A cooperative game theory analysis for transmission loss allocation

This paper presents an analysis and discussion, based on cooperative game theory, for the allocation of the cost of losses to generators and demands in transmission systems. We construct a cooperative game theory model in which the players are represented by equivalent bilateral exchanges and we search for a unique loss allocation solution, the Core. Other solution concepts, such as the Shapley Value, the Bilateral Shapley Value and the Kernel are also explored. Our main objective is to illustrate why is not possible to find an optimal solution for allocating the cost of losses to the users of a network. Results and relevant conclusions are presented for a 4-bus system and a 14-bus system. (c) 2007 Elsevier B.V. All rights reserved.

An Uphill Battle: Incorporating cooperative learning using a largely individualized curriculum

In this action research study of my classroom of 8th grade mathematics, I investigated if cooperative learning could be an effective teaching method with the Saxon curriculum. Saxon curriculum is largely individualized in that most lessons could be completed without much group interaction. I discovered that cooperative learning was very successful with the curriculum as long as it was structured. Ninety-five percent of the students in the study preferred to work in groups, and I observed mathematical communication grow with most of the students. As a result of this research, I plan to continue to incorporate cooperative learning into my mathematics classroom. I will use cooperative learning with all of my mathematics classes, even the ones that do not use the Saxon curriculum. I believe in the power of working together.

Cooperative communication and distributed detection in wireless sensor networks

Recent progress in microelectronic and wireless communications have enabled the development of low cost, low power, multifunctional sensors, which has allowed the birth of new type of networks named wireless sensor networks (WSNs). The main features of such networks are: the nodes can be positioned randomly over a given field with a high density; each node operates both like sensor (for collection of environmental data) as well as transceiver (for transmission of information to the data retrieval); the nodes have limited energy resources. The use of wireless communications and the small size of nodes, make this type of networks suitable for a large number of applications. For example, sensor nodes can be used to monitor a high risk region, as near a volcano; in a hospital they could be used to monitor physical conditions of patients. For each of these possible application scenarios, it is necessary to guarantee a trade-off between energy consumptions and communication reliability. The thesis investigates the use of WSNs in two possible scenarios and for each of them suggests a solution that permits to solve relating problems considering the trade-off introduced. The first scenario considers a network with a high number of nodes deployed in a given geographical area without detailed planning that have to transmit data toward a coordinator node, named sink, that we assume to be located onboard an unmanned aerial vehicle (UAV). This is a practical example of reachback communication, characterized by the high density of nodes that have to transmit data reliably and efficiently towards a far receiver. It is considered that each node transmits a common shared message directly to the receiver onboard the UAV whenever it receives a broadcast message (triggered for example by the vehicle). We assume that the communication channels between the local nodes and the receiver are subject to fading and noise. The receiver onboard the UAV must be able to fuse the weak and noisy signals in a coherent way to receive the data reliably. It is proposed a cooperative diversity concept as an effective solution to the reachback problem. In particular, it is considered a spread spectrum (SS) transmission scheme in conjunction with a fusion center that can exploit cooperative diversity, without requiring stringent synchronization between nodes. The idea consists of simultaneous transmission of the common message among the nodes and a Rake reception at the fusion center. The proposed solution is mainly motivated by two goals: the necessity to have simple nodes (to this aim we move the computational complexity to the receiver onboard the UAV), and the importance to guarantee high levels of energy efficiency of the network, thus increasing the network lifetime. The proposed scheme is analyzed in order to better understand the effectiveness of the approach presented. The performance metrics considered are both the theoretical limit on the maximum amount of data that can be collected by the receiver, as well as the error probability with a given modulation scheme. Since we deal with a WSN, both of these performance are evaluated taking into consideration the energy efficiency of the network. The second scenario considers the use of a chain network for the detection of fires by using nodes that have a double function of sensors and routers. The first one is relative to the monitoring of a temperature parameter that allows to take a local binary decision of target (fire) absent/present. The second one considers that each node receives a decision made by the previous node of the chain, compares this with that deriving by the observation of the phenomenon, and transmits the final result to the next node. The chain ends at the sink node that transmits the received decision to the user. In this network the goals are to limit throughput in each sensor-to-sensor link and minimize probability of error at the last stage of the chain. This is a typical scenario of distributed detection. To obtain good performance it is necessary to define some fusion rules for each node to summarize local observations and decisions of the previous nodes, to get a final decision that it is transmitted to the next node. WSNs have been studied also under a practical point of view, describing both the main characteristics of IEEE802:15:4 standard and two commercial WSN platforms. By using a commercial WSN platform it is realized an agricultural application that has been tested in a six months on-field experimentation.

Cooperative Wireless Systems

This Ph.D. dissertation reports on the work performed at the Wireless Communication Laboratory - University of Bologna and National Research Council - as well as, for six months, at the Fraunhofer Institute for Integrated Circuit (IIS) in Nürnberg. The work of this thesis is in the area of wireless communications, especially with regards to cooperative communications aspects in narrow-band and ultra-wideband systems, cooperative links characterization, network geometry, power allocation techniques,and synchronization between nodes. The underpinning of this work is devoted to developing a general framework for design and analysis of wireless cooperative communication systems, which depends on propagation environment, transmission technique, diversity method, power allocation for various scenarios and relay positions. The optimal power allocation for minimizing the bit error probability at the destination is derived. In addition, a syncronization algorithm for master-slave communications is proposed with the aim of jointly compensate the clock drift and offset of wireless nodes composing the network.

Renal microvascular assembly and repair: power and promise of molecular definition.

Developmental assembly of the renal microcirculation is a precise and coordinated process now accessible to experimental scrutiny. Although definition of the cellular and molecular determinants is incomplete, recent findings have reframed concepts and questions about the origins of vascular cells in the glomerulus and the molecules that direct cell recruitment, specialization and morphogenesis. New findings illustrate principles that may be applied to defining critical steps in microvascular repair following glomerular injury. Developmental assembly of endothelial, mesangial and epithelial cells into glomerular capillaries requires that a coordinated, temporally defined series of steps occur in an anatomically ordered sequence. Recent evidence shows that both vasculogenic and angiogenic processes participate. Local signals direct cell migration, proliferation, differentiation, cell-cell recognition, formation of intercellular connections, and morphogenesis. Growth factor receptor tyrosine kinases on vascular cells are important mediators of many of these events. Cultured cell systems have suggested that basic fibroblast growth factor (bFGF), hepatocyte growth factor (HGF), and vascular endothelial growth factor (VEGF) promote endothelial cell proliferation, migration or morphogenesis, while genetic deletion experiments have defined an important role for PDGF beta receptors and platelet-derived growth factor (PDGF) B in glomerular development. Receptor tyrosine kinases that convey non-proliferative signals also contribute in kidney and other sites. The EphB1 receptor, one of a diverse class of Eph receptors implicated in neural cell targeting, directs renal endothelial migration, cell-cell recognition and assembly, and is expressed with its ligand in developing glomeruli. Endothelial TIE2 receptors bind angiopoietins (1 and 2), the products of adjacent supportive cells, to signals direct capillary maturation in a sequence that defines cooperative roles for cells of different lineages. Ultimately, definition of the cellular steps and molecular sequence that direct microvascular cell assembly promises to identify therapeutic targets for repair and adaptive remodeling of injured glomeruli.

Bargaining for power and information : an experimental and theoretical analysis of the interaction between institutions, externalities and adverse selection

Bargaining is the building block of many economic interactions, ranging from bilateral to multilateral encounters and from situations in which the actors are individuals to negotiations between firms or countries. In all these settings, economists have been intrigued for a long time by the fact that some projects, trades or agreements are not realized even though they are mutually beneficial. On the one hand, this has been explained by incomplete information. A firm may not be willing to offer a wage that is acceptable to a qualified worker, because it knows that there are also unqualified workers and cannot distinguish between the two types. This phenomenon is known as adverse selection. On the other hand, it has been argued that even with complete information, the presence of externalities may impede efficient outcomes. To see this, consider the example of climate change. If a subset of countries agrees to curb emissions, non-participant regions benefit from the signatories’ efforts without incurring costs. These free riding opportunities give rise to incentives to strategically improve ones bargaining power that work against the formation of a global agreement. This thesis is concerned with extending our understanding of both factors, adverse selection and externalities. The findings are based on empirical evidence from original laboratory experiments as well as game theoretic modeling. On a very general note, it is demonstrated that the institutions through which agents interact matter to a large extent. Insights are provided about which institutions we should expect to perform better than others, at least in terms of aggregate welfare. Chapters 1 and 2 focus on the problem of adverse selection. Effective operation of markets and other institutions often depends on good information transmission properties. In terms of the example introduced above, a firm is only willing to offer high wages if it receives enough positive signals about the worker’s quality during the application and wage bargaining process. In Chapter 1, it will be shown that repeated interaction coupled with time costs facilitates information transmission. By making the wage bargaining process costly for the worker, the firm is able to obtain more accurate information about the worker’s type. The cost could be pure time cost from delaying agreement or cost of effort arising from a multi-step interviewing process. In Chapter 2, I abstract from time cost and show that communication can play a similar role. The simple fact that a worker states to be of high quality may be informative. In Chapter 3, the focus is on a different source of inefficiency. Agents strive for bargaining power and thus may be motivated by incentives that are at odds with the socially efficient outcome. I have already mentioned the example of climate change. Other examples are coalitions within committees that are formed to secure voting power to block outcomes or groups that commit to different technological standards although a single standard would be optimal (e.g. the format war between HD and BlueRay). It will be shown that such inefficiencies are directly linked to the presence of externalities and a certain degree of irreversibility in actions. I now discuss the three articles in more detail. In Chapter 1, Olivier Bochet and I study a simple bilateral bargaining institution that eliminates trade failures arising from incomplete information. In this setting, a buyer makes offers to a seller in order to acquire a good. Whenever an offer is rejected by the seller, the buyer may submit a further offer. Bargaining is costly, because both parties suffer a (small) time cost after any rejection. The difficulties arise, because the good can be of low or high quality and the quality of the good is only known to the seller. Indeed, without the possibility to make repeated offers, it is too risky for the buyer to offer prices that allow for trade of high quality goods. When allowing for repeated offers, however, at equilibrium both types of goods trade with probability one. We provide an experimental test of these predictions. Buyers gather information about sellers using specific price offers and rates of trade are high, much as the model’s qualitative predictions. We also observe a persistent over-delay before trade occurs, and this mitigates efficiency substantially. Possible channels for over-delay are identified in the form of two behavioral assumptions missing from the standard model, loss aversion (buyers) and haggling (sellers), which reconcile the data with the theoretical predictions. Chapter 2 also studies adverse selection, but interaction between buyers and sellers now takes place within a market rather than isolated pairs. Remarkably, in a market it suffices to let agents communicate in a very simple manner to mitigate trade failures. The key insight is that better informed agents (sellers) are willing to truthfully reveal their private information, because by doing so they are able to reduce search frictions and attract more buyers. Behavior observed in the experimental sessions closely follows the theoretical predictions. As a consequence, costless and non-binding communication (cheap talk) significantly raises rates of trade and welfare. Previous experiments have documented that cheap talk alleviates inefficiencies due to asymmetric information. These findings are explained by pro-social preferences and lie aversion. I use appropriate control treatments to show that such consideration play only a minor role in our market. Instead, the experiment highlights the ability to organize markets as a new channel through which communication can facilitate trade in the presence of private information. In Chapter 3, I theoretically explore coalition formation via multilateral bargaining under complete information. The environment studied is extremely rich in the sense that the model allows for all kinds of externalities. This is achieved by using so-called partition functions, which pin down a coalitional worth for each possible coalition in each possible coalition structure. It is found that although binding agreements can be written, efficiency is not guaranteed, because the negotiation process is inherently non-cooperative. The prospects of cooperation are shown to crucially depend on i) the degree to which players can renegotiate and gradually build up agreements and ii) the absence of a certain type of externalities that can loosely be described as incentives to free ride. Moreover, the willingness to concede bargaining power is identified as a novel reason for gradualism. Another key contribution of the study is that it identifies a strong connection between the Core, one of the most important concepts in cooperative game theory, and the set of environments for which efficiency is attained even without renegotiation.

Cooperative Multi-robot Patrolling: A study of distributed approaches based on mathematical models of game theory to protect infrastructures

El principio de Teoría de Juegos permite desarrollar modelos estocásticos de patrullaje multi-robot para proteger infraestructuras criticas. La protección de infraestructuras criticas representa un gran reto para los países al rededor del mundo, principalmente después de los ataques terroristas llevados a cabo la década pasada. En este documento el termino infraestructura hace referencia a aeropuertos, plantas nucleares u otros instalaciones. El problema de patrullaje se define como la actividad de patrullar un entorno determinado para monitorear cualquier actividad o sensar algunas variables ambientales. En esta actividad, un grupo de robots debe visitar un conjunto de puntos de interés definidos en un entorno en intervalos de tiempo irregulares con propósitos de seguridad. Los modelos de partullaje multi-robot son utilizados para resolver este problema. Hasta el momento existen trabajos que resuelven este problema utilizando diversos principios matemáticos. Los modelos de patrullaje multi-robot desarrollados en esos trabajos representan un gran avance en este campo de investigación. Sin embargo, los modelos con los mejores resultados no son viables para aplicaciones de seguridad debido a su naturaleza centralizada y determinista. Esta tesis presenta cinco modelos de patrullaje multi-robot distribuidos e impredecibles basados en modelos matemáticos de aprendizaje de Teoría de Juegos. El objetivo del desarrollo de estos modelos está en resolver los inconvenientes presentes en trabajos preliminares. Con esta finalidad, el problema de patrullaje multi-robot se formuló utilizando conceptos de Teoría de Grafos, en la cual se definieron varios juegos en cada vértice de un grafo. Los modelos de patrullaje multi-robot desarrollados en este trabajo de investigación se han validado y comparado con los mejores modelos disponibles en la literatura. Para llevar a cabo tanto la validación como la comparación se ha utilizado un simulador de patrullaje y un grupo de robots reales. Los resultados experimentales muestran que los modelos de patrullaje desarrollados en este trabajo de investigación trabajan mejor que modelos de trabajos previos en el 80% de 150 casos de estudio. Además de esto, estos modelos cuentan con varias características importantes tales como distribución, robustez, escalabilidad y dinamismo. Los avances logrados con este trabajo de investigación dan evidencia del potencial de Teoría de Juegos para desarrollar modelos de patrullaje útiles para proteger infraestructuras. ABSTRACT Game theory principle allows to developing stochastic multi-robot patrolling models to protect critical infrastructures. Critical infrastructures protection is a great concern for countries around the world, mainly due to terrorist attacks in the last decade. In this document, the term infrastructures includes airports, nuclear power plants, and many other facilities. The patrolling problem is defined as the activity of traversing a given environment to monitoring any activity or sensing some environmental variables If this activity were performed by a fleet of robots, they would have to visit some places of interest of an environment at irregular intervals of time for security purposes. This problem is solved using multi-robot patrolling models. To date, literature works have been solved this problem applying various mathematical principles.The multi-robot patrolling models developed in those works represent great advances in this field. However, the models that obtain the best results are unfeasible for security applications due to their centralized and predictable nature. This thesis presents five distributed and unpredictable multi-robot patrolling models based on mathematical learning models derived from Game Theory. These multi-robot patrolling models aim at overcoming the disadvantages of previous work. To this end, the multi-robot patrolling problem was formulated using concepts of Graph Theory to represent the environment. Several normal-form games were defined at each vertex of a graph in this formulation. The multi-robot patrolling models developed in this research work have been validated and compared with best ranked multi-robot patrolling models in the literature. Both validation and comparison were preformed by using both a patrolling simulator and real robots. Experimental results show that the multirobot patrolling models developed in this research work improve previous ones in as many as 80% of 150 cases of study. Moreover, these multi-robot patrolling models rely on several features to highlight in security applications such as distribution, robustness, scalability, and dynamism. The achievements obtained in this research work validate the potential of Game Theory to develop patrolling models to protect infrastructures.

Energy hole mitigation through cooperative transmission in wireless sensor networks

The energy balancing capability of cooperative communication is utilized to solve the energy hole problem in wireless sensor networks. We first propose a cooperative transmission strategy, where intermediate nodes participate in two cooperative multi-input single-output (MISO) transmissions with the node at the previous hop and a selected node at the next hop, respectively. Then, we study the optimization problems for power allocation of the cooperative transmission strategy by examining two different approaches: network lifetime maximization (NLM) and energy consumption minimization (ECM). For NLM, the numerical optimal solution is derived and a searching algorithm for suboptimal solution is provided when the optimal solution does not exist. For ECM, a closed-form solution is obtained. Numerical and simulation results show that both the approaches have much longer network lifetime than SISO transmission strategies and other cooperative communication schemes. Moreover, NLM which features energy balancing outperforms ECM which focuses on energy efficiency, in the network lifetime sense.

Outage-optimal relay strategy under outdated channel state information in decode-and-forward cooperative communication systems

In this study, the authors investigate the outage-optimal relay strategy under outdated channel state information (CSI) in a decode-and-forward cooperative communication system. They first confirm mathematically that minimising the outage probability under outdated CSI is equivalent to minimising the conditional outage probability on the outdated CSI of all the decodable relays' links. They then propose a multiple-relay strategy with optimised transmitting power allocation (MRS-OTPA) that minimises the conditional outage probability. It is shown that this MRS is a generalised relay approach to achieve the outage optimality under outdated CSI. To reduce the complexity, they also propose a MRS with equal transmitting power allocation (MRS-ETPA) that achieves near-optimal outage performance. It is proved that full spatial diversity, which has been achieved under ideal CSI, can still be achieved under outdated CSI through MRS-OTPA and MRS-ETPA. Finally, the outage performance and diversity order of MRS-OTPA and MRS-ETPA are evaluated by simulation.

Az ellenzék ereje - általánosított súlyozott szavazási játékok (Minority power - generalized weighted voting games)

A hagyományos szavazási játékok speciális átruházható hasznosságú, kooperatív játékok, úgynevezett egyszerű játékok, ahol a játékosok a pártok, és az egyes koalíciók értéke 1 vagy 0 attól függően, hogy az adott koalíció elég erős-e az adott jogszabály elfogadásához, vagy sem. Ebben a cikkben bevezetjük az általánosított súlyozott szavazási játékok fogalmát, ahol a pártok mandátumainak száma a valószínűségi változó. Magyar példákon keresztül mutatjuk be az új megközelítés használhatóságát. / === / Voting games are cooperative games with transferable utility, so-called simple games, where the players are parties and the value of a coalition may be 0 or 1 depending on its ability to pass a new law. The authors introduce the concept of generalized weighted voting games where the parties' strengths are random variables. taking examples from Hungary to illustrate the use of this approach.

Benefits of a marketing cooperative in transition agriculture: Mórakert purchasing and service co-operative

The paper analyses the potential benefits of marketing cooperatives in Hungary, employing a transaction cost economics framework. We found that the purchased quantity, the existence of contracts, flexibility and trust are the most important factors farmers consider when selling their products via a cooperative. The most striking result is that diversification has positive influences on the share of cooperatives in farmers’ sale. Furthermore, farmers with larger bargaining power have less willingness to sell their product to the cooperative. Surprisingly, asset specificity has rather negative effects on the share of cooperatives in members’ sales.

Cooperative routing for collision minimization in wireless sensor networks

Cooperative communication has gained much interest due to its ability to exploit the broadcasting nature of the wireless medium to mitigate multipath fading. There has been considerable amount of research on how cooperative transmission can improve the performance of the network by focusing on the physical layer issues. During the past few years, the researchers have started to take into consideration cooperative transmission in routing and there has been a growing interest in designing and evaluating cooperative routing protocols. Most of the existing cooperative routing algorithms are designed to reduce the energy consumption; however, packet collision minimization using cooperative routing has not been addressed yet. This dissertation presents an optimization framework to minimize collision probability using cooperative routing in wireless sensor networks. More specifically, we develop a mathematical model and formulate the problem as a large-scale Mixed Integer Non-Linear Programming problem. We also propose a solution based on the branch and bound algorithm augmented with reducing the search space (branch and bound space reduction). The proposed strategy builds up the optimal routes from each source to the sink node by providing the best set of hops in each route, the best set of relays, and the optimal power allocation for the cooperative transmission links. To reduce the computational complexity, we propose two near optimal cooperative routing algorithms. In the first near optimal algorithm, we solve the problem by decoupling the optimal power allocation scheme from optimal route selection. Therefore, the problem is formulated by an Integer Non-Linear Programming, which is solved using a branch and bound space reduced method. In the second near optimal algorithm, the cooperative routing problem is solved by decoupling the transmission power and the relay node se- lection from the route selection. After solving the routing problems, the power allocation is applied in the selected route. Simulation results show the algorithms can significantly reduce the collision probability compared with existing cooperative routing schemes.

Using Coding to Improve Localization and Backscatter Communication Performance in Low-Power Sensor Networks

Backscatter communication is an emerging wireless technology that recently has gained an increase in attention from both academic and industry circles. The key innovation of the technology is the ability of ultra-low power devices to utilize nearby existing radio signals to communicate. As there is no need to generate their own energetic radio signal, the devices can benefit from a simple design, are very inexpensive and are extremely energy efficient compared with traditional wireless communication. These benefits have made backscatter communication a desirable candidate for distributed wireless sensor network applications with energy constraints.

The backscatter channel presents a unique set of challenges. Unlike a conventional one-way communication (in which the information source is also the energy source), the backscatter channel experiences strong self-interference and spread Doppler clutter that mask the information-bearing (modulated) signal scattered from the device. Both of these sources of interference arise from the scattering of the transmitted signal off of objects, both stationary and moving, in the environment. Additionally, the measurement of the location of the backscatter device is negatively affected by both the clutter and the modulation of the signal return.

This work proposes a channel coding framework for the backscatter channel consisting of a bi-static transmitter/receiver pair and a quasi-cooperative transponder. It proposes to use run-length limited coding to mitigate the background self-interference and spread-Doppler clutter with only a small decrease in communication rate. The proposed method applies to both binary phase-shift keying (BPSK) and quadrature-amplitude modulation (QAM) scheme and provides an increase in rate by up to a factor of two compared with previous methods.

Additionally, this work analyzes the use of frequency modulation and bi-phase waveform coding for the transmitted (interrogating) waveform for high precision range estimation of the transponder location. Compared to previous methods, optimal lower range sidelobes are achieved. Moreover, since both the transmitted (interrogating) waveform coding and transponder communication coding result in instantaneous phase modulation of the signal, cross-interference between localization and communication tasks exists. Phase discriminating algorithm is proposed to make it possible to separate the waveform coding from the communication coding, upon reception, and achieve localization with increased signal energy by up to 3 dB compared with previous reported results.

The joint communication-localization framework also enables a low-complexity receiver design because the same radio is used both for localization and communication.

Simulations comparing the performance of different codes corroborate the theoretical results and offer possible trade-off between information rate and clutter mitigation as well as a trade-off between choice of waveform-channel coding pairs. Experimental results from a brass-board microwave system in an indoor environment are also presented and discussed.

Full-Duplex Spectrum Sharing in Cooperative Single Carrier Systems

We propose cyclic prefix single carrier full-duplex transmission in amplify-and-forward cooperative spectrum sharing networks to achieve multipath diversity and full-duplex spectral efficiency. Integrating full-duplex transmission into cooperative spectrum sharing systems results in two intrinsic problems: 1) the residual loop interference occurs between the transmit and the receive antennas at the secondary relays and 2) the primary users simultaneously suffer interference from the secondary source (SS) and the secondary relays (SRs). Thus, examining the effects of residual loop interference under peak interference power constraint at the primary users and maximum transmit power constraints at the SS and the SRs is a particularly challenging problem in frequency selective fading channels. To do so, we derive and quantitatively compare the lower bounds on the outage probability and the corresponding asymptotic outage probability for max–min relay selection, partial relay selection, and maximum interference relay selection policies in frequency selective fading channels. To facilitate comparison, we provide the corresponding analysis for half-duplex. Our results show two complementary regions, named as the signal-to-noise ratio (SNR) dominant region and the residual loop interference dominant region, where the multipath diversity and spatial diversity can be achievable only in the SNR dominant region, however the diversity gain collapses to zero in the residual loop interference dominant region.

Power control in cognitive radios, Internet-of Things (IoT) for factories and industrial automation

Cognitive radio (CR) is fast emerging as a promising technology that can meet the machine-to machine (M2M) communication requirements for spectrum utilization and power control for large number of machines/devices expected to be connected to the Internet-of Things (IoT). Power control in CR as a secondary user can been modelled as a non-cooperative game cost function to quantify and reduce its effects of interference while occupying the same spectrum as primary user without adversely affecting the required quality of service (QoS) in the network. In this paper a power loss exponent that factors in diverse operating environments for IoT is employed in the non-cooperative game cost function to quantify the required power of transmission in the network. The approach would enable various CRs to transmit with lesser power thereby saving battery consumption or increasing the number of secondary users thereby optimizing the network resources efficiently.