Heterogeneous wireless networking technologies such as satellite, UMTS, WiMax and WLAN are being used to provide network access for both voice and data services. In big cities, the densely populated areas like town centres, shopping centres and train stations may have coverage of multiple wireless networks. Traditional Radio Access Technology (RAT) selection algorithms are mainly based on the 'Always Best Connected' paradigm whereby the mobile nodes are always directed towards the available network which has the strongest and fastest link. Hence a large number of mobile users may be connected to the more common UMTS while the other networks like WiMax and WLAN would be underutilised, thereby creating an unbalanced load across these different wireless networks. This high variation among the load across different co-located networks may cause congestion on overloaded network leading to high call blocking and call dropping probabilities. This can be alleviated by moving mobile users from heavily loaded networks to least loaded networks. This thesis presents a novel framework for load balancing in heterogeneous wireless networks incorporating the IEEE 802.21 Media Independent Handover (MIH). The framework comprises of novel load-aware RAT selection techniques and novel network load balancing mechanism. Three new different load balancing algorithms i.e. baseline, fuzzy and neural-fuzzy algorithms have also been presented in this thesis that are used by the framework for efficient load balancing across the different co-located wireless networks. A simulation model developed in NS2 validates the performance of the proposed load balancing framework. Different attributes like load distribution in all wireless networks, handover latencies, packet drops, throughput at mobile nodes and network utilization have been observed to evaluate the effects of load balancing using different scenarios. The simulation results indicate that with load balancing the performance efficiency improves as the overloaded situation is avoided by load balancing.

This work concentrates on the application of diversity techniques and space time block coding for future mobile wireless communications. The initial system analysis employs a space-time coded OFDM transmitter over a multipath Rayleigh channel, and a receiver which uses a selection combining diversity technique. The performance of this combined scenario is characterised in terms of the bit error rate and throughput. A novel four element QOSTBC scheme is introduced, it is created by reforming the detection matrix of the original QOSTBC scheme, for which an orthogonal channel matrix is derived. This results in a computationally less complex linear decoding scheme as compared with the original QOSTBC. Space time coding schemes for three, four and eight transmitters were also derived using a Hadamard matrix. The practical optimization of multi-antenna networks is studied for realistic indoor and mixed propagation scenarios. The starting point is a detailed analysis of the throughput and field strength distributions for a commercial dual band 802.11n MIMO radio operating indoors in a variety of line of sight and non-line of sight scenarios. The physical model of the space is based on architectural schematics, and realistic propagation data for the construction materials. The modelling is then extended and generalized to a multi-storey indoor environment, and a large mixed site for indoor and outdoor channels based on the Bradford University campus. The implications for the physical layer are also explored through the specification of antenna envelope correlation coefficients. Initially this is for an antenna module configuration with two independent antennas in close proximity. An operational method is proposed using the scattering parameters of the system and which incorporates the intrinsic power losses of the radiating elements. The method is extended to estimate the envelope correlation coefficient for any two elements in a general (N,N) MIMO antenna array. Three examples are presented to validate this technique, and very close agreement is shown to exist between this method and the full electromagnetic analysis using the far field antenna radiation patterns.

The proliferation of modern wireless networks increases demand for high capacity and throughput in order to provide faster, more robust, efficient and broadband services to end users. Mobile WiMAX and LTE are examples of such networks in which for some cases they have exposed limited connectivity due to harsh environment. Relay stations are preferred to overcome problems of weak or no access for such network devices, that are placed in specific positions to maintain high quality of data transfer at low cost and provide the required connectivity anywhere anytime. These stations should be equipped with an antenna system capable of establishing communication between base station (backhaul link) and end users (access link). This thesis focuses on the design and development of a new antenna system that is suitable for a relay-based wireless network. Planar geometries of microstrip patch antennas are utilized. The antenna system comprises two antenna modules: a new design of a single antenna for access link and a new design of an antenna array for backhaul link realization. Both antenna specifications are compatible with the IEEE802.16j protocol standard. Hence, relay station should be capable of pointing its radiation pattern to the base station antenna, thus to achieve the desired radiation pattern of the relay station, a new beam-forming module is proposed, designed and developed to generate the proper radiation pattern. The beam-forming module incorporating digital phase shifters and attenuator chips is fabricated and tested. The optimization process using the Least Mean Square (LMS) algorithm is considered in this study to assign the proper phase and amplitude that is necessary to each radiation element excitation current, to produce the desired steered radiation pattern. A comprehensive study on the coupling effects for several relative positions between two new backhaul and access link antenna elements is performed. Two new antenna configurations for coupling reduction are tested and the simulated and measured results in terms of antenna radiation performances were compared and commented.

Les dernières décennies ont connu l’apogée des transmissions hertziennes, et celles à venir connaîtront incontestablement le développement et le déploiement intense de systèmes de communications sans-fil. Dès à présent, il est possible de communiquer par onde sur petite et très petite distance (LAN et PAN). Les populations se sont familiariséesavec les interfaces bluetooth (IEEE802.15) présentes dans la majorité des objetscommuniquant (ordinateur portable, téléphone, PDA, etc...). Les foyers s’équipentmaintenant facilement et à bas prix d’interfaceWi-Fi (IEEE802.11), afin de profiter d’uneutilisation nomade de leur accès internet. Ainsi, la forte croissance dumarché des offresinternet combinée avec celle du marché des téléphones mobiles ont habitués un large spectre d’utilisateurs à communiquer sans fil. Ce contexte sociologique et financier encourage donc l’arrivée de solutions nouvelles répondant à des besoins latents. Parmi ceux-là, le marché met en évidence le manque de système de communication sur moyenne distance (MAN). Les réseaux ad-hoc peuvent répondre à ce genre de besoin. Mais àce jour, les performances sont trop faibles pour les besoins des utilisateurs et elles dépendenttrop fortement de la densité desmachines nomades. Aussi, le consortiumIEEEcherche au travers de sa norme IEEE802.16 à fournir un système complet de communicationsans-fil sur moyenne distance (MAN). Appelé aussiWiMAX, ce système se basesur une architecture composée d’une station de base (BS) et de nombreux mobiles utilisateurs(SS). Le standard IEEE802.16 définit les caractéristiques de la couche physiqueet de la couche MAC. Il décrit l’ensemble des interactions et événements pouvant avoirlieu entre la station de base et les stations mobiles. Enfin, le standard fournit différents paramètres et variables servant aux mécanismes de communication. Comme tout nouveau standard émergeant, la norme IEEE802.16 ne profite pas d’un état de l’art aussi développé que celui du IEEE802.11 par exemple. Aussi, de nombreuses études et idées sont à développer.En premier lieu, nous effectuons un large rappel de la norme WiMAX et en particulier le IEEE802.16e. Associé à cela, nous dressons un état de l’art des travaux traitant des aspects et perspectives liés au sujet de notre étude.Par la suite, nous proposons un modèle novateur de performance des communicationsIEEE802.16e. Au travers de ce modèle, nous développons une étude générale et exhaustive des principaux paramètres de communication. L’étude explicite l’impact deces paramètres ainsi que l’influence de leur évolutions possibles. De cela, nous critiquonsla pertinence de chacun d’eux en proposant des alternatives de configurations.5En sus, nous proposons un mécanisme novateur favorisant le respect de qualité de service(QoS) sur couche AC.Nous développons un principe original d’établissement de connexion favorisant l’accès aux communications sensibles aux délais de transmission.Dans une dernière partie, nous déterminons la capacité d’un système IEEE802.16 à gérer les arrivées et départs des utilisateurs. Tout en y associant une étude de performance d’un nouvel algorithme de contrôle d’admission. Cet algorithme d’admission vise à remplir des objectifs multiples : empêcher les famines de ressources sur les trafics les moins prioritaires, favoriser l’admission des utilisateurs en maintenant une gestion optimale de la ressource radio. Notre étude aboutit à une modélisation et une critique des variations de paramètre associés à ce nouvel algorithme. Nous y intégrons par la suite le principe de mobilité où les utilisateurs ont la capacité de se mouvoir au sein d’une cellule. Cette intégration se fait en y associant des mécanismes originaux afin d’assurer la pérennité du service aux utilisateurs mobiles. / The last decade witnessed the peak of the hertzian communications. The following ones will undoubtedly testify the intensive deployment and the development of all wireless ways of transmission. Due to cheaper equipments, the people are now used with all sorts of connected objects : laptop, smartphone, pad, and more recently, Connected Video display and audio diffusers. All these stuffs allow to keep an access to internet, even in a nomad use. This economical and sociological context promotes the emerging of new solutions metting latent needs by offering better performances. Consumer studies highlight particularly the lack of transmissions solution for Metropolitan Area Networks (MAN). Ad-hoc wireless solutions lead to satisfy the MAN needs, but the throughput is too importantly related to the ad-hoc customer capacity and density over the MAN coverage.The IEEE consortium seeks, through its IEEE802.16e standart, to provide a wireless transmission technology specifically design for the middle range network. Knowed as WiMAX, this system are based on a point to multipoint architecture. WiMAX standart gathers Base Station (BS) and Subscriber Stations (SS), and defines for both the Physical and MAC layer in the OSI Model. In addition, the standart proposes a set of default parameters for the two first OSI Layers.As any emerging standart, the IEEE802.16e suffers form a lack of litterature (works, studies and enhancement proposals). More studies are explicitly needed to craft and tune the IEEE802.16e standart in order to better answer to the specific issues met in the actual context of transmission.In a first step, we present in a large scale the IEEE802.16e standart specifications. In addition we highlight the main state of art linked to this subject.Second, we propose an original performance model, the first one that takes in account all the MAC layer parameters of the standart. Based on this model, we lead a general and exhaustive performance study of each communication parameters. This study highlights the importance of each parameters and propose some enhancements in fonction of the type of Quality of Service (QoS). In addition, we introduce an call engaging mecanism which respects the QoS on the MAC layer.In a last part, we compute the IEEE802.16e capacity to manage the incoming and leaving calls. we perform this study by introducing a new Connection Admission Control (CAC). The CAC algorithm achieves sevral objectives : prevent from the lack of ressource for the lowest priority flows as well as optimize the radio resource consumption to facilitate the access for the users. Our study is concluded by proposing an new capacity model and algorithm for the CAC. Moreover, this last proposal prevents the call drop due to user mobility.

Submitted by Edisangela Bastos (edisangela@ufpa.br) on 2014-01-13T19:18:21Z No. of bitstreams: 2 license_rdf: 23898 bytes, checksum: e363e809996cf46ada20da1accfcd9c7 (MD5) Dissertacao_AvaliacaoTecnologiaFemtocell.pdf: 6899905 bytes, checksum: 6f9fe92f8092f1159ecbcd1e607afc6e (MD5) / Approved for entry into archive by Ana Rosa Silva(arosa@ufpa.br) on 2014-01-16T12:20:24Z (GMT) No. of bitstreams: 2 license_rdf: 23898 bytes, checksum: e363e809996cf46ada20da1accfcd9c7 (MD5) Dissertacao_AvaliacaoTecnologiaFemtocell.pdf: 6899905 bytes, checksum: 6f9fe92f8092f1159ecbcd1e607afc6e (MD5) / Made available in DSpace on 2014-01-16T12:20:24Z (GMT). No. of bitstreams: 2 license_rdf: 23898 bytes, checksum: e363e809996cf46ada20da1accfcd9c7 (MD5) Dissertacao_AvaliacaoTecnologiaFemtocell.pdf: 6899905 bytes, checksum: 6f9fe92f8092f1159ecbcd1e607afc6e (MD5) Previous issue date: 2013 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Mensurar os impactos do tráfego de aplicações interativas para TV Digital nas redes sem fio de 4a geração em especial WIMAX e femtocell tem sido um grande desafio para pesquisadores em todo o mundo, o teste destas tecnologias se mostra promissora para a melhor qualidade de serviço prestado pelas operadoras. Inicialmente, identificando o padrão de tráfego de rede através da aferição e caracterização de tráfego de uma aplicação interativa de TV Digital do Sistema Brasileiro de TV Digital (SBTVD). A partir de então, as simulações são feitas sobre uma rede sem fio. Para este estudo, a rede WiMAX foi escolhida como um de nossos estudo de caso. Um estudo dos impactos do uso desta aplicação em uma WMAN (Wireless Metropolitan Área Network) com WiMAX e também utilizando femtocells. Evidentemente, tecnologias sem fio apresentam uma grande variação da qualidade do sinal. Deste modo, é necessário utilizar uma solução para reduzir essa degradação no sinal. Dentre as possíveis soluções, o uso de femtocells surge como alternativa viável para estas melhorias, lembrando que uso de femtocell esta diretamente ligado para áreas onde o sinal é zero ou muito baixo. A utilização de simulações discretas através de ferramentas apropriadas como o OPNET, se mostram bastante úteis para viabilizar a utilização das tecnologias existentes, expondo-as a condições mais adversas de fluxo, carga , numero de usuários e distancias que certamente influenciam no desempenha de cada uma delas. / Traffic measurement on Digital TV interactive applications for fourth generation networks, especially WiMAX and femtocell, has been a challenge to researchers around the world. The traffic pattern of an interactive application on the Brazillian System of Digital TV (SBTVD) was identified. Simulations on a wireless network were carried out using data obtained of traffic analysis. In this work a WiMAX and a femtocell network were chosen to simulate the return channel of a Digital TV application on a WMAN (Wireless Metropolitan Area Network). In order to reduce signal attenuation, femtocell arises as a promising solution, reducing macrocell usage, as femtocells cover indoor environments. The simulations is this work were executed using OPNET software. Through them it is possible to estimate the feasibility of femtocell and WiMAX technologies as return channel for Digital TV.

Wireless communications have been an indispensable aspect of everyday life, and there is an increasing consumer demand for accessing several wireless communication technologies from a single, compact, mobile device. System-on-package (SOP) technology is an advanced packaging technology that has been proven to realize the convergence of multiple functions into miniaturized, high-performance systems to meet this demand. With the advancements in the SOP technology, the miniaturization of the front-end module has been achieved using embedded passives in multilayer packages. However, the integration of the antenna directly on the module package is still the barrier to achieve a fully-integrated, high-performance RF SOP system. The main reason for this missing link is that integrating the antenna on the package requires miniaturizing the antenna, which is a difficult task. The focus of this dissertation is to design high-performance antennas along with developing techniques for miniaturization and system-on-package (SOP) integration of these antennas to achieve fully-integrated SOP systems using advanced multilayer organic substrates and thin-film magneto-dielectric materials. The targeted spectrum for the antenna designs are 2.4/5 GHz WLAN/WiMAX and 60 GHz WPAN bands. Several novel antenna designs and configurations to integrate the antenna on the package along with the module are discussed in this dissertation. The advanced polymers used in this research are Liquid Crystalline Polymer (LCP), RXP, and thin-film magneto-dielectrics.

IEEE 802.16 是一支援都會型無線網路的協定，IEEE 802.16支援PMP模式(點對多點)和網狀模式兩種。在網狀模式中，所有節點的構成仿如ad-hoc方式，並依據在控制性子框中的排程資訊來計算下次遞送時間。在資料傳送之前，會有一段設定連線的時間。這段時間，每一個節點都必須跟鄰節點競爭，以取得廣播它的排程資訊給鄰節點的機會。這樣的行為跟它過去的歷史無關。換句話說，它具有”時間同質性”而適合以隨機程序來模擬。在這篇論文中，我們將用排隊程序來建立排程行為的模型，然後以馬可夫鏈來估計它的平均延遲時間，也就是一節點持續地競爭直到贏為止的這段等待時間。 / The IEEE 802.16 standard is a protocol for wireless metropolitan networks. IEEE 802.16 MAC protocol supports both of PMP (point to multipoint) and Mesh mode. In the mesh mode, all nodes are organized in a fashion similar ad-hoc and calculate their next transmission time based on the scheduling information performed in the control subframe. Before data transmission for a certain node, there is a period of time to setup the connection. During this period, each node has to compete with each other for the opportunity to advertise scheduling messages to its neighbors. This behavior does not depend on past history. In other words, it is a “Time Homogeneous” and suitable for being modeled by stochastic process. In this thesis, we will model this scheduling behavior by queuing process, and apply the Markov Chain to estimate its average delay time which a node keep waiting until it win the competition.

Les travaux de cette thèse s'inscrivent dans le contexte des réseaux sans fil et des réseaux d'accès par Satellite en particulier, qui facilitent l'installation d'infrastructures réseau dans les zones géographiquement reculées et faiblement peuplées. Cependant, ces derniers présentent certains inconvénients lorsqu'il s'agit de déployer des applications multimédia interactives. En effet, de telles applications requièrent un délai de bout en bout aussi faible que possible et plus généralement exigent une meilleure Qualité de Service (QdS) du système de communication que le classique Meilleur-Effort (BE) afin de fonctionner correctement. Or, les réseaux d'accès par satellite géostationnaires souffrent déjà d'un délai de propagation non négligeable d'autant plus accru que la transmission des données est assurée par des mécanismes d'allocation dynamique, par exemple dans un système DVB-S2/RCS. Dans ces travaux de thèse, nous proposons d'utiliser les informations de signalisation de session des applications multimédia basées sur le protocole de session SIP afin d'ajuster le paramétrage du système de communication selon une approche " cross-layer " qui permet alors d'améliorer de façon significative la réactivité du système. Nous avons proposé plusieurs solutions pour, d'abord réduire le temps entre la demande de communication et le démarrage effectif du transfert des flux multimédia, ensuite réduire le délai de transmission des données multimédia durant la communication (tout en utilisant de manière optimale les ressources réseau disponibles sur la voie retour), et enfin accroître le nombre de flux multimédia admissibles dans le réseau satellite tout en leur garantissant un niveau de QdS satisfaisant. Afin de faciliter l'intégration et l'implémentation des solutions proposées dans un système de communication réel, un mécanisme de communication inter-couches d'optimisation est proposé et développé. De plus, une architecture orientée web services est utilisée afin de faciliter la découverte et l'invocation des différentes niveaux de services de communication présents dans de tels réseaux d'accès. Les solutions proposées ont été évaluées dans des environnements sans fil émulés et réels

Submitted by João Arthur Martins (joao.arthur@ufpe.br) on 2015-03-11T18:10:20Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertaçao JOSIAS de LIMA JUNIOR.pdf: 4252506 bytes, checksum: 714cb7aa7e2dc62943c697bd35a222ed (MD5) / Approved for entry into archive by Daniella Sodre (daniella.sodre@ufpe.br) on 2015-03-13T13:00:53Z (GMT) No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertaçao JOSIAS de LIMA JUNIOR.pdf: 4252506 bytes, checksum: 714cb7aa7e2dc62943c697bd35a222ed (MD5) / Made available in DSpace on 2015-03-13T13:00:53Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertaçao JOSIAS de LIMA JUNIOR.pdf: 4252506 bytes, checksum: 714cb7aa7e2dc62943c697bd35a222ed (MD5) Previous issue date: 2013-05 / Recent years have witnessed the emergence of new communication techniques in Computer Science that use both wireless technologies and self-organizing features. Their combination eliminates the need for using pre-defined wired structures and prior configurations. In this work, we develop a simulated version, using the network simulator 3 (ns-3), of the Heterogeneous Technologies Routing (HTR) framework that is suitable for interconnecting devices in a heterogeneous ad hoc network, extending its supported heterogeneous technologies with the addition of WiMAX and LTE devices, proposes an extension to enable multipath routing over this framework and investigates the impact of tuning routing parameters on convergence interval and energy consumption. Although a large number of works exist that investigate the tuning of routing parameter settings, to the best of our knowledge, none of them investigate the impact of these on protocol convergence and energy consumption. Multipath HTR routing, the extension we propose, offers several benefits such as load balancing, fault tolerance, routing loop prevention, energy-conservation, low end-to-end delay, and congestion avoidance, among others. This work performs a comparative analysis of the proposed HTR extension, with the baseline HTR, and the widely used Optimized Link State Routing (OLSR) protocol. Moreover, we investigate the impacts of tuning the HELLO refresh interval and perform a comparative analysis of the tuned HTR with the OLSR protocol. Both evaluations are validated through the simulation of heterogeneous technologies such as WiMAX, 3GPP LTE and Wi-Fi. Results show that the multipath extension effectively improves the data delivery ratio, and reduces the end-to-end delay without major impact on network energy consumption. For the tuned HTR, results show that varying the HELLO refresh interval can improve the convergence of the protocol and reduce the energy consumption. / Recentemente, novas técnicas de comunicação surgiram que usam tecnologia sem fio e são capazes de se autoconfigurar. A combinação desses fatores elimina a necessidade de utilizar estruturas cabeadas e configurações pré-definidas. Neste trabalho, o autor desenvolve uma versão simulada, através do simulador de rede “network Simulator 3” (ns-3), do arcabouço “Heterogeneous Technologies Routing” (HTR), que se propõe à interconectar dispositivos em redes heterogêneas ad hoc, estendendo o seu suporte às tecnologias heterogêneas com a adição de dispositivos WiMAX e LTE, propõe uma extensão para fornecer um roteamento baseado em múltiplos caminhos (“Multipath”) e investiga o impacto de modificar os parâmetros de configuração do roteamento no tempo de convergência da rede e consumo de energia. Apesar de um grande número de obras existentes que investigam o impacto da mudança de parâmetros de configuração do roteamento, no meu conhecimento, nenhum deles investiga o impacto destes no tempo de convergência do protocolo e consumo de energia. O “Multipath HTR”, a extensão proposta, oferece vários benefícios como balanceamento de carga, tolerância a falhas, prevenção de “loops” de roteamento, conservação de energia, baixo atraso fim-a-fim, e evita o congestionamento, entre outros. Este trabalho faz uma análise comparativa da extensão ao HTR proposta, com a base do HTR, e o protocolo amplamente utilizado “Optimized Link State Routing” (OLSR). Além disso, o esse trabalho investiga o impacto de variar o intervalo de envio de mensagens de HELLO e realiza uma análise comparativa do HTR modificado (“Tuned HTR”) com o protocolo OLSR. As duas avaliações são realizadas através de simulação usando tecnologias heterogêneas como WiMAX, 3GPP LTE e Wi-Fi. Resultados mostram que a extensão de múltiplos caminhos proposta melhora a taxa de transmissão de dados, e reduz o atraso fim-a-fim sem maiores impactos no consumo de energia da rede. Para o “Tuned HTR”, resultados mostram que a variação do intervalo de envio de mensagens de HELLO pode melhorar a convergência do protocolo e reduz o consumo de energia.

Scheduling has always been an indispensable part of resource allocation in wireless networks. Accurate information about channel-state is assumed as a modeling simplification. However, in a real-life network ,e.g., Long Term Evolution(LTE) or IEEE 802.16e WiMAX, the channel-state information feedback to the transmitter can have uncertainty. The primary reason being that although resource allocation is done at the finer granularity of a Physical Resource Block (PRB), channel-state information is still feedback at the coarser granularity of a sub band, which is a group of PRBs. This is done to reduce the feedback traffic from the users to the Base Station. However, this averaging causes information loss and hence, the resulting uncertainty at the scheduler. Moreover, uncertainty might be present in the channel-estimates because of the very process of estimation. In the first part of the thesis, we model the channel-estimate in accuracy and characterize the network stability region. Compared to earlier works, we allow the channel estimates to have dependence among themselves, which is a more realistic situation in a modern LTE or WiMax network. We then propose two simple Max Weight based scheduling schemes that achieve any rate in the interior of the stability region. We also derive an asymptotically tight upper bound on the mean queueing delay in our system under one of the throughput-optimal policies we propose. The above policies ensure stability of the network and we have also obtained bounds on the mean queueing delays. However, different applications may require certain quality of service which may not be satisfied by these policies. Thus, we also propose a throughput-optimal policy for the network under traffic with heterogeneous QoS constraints and present some numerical results studying its performance. In the second part of the thesis, we study the problem of energy-efficient scheduling under average delay constraint. For wireless access technologies, the largest power consumer is the Base Station(BS). Any reduction in the power consumption in a BS will reduce carbon footprint from the Information and Communication Technology sector. We concentrate on the problem of minimizing the total non-renewable power consumed in a Green BS, that is powered by renewable energy sources ,e.g., solar/wind energy and may also be connected to the power grid or diesel generators. Specifically, we consider the problem of minimizing the average grid power consumption of a Green BS downlink in scheduling multiple users with average delay constraints. We have a packetized model for the data packets (i.e., the packets cannot be fragmented) which is a more realistic model for packet-switched networks. The power function is a non-decreasing convex function of the queue-lengths and only one user is allowed to transmit in a slot. We prove the existence of a power optimal policy under delay constraints for multiple users. We analyse the problem and provide some structural results for the optimal policy.