study which examines the use of aircraft as wind sensors in a terminal area for real-time wind estimation in order to improve aircraft trajectory prediction is presented in this paper. We describe not only different sources in the aircraft systems that provide the variables needed to derivate the wind velocity but the capabilities which allow us to present this information for ATM Applications. Based on wind speed samples from aircraft landing at Madrid-Barajas airport, a real-time wind field will be estimated using a data processing approach through a minimum variance method. Finally the accuracy of this procedure will be evaluated for this information to be useful to Air Traffic Control.

Planning and Management of Mobility in Natural Protected Areas

The paper describes some relevant results of an on-going research aiming to elaborate a methodology to help the mobility management in natural parks, compatible with their protection missions: it has been developed a procedure to reproduce the mobility-environment relationships in various operational conditions. The final purpose is the identification of: a) the effects of various choices in transport planning, both at long term and strategic level; b) the most effective policies of mobility management. The work is articulated in the following steps: 1) definition of protected area on the basis of ecological and socio-economic criteria and legislative constraints; 2) analysis of mobility needs in the protected areas; 3) reconstruction of the state of the art of mobility management in natural parks at European level; 4) analysis of used traffic flows measurement methods; 5) analysis of environmental impacts due to transport systems modelling (air pollution and noise only); 6) identification of mitigation measures to be potentially applied. The whole methodology has been tested and validated on Italian case studies: i) the concerned area has been zoned according to the land-use peculiarities; ii) the local situations of transport infrastructure (roads and parking), services (public transport systems) and rules (traffic regulations) have been mapped with references to physical and functional attributes; iii) the mobility, both systematic and touristic, has been represented in an origin-destination matrix. By means of an assignment model the flows have been distributed and the corresponding average speeds to quantify gaseous and noise emissions was calculated, the criticalities in the reference scenario have been highlighted, as well as some alternative scenarios, including both operational and infrastructural measures have been identified. The comparison between projects and reference scenario allowed the quantification of effects (variation of emissions) for each scenario and a selection of the most effective management actions to be taken.

Development of the infrastructure for a multi-agent traffic management system simulation

This document contains detailed description of the design and the implementation of a multi-agent application controlling traffic lights in a city together with a system for simulating traffic and testing. The goal of this thesis is to design and build a simplified intelligent and distributed solution to the problem with the traffic in the big cities following different good practices in order to allow future refining of the model of the real world. The problem of the traffic in the big cities is still a problem that cannot be solved. Not only is the increasing number of cars a reason for the traffic jams, but also the way the traffic is organized. Usually, the intersections with traffic lights are replaced by roundabouts or interchanges to increase the number of cars that can cross the intersection in certain time. But still there are places where the infrastructure cannot be changed and the traffic light semaphores are the only way to control the car flows. In real life, the traffic lights have a predefined plan for change or they receive information from a centralized system when and how they have to change. But what if the traffic lights can cooperate and decide on their own when and how to change? Using this problem, the purpose of the thesis is to explore different agent-based software engineering approaches to design and build a non-conventional distributed system. From the software engineering point of view, the goal of the thesis is to apply the knowledge and use the skills, acquired during the various courses of the master program in Software Engineering, while solving a practical and complex problem such as the traffic in the cities.

Planning and management of mobility in natural protected areas

The final purpose is the identification of: a) the effects of various choices in transport planning, both at long term and strategic level; b) the most effective policies of mobility management. The preliminary work was articulated in the following steps: 1) definition of protected area on the basis of ecological and socio-economic criteria and legislative constraints; 2) analysis of mobility needs in the protected areas; 3) reconstruction of the state of the art of mobility management in natural parks at European level; 4) analysis of used traffic flows measurement methods; 5) analysis of environmental impacts due to transport systems modelling (limited to air pollution and noise); 6) identification of mitigation measures to the potentially applied. The whole methodology has been firstly tested on the case study of the National Park of ?Gran Sasso and Monti della Laga? and further validated on the National Park of ?Gargano?, both located Italy: i) the concerned area has been zoned according to the land-use peculiarities; ii) the local situations of transport infrastructure (roads and parking), services (public transport systems) and rules (traffic regulations) have been mapped with references to physical and functional attributes; iii) the mobility, both systematic and touristic, has been synthetically represented in an origin-destination matrix. By means of an assignment model it has been determined the distribution of flows and the corresponding average speeds to quantify gaseous and noise emissions. On this basis the environmental criticalities in the reference scenario have been highlighted, as well as some alternative scenarios including both operational and infrastructural measures have been identified. The comparison between the projects and the reference scenario allowed the quantification of the effects (variation of emissions) for each scenario and a selection of the most effective management actions to be taken.

Event-based time series data preprocessing: application to traffic flow time series

Traffic flow time series data are usually high dimensional and very complex. Also they are sometimes imprecise and distorted due to data collection sensor malfunction. Additionally, events like congestion caused by traffic accidents add more uncertainty to real-time traffic conditions, making traffic flow forecasting a complicated task. This article presents a new data preprocessing method targeting multidimensional time series with a very high number of dimensions and shows its application to real traffic flow time series from the California Department of Transportation (PEMS web site). The proposed method consists of three main steps. First, based on a language for defining events in multidimensional time series, mTESL, we identify a number of types of events in time series that corresponding to either incorrect data or data with interference. Second, each event type is restored utilizing an original method that combines real observations, local forecasted values and historical data. Third, an exponential smoothing procedure is applied globally to eliminate noise interference and other random errors so as to provide good quality source data for future work.

Development and assessment of traffic-related emission abatement measures for the Madrid city (Spain) through the WRF-SMOKE-CMAQ modelling system

The achievement of the limit values established in the European legislation pose an important handicap for large urban areas with intense road traffic, such as Madrid (Spain). Despite permanent measures included in air quality plans it is important to assess additional measures that may be temporally applied under unfavourable conditions. This paper reports on the simulation of different traffic restriction strategies in Madrid for high-pollution episodes.

Predicción de tráfico de contenedores a corto plazo mediante técnicas de minería de datos : redes neuronales artificiales y redes bayesianas

El correcto pronóstico en el ámbito de la logística de transportes es de vital importancia para una adecuada planificación de medios y recursos, así como de su optimización. Hasta la fecha los estudios sobre planificación portuaria se basan principalmente en modelos empíricos; que se han utilizado para planificar nuevas terminales y desarrollar planes directores cuando no se dispone de datos iniciales, analíticos; más relacionados con la teoría de colas y tiempos de espera con formulaciones matemáticas complejas y necesitando simplificaciones de las mismas para hacer manejable y práctico el modelo o de simulación; que requieren de una inversión significativa como para poder obtener resultados aceptables invirtiendo en programas y desarrollos complejos. La Minería de Datos (MD) es un área moderna interdisciplinaria que engloba a aquellas técnicas que operan de forma automática (requieren de la mínima intervención humana) y, además, son eficientes para trabajar con las grandes cantidades de información disponible en las bases de datos de numerosos problemas prácticos. La aplicación práctica de estas disciplinas se extiende a numerosos ámbitos comerciales y de investigación en problemas de predicción, clasificación o diagnosis. Entre las diferentes técnicas disponibles en minería de datos las redes neuronales artificiales (RNA) y las redes probabilísticas o redes bayesianas (RB) permiten modelizar de forma conjunta toda la información relevante para un problema dado. En el presente trabajo se han analizado dos aplicaciones de estos casos al ámbito portuario y en concreto a contenedores. En la Tesis Doctoral se desarrollan las RNA como herramienta para obtener previsiones de tráfico y de recursos a futuro de diferentes puertos, a partir de variables de explotación, obteniéndose valores continuos. Para el caso de las redes bayesianas (RB), se realiza un trabajo similar que para el caso de las RNA, obteniéndose valores discretos (un intervalo). El principal resultado que se obtiene es la posibilidad de utilizar tanto las RNA como las RB para la estimación a futuro de parámetros físicos, así como la relación entre los mismos en una terminal para una correcta asignación de los medios a utilizar y por tanto aumentar la eficiencia productiva de la terminal. Como paso final se realiza un estudio de complementariedad de ambos modelos a corto plazo, donde se puede comprobar la buena aceptación de los resultados obtenidos. Por tanto, se puede concluir que estos métodos de predicción pueden ser de gran ayuda a la planificación portuaria. The correct assets’ forecast in the field of transportation logistics is a matter of vital importance for a suitable planning and optimization of the necessary means and resources. Up to this date, ports planning studies were basically using empirical models to deal with new terminals planning or master plans development when no initial data are available; analytical models, more connected to the queuing theory and the waiting times, and very complicated mathematical formulations requiring significant simplifications to acquire a practical and easy to handle model; or simulation models, that require a significant investment in computer codes and complex developments to produce acceptable results. The Data Mining (DM) is a modern interdisciplinary field that include those techniques that operate automatically (almost no human intervention is required) and are highly efficient when dealing with practical problems characterized by huge data bases containing significant amount of information. These disciplines’ practical application extends to many commercial or research fields, dealing with forecast, classification or diagnosis problems. Among the different techniques of the Data Mining, the Artificial Neuronal Networks (ANN) and the probabilistic – or Bayesian – networks (BN) allow the joint modeling of all the relevant information for a given problem. This PhD work analyses their application to two practical cases in the ports field, concretely to container terminals. This PhD work details how the ANN have been developed as a tool to produce traffic and resources forecasts for several ports, based on exploitation variables to obtain continuous values. For the Bayesian networks case (BN), a similar development has been carried out, obtaining discreet values (an interval). The main finding is the possibility to use ANN and BN to estimate future needs of the port’s or terminal’s physical parameters, as well as the relationship between them within a specific terminal, that allow a correct assignment of the necessary means and, thus, to increase the terminal’s productive efficiency. The final step is a short term complementarily study of both models, carried out in order to verify the obtained results. It can thus be stated that these prediction methods can be a very useful tool in ports’ planning.

Aeroelastic effects in a traffic sign panel induced by a passing vehicle

Here, a simple theoretical model of the vehicle induced flow and its effects on traffic sign panels is presented. The model is a continuation of a previous one by Sanz-Andrés and coworkers, now including the flexibility of the panel (and, therefore, the flow effects associated to the motion of the panel). Through the paper an aeroelastic one-degree-of-freedom model is developed and the flow effects are computed from unsteady potential theory. The influence of panel's mechanical properties (mass, damping ratio, and stiffness) in the motion induced forces are numerically analyzed.

Vehicle-induced loads on traffic sign panels

The determination of the loads on traffic sign panels in the current standards does not, in general, take into account the vehicle-induced loads, as explained by Quinn, Baker and Wright (QBW in what follows) (J. Wind Eng. Ind. Aerodyn. 89 (2001) 831). On the other hand, a report from Cali and Covert (CC) (J. Wind Eng. Ind. Aerodyn. 84 (2000) 87) indicates that in highway sign support structures, vehicle-induced loads have led to premature failures in some cases. The aim of this paper is to present a mathematical model for the vehicle-induced load on a flat sign panel, simple enough to give analytical results, but able to explain the main characteristics of the phenomenon. The results of the theoretical model help to explain the behaviour observed in the experiments performed in previous studies.