Vehicular traffic surveillance and road lane detection using radar interferometry

Speed enforcement on public roadways is an important issue in order to guarantee road security and to reduce the number and seriousness of traffic accidents. Traditionally, this task has been partially solved using radar and/or laser technologies and, more recently, using video-camera based systems. All these systems have significant shortcomings that have yet to be overcome. The main drawback of classical Doppler radar technology is that the velocity measurement fails when several vehicles are in the radars beam. Modern radar systems are able to measure speed and range between vehicle and radar. However, this is not enough to discriminate the lane where the vehicle is driving on. The limitation of several vehicles in the beam is overcome using laser technology. However, laser systems have another important limitation: They cannot measure the speed of several vehicles simultaneously. Novel video-camera systems, based on license plate identification, solve the previous drawbacks, but they have the problem that they can only measure average speed but never top-speed. This paper studies the feasibility of using an interferometric linear frequency modulated continuous wave radar to improve top-speed enforcement on roadways. Two different systems based on down-the-road and across-the-road radar configurations are presented. The main advantage of the proposed solutions is they can simultaneously measure speed, range, and lane of several vehicles, allowing the univocal identification of the offenders. A detailed analysis about the operation and accuracy of these solutions is reported. In addition, the feasibility of the proposed techniques has been demonstrated with simulations and real experiments using a Ka-band interferometric radar developed by our research group.

Characterization of the Wikipedia Traffic

Since its inception, Wikipedia has grown to a solid and stable project and turned into a mass collaboration tool that allows the sharing and distribution of knowledge. The wiki approach that basis this initiative promotes the participation and collaboration of users. In addition to visits for browsing its contents, Wikipedia also receives the contributions of users to improve them. In the past, researchers paid attention to different aspects concerning authoring and quality of contents. However, little effort has been made to study the nature of the visits that Wikipedia receives. We conduct such an study using a sample of users' requests provided by the Wikimedia Foundation in the form of Squid log lines. Our sample contains more that 14,000 million requests from users all around the world and directed to all the projects maintained by the Wikimedia Foundation, including different editions of Wikipedia. This papers describes the work made to characterize the traffic directed to Wikipedia and consisting of the requests sent by its users. Our main aim is to obtain a detailed description of its composition in terms of the percentages corresponding to the different types of requests making part of it. The benefits from our work may range from the prediction of traffic peaks to the determination of the kind of resources most often requested, which can be useful for scalability considerations.

A speech interface for air traffic control terminals

Several issues concerning the current use of speech interfaces are discussed and the design and development of a speech interface that enables air traffic controllers to command and control their terminals by voice is presented. A special emphasis is made in the comparison between laboratory experiments and field experiments in which a set of ergonomics-related effects are detected that cannot be observed in the controlled laboratory experiments. The paper presents both objective and subjective performance obtained in field evaluation of the system with student controllers at an air traffic control (ATC) training facility. The system exhibits high word recognition test rates (0.4% error in Spanish and 1.5% in English) and low command error (6% error in Spanish and 10.6% error in English in the field tests). Subjective impression has also been positive, encouraging future development and integration phases in the Spanish ATC terminals designed by Aeropuertos Españoles y Navegación Aérea (AENA).

Reduction in Calculated Uncertainty of a Noise Map by Improving the Traffic Model Data Through Two Phases

The influence of applying European default traffic values to the making of a noise map was evaluated in a typical environment like Palma de Mallorca. To assess these default traffic values, a first model has been created and compared with measured noise levels. Subsequently a second traffic model, improving the input data used for the first one, has been created and validated according to the deviations. Different methodologies were also examined for collecting model input data that would be of higher quality, by analysing the improvement generated in the reduction in the uncertainty of the noise map introduced by the road traffic noise emission

Detection and Tracking of Traffic Signs Using a Recursive Bayesian Decision Framework

In this paper we propose a new method for the automatic detection and tracking of road traffic signs using an on-board single camera. This method aims to increase the reliability of the detections such that it can boost the performance of any traffic sign recognition scheme. The proposed approach exploits a combination of different features, such as color, appearance, and tracking information. This information is introduced into a recursive Bayesian decision framework, in which prior probabilities are dynamically adapted to tracking results. This decision scheme obtains a number of candidate regions in the image, according to their HS (Hue-Saturation). Finally, a Kalman filter with an adaptive noise tuning provides the required time and spatial coherence to the estimates. Results have shown that the proposed method achieves high detection rates in challenging scenarios, including illumination changes, rapid motion and significant perspective distortion

Dynamic effect of high speed railway traffic loads on the ballast track settlement

The traditional ballast track structures are still being used in high speed railways lines with success, however technical problems or performance features have led to non-ballast track solution in some cases. A considerable maintenance work is needed for ballasted tracks due to the track deterioration. Therefore it is very important to understand the mechanism of track deterioration and to predict the track settlement or track irregularity growth rate in order to reduce track maintenance costs and enable new track structures to be designed. The objective of this work is to develop the most adequate and efficient models for calculation of dynamic traffic load effects on railways track infrastructure, and then evaluate the dynamic effect on the ballast track settlement, using a ballast track settlement prediction model, which consists of the vehicle/track dynamic model previously selected and a track settlement law. The calculations are based on dynamic finite element models with direct time integration, contact between wheel and rail and interaction with railway cars. A initial irregularity profile is used in the prediction model. The track settlement law is considered to be a function of number of loading cycles and the magnitude of the loading, which represents the long-term behavior of ballast settlement. The results obtained include the track irregularity growth and the contact force in the final interaction of numerical simulation

On the efficiency of a dedicated LMA for multicast traffic distribution in PMIPv6 domains

IP multicast allows the efficient support of group communication services by reducing the number of IP flows needed for such communication. The increasing generalization in the use of multicast has also triggered the need for supporting IP multicast in mobile environments. Proxy Mobile IPv6 (PMIPv6) is a network-based mobility management solution, where the functionality to support the terminal movement resides in the network. Recently, a baseline solution has been adopted for multicast support in PMIPv6. Such base solution has inefficiencies in multicast routing because it may require multiple copies of a single stream to be received by the same access gateway. Nevertheless, there is an alternative solution to support multicast in PMIPv6 that avoids this issue. This paper evaluates by simulation the scalability of both solutions under realistic conditions, and provides an analysis of the sensitivity of the two proposals against a number of parameters.

Dynamic Analysis of high Speed Railway Traffic Loads on Ballasted Track

This paper reports the studies carried out to develop and calibrate the optimal models for the objectives of this work. In particular, quarter bogie model for vehicle, rail-wheel contact with Lagrangian multiplier method, 2D spatial discretization were selected as the optimal decisions. Furthermore, the 3D model of coupled vehicle-track also has been developed to contrast the results obtained in the 2D model. The calculations were carried out in the time domain and envelopes of relevant results were obtained for several track profiles and speed ranges. Distributed elevation irregularities were generated based on power spectral density (PSD) distributions. The results obtained include the wheel-rail contact forces, forces transmitted to the bogie by primary suspension. The latter loads are relevant for the purpose of evaluating the performance of the infrastructure

Ultrasonic sensors in urban traffic driving-aid systems

Currently, vehicles are often equipped with active safety systems to reduce the risk of accidents, most of which occur in urban environments. The most prominent include Antilock Braking Systems (ABS), Traction Control and Stability Control. All these systems use different kinds of sensors to constantly monitor the conditions of the vehicle, and act in an emergency. In this paper the use of ultrasonic sensors in active safety systems for urban traffic is proposed, and the advantages and disadvantages when compared to other sensors are discussed. Adaptive Cruise Control (ACC) for urban traffic based on ultrasounds is presented as an application example. The proposed system has been implemented in a fully-automated prototype vehicle and has been tested under real traffic conditions. The results confirm the good performance of ultrasonic sensors in these systems. ©2011 by the authors.

Optimization of urban mobility measures to achieve win-win strategies

European cities are essential in the development of Europe as they constitute the living environment of more than 60% of the population in the European Union and are drivers of the European economy – just under 85% of the EU’s gross domestic product is produced in urban areas (EC, 2007a). The car has been one of the main factors of development during the 20th century, but it is at the same time the origin of the key problems cities have to face: traffic increase. This has resulted in chronic congestion with many adverse consequences such as air pollution and noise. This loss of environmental quality is one of the reasons for urban sprawl in European cities during recent decades. But this urban sprawl at the same time worsens the environmental conditions. We must return to the dense city, but clean and competitive, and this implies reducing car use yet provides quality transport alternatives sufficient to recover and maintain the competitiveness of cities (EC, 2007a). Consequently, European cities need to establish an urban transport strategy which helps reduce their environmental problems –mainly emissions and noise – but without decreasing their trip attraction. This aspect is very important because a loss of trip attraction would result in an increase of people moving to more disperse areas, contributing towards worsening the current situation. This thesis is an attempt to contribute solutions to this problem in two ways: 1) The first is to analyze the complementarity and possible synergies of several urban transport measures aimed at improving a modal split to a more sustainable means of transport. This analysis will focus on the three aspects already mentioned: emissions, noise and attractiveness or competitiveness. 2) Once possible synergies and complementarities have been analyzed, the second objective is to propose the best combination of these measures, in terms of level of implementation, to achieve the maximum benefit with respect to the three aspects previously established: emissions, noise and attractiveness or competitiveness. Therefore, within the wide range of measures enhancing sustainable urban transport, three of them have been be selected in this thesis to establish a methodology for achieving these objectives. The analysis will be based on the region of Madrid, which is also the case study selected for this research. Las ciudades europeas son piezas fundamentales para el desarrollo europeo, ya que son el lugar de residencia de más del 60% de la población de la unión europea así como los motores de su economía – casi el 85% del PIB europeo se produce en áreas urbanas (EC, 2007a). El coche ha sido uno de los principales motores de desarrollo de las ciudades durante el siglo XX, pero se ha terminado por convertir a su vez en uno de los principales problemas con los que tiene que lidiar las ciudades: el aumento del tráfico. Esto ha derivado en unos niveles crónicos de congestión, con multitud de efectos adversos, entre los que cabe destacar la contaminación del aire y el ruido. Esta pérdida de calidad ambiental es una de las razones que ha propiciado la dispersión urbana que han experimentado las ciudades europeas en las últimas décadas. Pero esta dispersión urbana a su vez contribuye a empeorar las condiciones ambientales de las ciudades. Debemos retornar a la ciudad densa, pero limpia y competitiva, y esto implica reducir el uso del coche, pero proporcionando alternativas de transporte que permitan recuperar y mantener la competitividad de las ciudades (EC, 2007a). Por lo tanto, las ciudades europeas necesitan encontrar una estrategia de transporte urbano que ayude a reducir sus problemas medio ambientales – principalmente ruido y emisiones – pero sin hacerlas perder atractividad o competitividad. Este aspecto tiene gran importancia porque una pérdida de la misma se traduciría en un aumento de dispersión de la población hacia áreas periféricas, contribuyendo a empeorar la situación actual. Esta tesis contribuye a solucionar este problema de dos maneras: 1) La primera, analizando la complementariedad y posibles sinergias de diferentes medidas de transporte urbano orientadas a promover un reparto modal hacia modos más sostenibles. Este análisis se centrará en los tres aspectos anteriormente citados: emisiones, ruido y atractividad o competitividad. 2) Una vez las posibles sinergias y complementariedades se han analizado, el segundo objetivo es proponer la mejor combinación de estas medidas – en términos de grado de aplicación - para lograr el máximo beneficio en lo que respecta a los tres objetivos previamente establecidos. Para ello, en esta tesis se han seleccionado una serie de medidas que permitan establecer una metodología para alcanzar estos objetivos previamente definidos. El análisis se centra en la ciudad de Madrid y su área metropolitana, la cual se ha escogido como caso de estudio para realizar esta investigación.

Detecting Traffic Problems with ILP

Expert systems for decision support have recently been successfully introduced in road transport management. In this paper, we apply three state-of-the art ILP systems to learn how to detect traffic problems.

ILP Experiments in Detecting Traffic Problems

The paper describes experiments in automated acquisition of knowledge in traffic problem detection. Preliminary results show that ILP can be used to successfully learn to detect traffic problems.

Aspectos de la medición dinámica instantánea de emisiones de motores. Aplicación al desarrollo de un equipo portátil y una metodología para estudios de contaminación de vehículos en tráfico real.

Esta Tesis Doctoral se encuadra en el ámbito de la medida de emisiones contaminantes y de consumo de combustible en motores de combustión interna alternativos cuando se utilizan como plantas de potencia para propulsión de vehículos ligeros de carretera, y más concretamente en las medidas dinámicas con el vehículo circulando en tráfico real. En este ámbito, el objetivo principal de la Tesis es estudiar los problemas asociados a la medición en tiempo real con equipos embarcados de variables medioambientales, energéticas y de actividad, de vehículos ligeros propulsados por motores térmicos en tráfico real. Y como consecuencia, desarrollar un equipo y una metodología apropiada para este objetivo, con el fin de realizar consiguientemente un estudio sobre los diferentes factores que influyen sobre las emisiones y el consumo de combustible de vehículos turismo en tráfico real. La Tesis se comienza realizando un estudio prospectivo sobre los trabajos de otros autores relativos al desarrollo de equipos portátiles de medida de emisiones (Portable Emission Measurement Systems – PEMS), problemas asociados a la medición dinámica de emisiones y estudios de aplicación en tráfico real utilizando este tipo de equipos. Como resultado de este estudio se plantea la necesidad de disponer de un equipo específicamente diseñado para ser embarcado en un vehículo que sea capaz de medir en tiempo real las concentraciones de emisiones y el caudal de gases de escape, al mismo tiempo que se registran variables del motor, del vehículo y del entorno como son la pendiente y los datos meteorológicos. De esta forma se establecen las especificaciones y condiciones de diseño del equipo PEMS. Aunque al inicio de esta Tesis ya existían en el mercado algunos sistemas portátiles de medida de emisiones (PEMS: Portable Emissions Measurement Systems), en esta Tesis se investiga, diseña y construye un nuevo sistema propio, denominado MIVECO – PEMS. Se exponen, discuten y justifican todas las soluciones técnicas incorporadas en el sistema que incluyen los subsistema de análisis de gases, subsistemas de toma de muestra incluyendo caudalímetro de gases de escape, el subsistema de medida de variables del entorno y actividad del vehículo y el conjunto de sistemas auxiliares. El diseño final responde a las hipótesis y necesidades planteadas y se valida en uso real, en banco de rodillos y en comparación con otro equipos de medida de emisiones estacionarios y portátiles. En esta Tesis se presenta también toda la investigación que ha conducido a establecer la metodología de tratamiento de las señales registradas en tiempo real que incluye la sincronización, cálculos y propagación de errores. La metodología de selección y caracterización de los recorridos y circuitos y de las pautas de conducción, preparación del vehículo y calibración de los equipos forma también parte del legado de esta Tesis. Para demostrar la capacidad de medida del equipo y el tipo de resultados que pueden obtenerse y que son útiles para la comunidad científica, y las autoridades medioambientales en la parte final de esta Tesis se plantean y se presentan los resultados de varios estudios de variables endógenas y exógenas que afectan a las emisiones instantáneas y a los factores de emisión y consumo (g/km) como: el estilo de conducción, la infraestructura vial, el nivel de congestión del tráfico, tráfico urbano o extraurbano, el contenido de biocarburante, tipo de motor (diesel y encendido provocado), etc. Las principales conclusiones de esta Tesis son que es posible medir emisiones másicas y consumo de motores de vehículos en uso real y que los resultados permiten establecer políticas de reducción de impacto medio ambiental y de eficiencia energética, pero, se deben establecer unas metodologías precisas y se debe tener mucho cuidado en todo el proceso de calibración, medida y postratamientos de los datos. Abstract This doctoral thesis is in the field of emissions and fuel consumption measurement of reciprocating internal combustion engines when are used as power-trains for light-duty road vehicles, and especially in the real-time dynamic measurements procedures when the vehicle is being driven in real traffic. In this context, the main objective of this thesis is to study the problems associated with on-board real-time measuring systems of environmental, energy and activity variables of light vehicles powered by internal combustion engines in real traffic, and as a result, to develop an instrument and an appropriate methodology for this purpose, and consequently to make a study of the different factors which influence the emissions and the fuel consumption of passenger cars in real traffic. The thesis begins developing a prospective study on other authors’ works about development of Portable Emission Measurement Systems (PEMS), problems associated with dynamic emission measurements and application studies on actual traffic using PEMS. As a result of this study, it was shown that a measuring system specifically designed for being on-board on a vehicle, which can measure in real time emission concentrations and exhaust flow, and at the same time to record motor vehicle and environment variables as the slope and atmospheric data, is needed; and the specifications and design parameters of the equipment are proposed. Although at the beginning of this research work there were already on the market some PEMS, in this Thesis a new system is researched, designed and built, called MIVECO – PEMS, in order to meet such measurements needs. Following that, there are presented, discussed and justify all technical solutions incorporated in the system, including the gas analysis subsystem, sampling and exhaust gas flowmeter subsystem, the subsystem for measurement of environment variables and of the vehicle activity and the set of auxiliary subsystems. The final design meets the needs and hypotheses proposed, and is validated in real-life use and chassis dynamometer testing and is also compared with other stationary and on-board systems. This thesis also presents all the research that has led to the methodology of processing the set of signals recorded in real time including signal timing, calculations and error propagation. The methodology to select and characterize of the routes and circuits, the driving patterns, and the vehicle preparation and calibration of the instruments and sensors are part of the legacy of this thesis. To demonstrate the measurement capabilities of the system and the type of results that can be obtained and that are useful for the scientific community and the environmental authorities, at the end of this Thesis is presented the results of several studies of endogenous and exogenous variables that affect the instantaneous and averaged emissions and consumption factors (g/km), as: driving style, road infrastructure, the level of traffic congestion, urban and extra-urban traffic, biofuels content, type of engine (diesel or spark ignition) etc. The main conclusions of this thesis are that it is possible to measure mass emissions and consumption of vehicle engines in actual use and that the results allow us to establish policies to reduce environmental impact and improve energy efficiency, but, to establish precise methodologies and to be very careful in the entire process of calibration, measurement and data post-treatment is necessary.

Distributed collaborative processing in wireless sensor networks with application to target localization and beamforming

Abstract The proliferation of wireless sensor networks and the variety of envisioned applications associated with them has motivated the development of distributed algorithms for collaborative processing over networked systems. One of the applications that has attracted the attention of the researchers is that of target localization where the nodes of the network try to estimate the position of an unknown target that lies within its coverage area. Particularly challenging is the problem of estimating the target’s position when we use received signal strength indicator (RSSI) due to the nonlinear relationship between the measured signal and the true position of the target. Many of the existing approaches suffer either from high computational complexity (e.g., particle filters) or lack of accuracy. Further, many of the proposed solutions are centralized which make their application to a sensor network questionable. Depending on the application at hand and, from a practical perspective it could be convenient to find a balance between localization accuracy and complexity. Into this direction we approach the maximum likelihood location estimation problem by solving a suboptimal (and more tractable) problem. One of the main advantages of the proposed scheme is that it allows for a decentralized implementation using distributed processing tools (e.g., consensus and convex optimization) and therefore, it is very suitable to be implemented in real sensor networks. If further accuracy is needed an additional refinement step could be performed around the found solution. Under the assumption of independent noise among the nodes such local search can be done in a fully distributed way using a distributed version of the Gauss-Newton method based on consensus. Regardless of the underlying application or function of the sensor network it is al¬ways necessary to have a mechanism for data reporting. While some approaches use a special kind of nodes (called sink nodes) for data harvesting and forwarding to the outside world, there are however some scenarios where such an approach is impractical or even impossible to deploy. Further, such sink nodes become a bottleneck in terms of traffic flow and power consumption. To overcome these issues instead of using sink nodes for data reporting one could use collaborative beamforming techniques to forward directly the generated data to a base station or gateway to the outside world. In a dis-tributed environment like a sensor network nodes cooperate in order to form a virtual antenna array that can exploit the benefits of multi-antenna communications. In col-laborative beamforming nodes synchronize their phases in order to add constructively at the receiver. Some of the inconveniences associated with collaborative beamforming techniques is that there is no control over the radiation pattern since it is treated as a random quantity. This may cause interference to other coexisting systems and fast bat-tery depletion at the nodes. Since energy-efficiency is a major design issue we consider the development of a distributed collaborative beamforming scheme that maximizes the network lifetime while meeting some quality of service (QoS) requirement at the re¬ceiver side. Using local information about battery status and channel conditions we find distributed algorithms that converge to the optimal centralized beamformer. While in the first part we consider only battery depletion due to communications beamforming, we extend the model to account for more realistic scenarios by the introduction of an additional random energy consumption. It is shown how the new problem generalizes the original one and under which conditions it is easily solvable. By formulating the problem under the energy-efficiency perspective the network’s lifetime is significantly improved. Resumen La proliferación de las redes inalámbricas de sensores junto con la gran variedad de posi¬bles aplicaciones relacionadas, han motivado el desarrollo de herramientas y algoritmos necesarios para el procesado cooperativo en sistemas distribuidos. Una de las aplicaciones que suscitado mayor interés entre la comunidad científica es la de localization, donde el conjunto de nodos de la red intenta estimar la posición de un blanco localizado dentro de su área de cobertura. El problema de la localization es especialmente desafiante cuando se usan niveles de energía de la seal recibida (RSSI por sus siglas en inglés) como medida para la localization. El principal inconveniente reside en el hecho que el nivel de señal recibida no sigue una relación lineal con la posición del blanco. Muchas de las soluciones actuales al problema de localization usando RSSI se basan en complejos esquemas centralizados como filtros de partículas, mientas que en otras se basan en esquemas mucho más simples pero con menor precisión. Además, en muchos casos las estrategias son centralizadas lo que resulta poco prácticos para su implementación en redes de sensores. Desde un punto de vista práctico y de implementation, es conveniente, para ciertos escenarios y aplicaciones, el desarrollo de alternativas que ofrezcan un compromiso entre complejidad y precisión. En esta línea, en lugar de abordar directamente el problema de la estimación de la posición del blanco bajo el criterio de máxima verosimilitud, proponemos usar una formulación subóptima del problema más manejable analíticamente y que ofrece la ventaja de permitir en¬contrar la solución al problema de localization de una forma totalmente distribuida, convirtiéndola así en una solución atractiva dentro del contexto de redes inalámbricas de sensores. Para ello, se usan herramientas de procesado distribuido como los algorit¬mos de consenso y de optimización convexa en sistemas distribuidos. Para aplicaciones donde se requiera de un mayor grado de precisión se propone una estrategia que con¬siste en la optimización local de la función de verosimilitud entorno a la estimación inicialmente obtenida. Esta optimización se puede realizar de forma descentralizada usando una versión basada en consenso del método de Gauss-Newton siempre y cuando asumamos independencia de los ruidos de medida en los diferentes nodos. Independientemente de la aplicación subyacente de la red de sensores, es necesario tener un mecanismo que permita recopilar los datos provenientes de la red de sensores. Una forma de hacerlo es mediante el uso de uno o varios nodos especiales, llamados nodos “sumidero”, (sink en inglés) que actúen como centros recolectores de información y que estarán equipados con hardware adicional que les permita la interacción con el exterior de la red. La principal desventaja de esta estrategia es que dichos nodos se convierten en cuellos de botella en cuanto a tráfico y capacidad de cálculo. Como alter¬nativa se pueden usar técnicas cooperativas de conformación de haz (beamforming en inglés) de manera que el conjunto de la red puede verse como un único sistema virtual de múltiples antenas y, por tanto, que exploten los beneficios que ofrecen las comu¬nicaciones con múltiples antenas. Para ello, los distintos nodos de la red sincronizan sus transmisiones de manera que se produce una interferencia constructiva en el recep¬tor. No obstante, las actuales técnicas se basan en resultados promedios y asintóticos, cuando el número de nodos es muy grande. Para una configuración específica se pierde el control sobre el diagrama de radiación causando posibles interferencias sobre sis¬temas coexistentes o gastando más potencia de la requerida. La eficiencia energética es una cuestión capital en las redes inalámbricas de sensores ya que los nodos están equipados con baterías. Es por tanto muy importante preservar la batería evitando cambios innecesarios y el consecuente aumento de costes. Bajo estas consideraciones, se propone un esquema de conformación de haz que maximice el tiempo de vida útil de la red, entendiendo como tal el máximo tiempo que la red puede estar operativa garantizando unos requisitos de calidad de servicio (QoS por sus siglas en inglés) que permitan una decodificación fiable de la señal recibida en la estación base. Se proponen además algoritmos distribuidos que convergen a la solución centralizada. Inicialmente se considera que la única causa de consumo energético se debe a las comunicaciones con la estación base. Este modelo de consumo energético es modificado para tener en cuenta otras formas de consumo de energía derivadas de procesos inherentes al funcionamiento de la red como la adquisición y procesado de datos, las comunicaciones locales entre nodos, etc. Dicho consumo adicional de energía se modela como una variable aleatoria en cada nodo. Se cambia por tanto, a un escenario probabilístico que generaliza el caso determinista y se proporcionan condiciones bajo las cuales el problema se puede resolver de forma eficiente. Se demuestra que el tiempo de vida de la red mejora de forma significativa usando el criterio propuesto de eficiencia energética.