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130
Efficient power control via pricing in wireless data networks
 IEEE Trans. on Commun
, 2002
"... Abstract—A major challenge in the operation of wireless communications systems is the efficient use of radio resources. One important component of radio resource management is power control, which has been studied extensively in the context of voice communications. With the increasing demand for wir ..."
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Cited by 339 (8 self)
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Abstract—A major challenge in the operation of wireless communications systems is the efficient use of radio resources. One important component of radio resource management is power control, which has been studied extensively in the context of voice communications. With the increasing demand for wireless data services, it is necessary to establish power control algorithms for information sources other than voice. We present a power control solution for wireless data in the analytical setting of a game theoretic framework. In this context, the quality of service (QoS) a wireless terminal receives is referred to as the utility and distributed power control is a noncooperative power control game where users maximize their utility. The outcome of the game results in a Nash equilibrium that is inefficient. We introduce pricing of transmit powers in order to obtain Pareto improvement of the noncooperative power control game, i.e., to obtain improvements in user utilities relative to the case with no pricing. Specifically, we consider a pricing function that is a linear function of the transmit power. The simplicity of the pricing function allows a distributed implementation where the price can be broadcast by the base station to all the terminals. We see that pricing is especially helpful in a heavily loaded system. Index Terms—Game theory, Pareto efficiency, power control, pricing, wireless data. I.
Joint Scheduling and Power Control for Wireless Adhoc Networks
, 2002
"... In this pape we introduce powe r control as a solution tothe multiple accel proble in conte tionbase wirenb adhocne works.The motivation for this study is two fold, limiting multiuse intej toincre single hop throughput, andrej powe r consumption to increj batte life We focus onne ne bor transmi ..."
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Cited by 283 (6 self)
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In this pape we introduce powe r control as a solution tothe multiple accel proble in conte tionbase wirenb adhocne works.The motivation for this study is two fold, limiting multiuse intej toincre single hop throughput, andrej powe r consumption to increj batte life We focus onne ne bor transmissions whes node are rej tose information packe  tothe re e e re e sub jej to a constraint on the signaltointealtoinjj ratio.The multiple acce  proble is solve via twoaltej phase name schej and powe r control.The sche algorithm isej tial to coordinate the transmissions ofinde ede t use inorde toejj strong intej (e.g selfinterference) that can not be ove by powe r control. On the othe hand, powe r control isej in adistribute fashion to dej the admissible powe r ve ifone ene that can be use bythe sche use to satisfy thei singlej transmissionrensmissi ts. This isdone for two type s ofne works, namej TDMA and TDMA/CDMA wire/CD adhocne works.
A Tutorial on Decomposition Methods for Network Utility Maximization
 IEEE J. SEL. AREAS COMMUN
, 2006
"... A systematic understanding of the decomposability structures in network utility maximization is key to both resource allocation and functionality allocation. It helps us obtain the most appropriate distributed algorithm for a given network resource allocation problem, and quantifies the comparison ..."
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Cited by 185 (4 self)
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A systematic understanding of the decomposability structures in network utility maximization is key to both resource allocation and functionality allocation. It helps us obtain the most appropriate distributed algorithm for a given network resource allocation problem, and quantifies the comparison across architectural alternatives of modularized network design. Decomposition theory naturally provides the mathematical language to build an analytic foundation for the design of modularized and distributed control of networks. In this tutorial paper, we first review the basics of convexity, Lagrange duality, distributed subgradient method, Jacobi and Gauss–Seidel iterations, and implication of different time scales of variable updates. Then, we introduce primal, dual, indirect, partial, and hierarchical decompositions, focusing on network utility maximization problem formulations and the meanings of primal and dual decompositions in terms of network architectures. Finally, we present recent examples on: systematic search for alternative decompositions; decoupling techniques for coupled objective functions; and decoupling techniques for coupled constraint sets that are not readily decomposable.
Power control by geometric programming
 IEEE Trans. on Wireless Commun
, 2005
"... Abstract — In wireless cellular or ad hoc networks where Quality of Service (QoS) is interferencelimited, a variety of power control problems can be formulated as nonlinear optimization with a systemwide objective, e.g., maximizing the total system throughput or the worst user throughput, subject ..."
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Cited by 130 (16 self)
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Abstract — In wireless cellular or ad hoc networks where Quality of Service (QoS) is interferencelimited, a variety of power control problems can be formulated as nonlinear optimization with a systemwide objective, e.g., maximizing the total system throughput or the worst user throughput, subject to QoS constraints from individual users, e.g., on data rate, delay, and outage probability. We show that in the high SignaltoInterference Ratios (SIR) regime, these nonlinear and apparently difficult, nonconvex optimization problems can be transformed into convex optimization problems in the form of geometric programming; hence they can be very efficiently solved for global optimality even with a large number of users. In the medium to low SIR regime, some of these constrained nonlinear optimization of power control cannot be turned into tractable convex formulations, but a heuristic can be used to compute in most cases the optimal solution by solving a series of geometric programs through the approach of successive convex approximation. While efficient and robust algorithms have been extensively studied for centralized solutions of geometric programs, distributed algorithms have not been explored before. We present a systematic method of distributed algorithms for power control that is geometricprogrammingbased. These techniques for power control, together with their implications to admission control and pricing in wireless networks, are illustrated through several numerical examples. Index Terms — Convex optimization, CDMA power control, Distributed algorithms. I.
Crosslayer optimization for OFDM wireless network Part I: Theoretical framework
 IEEE TRANS. WIRELESS COMMUN
, 2005
"... In this paper, we provide a theoretical framework for crosslayer optimization for orthogonal frequency division multiplexing (OFDM) wireless networks. The utility is used in our study to build a bridge between the physical layer and the media access control (MAC) layer and to balance the efficien ..."
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Cited by 128 (3 self)
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In this paper, we provide a theoretical framework for crosslayer optimization for orthogonal frequency division multiplexing (OFDM) wireless networks. The utility is used in our study to build a bridge between the physical layer and the media access control (MAC) layer and to balance the efficiency and fairness of wireless resource allocation. We formulate the crosslayer optimization problem as one that maximizes the average utility of all active users subject to certain conditions, which are determined by adaptive resource allocation schemes. We present necessary and sufficient conditions for utilitybased optimal subcarrier assignment and power allocation and discuss the convergence properties of optimization. Numerical results demonstrate a significant performance gain for the crosslayer optimization and the gain increases with the number of active users in the networks.
BAn energyefficient approach to power control and receiver design in wireless data networks,[
 IEEE Trans. Commun.,
, 2005
"... ..."
Energyefficient resource allocation in wireless networks: An overview of gametheoretic approaches
 IEEE Signal Process. Magazine
, 2007
"... A gametheoretic model is proposed to study the crosslayer problem of joint power and rate control with quality of service (QoS) constraints in multipleaccess networks. In the proposed game, each user seeks to choose its transmit power and rate in a distributed manner in order to maximize its own ..."
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Cited by 55 (8 self)
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A gametheoretic model is proposed to study the crosslayer problem of joint power and rate control with quality of service (QoS) constraints in multipleaccess networks. In the proposed game, each user seeks to choose its transmit power and rate in a distributed manner in order to maximize its own utility while satisfying its QoS requirements. The user’s QoS constraints are specified in terms of the average source rate and an upper bound on the average delay where the delay includes both transmission and queuing delays. The utility function considered here measures energy efficiency and is particularly suitable for wireless networks with energy constraints. The Nash equilibrium solution for the proposed noncooperative game is derived and a closedform expression for the utility achieved at equilibrium is obtained. It is shown that the QoS requirements of a user translate into a “size ” for the user which is an indication of the amount of network resources consumed by the user. Using this competitive multiuser framework, the tradeoffs among throughput, delay, network capacity and energy efficiency are studied. In addition, analytical expressions are given for users ’ delay profiles and the delay performance of the users at Nash equilibrium is quantified.
Introducing Hierarchy in Energy Games
, 2009
"... In this work we introduce hierarchy in wireless networks that can be modeled by a decentralized multiple access channel and for which energyefficiency is the main performance index. In these networks users are free to choose their power control strategy to selfishly maximize their energyefficiency ..."
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Cited by 44 (29 self)
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In this work we introduce hierarchy in wireless networks that can be modeled by a decentralized multiple access channel and for which energyefficiency is the main performance index. In these networks users are free to choose their power control strategy to selfishly maximize their energyefficiency. Specifically, we introduce hierarchy in two different ways: 1. Assuming singleuser decoding at the receiver, we investigate a Stackelberg formulation of the game where one user is the leader whereas the other users are assumed to be able to react to the leader’s decisions; 2. Assuming neither leader nor followers among the users, we introduce hierarchy by assuming successive interference cancellation at the receiver. It is shown that introducing a certain degree of hierarchy in noncooperative power control games not only improves the individual energy efficiency of all the users but can also be a way of insuring the existence of a nonsaturated equilibrium and reaching a desired tradeoff between the global network performance at the equilibrium and the requested amount of signaling. In this respect, the way of measuring the global performance of an energyefficient network is shown to be a critical issue.
Mandayam, “Pricing for enabling forwarding in selfconfiguring ad hoc networks
 IEEE Journal on Selected Areas in Communications
, 2005
"... Abstract—The assumption that all nodes cooperate to relay packets for each other may not be realistic for commercial wireless ad hoc networks. An autonomous (selfish) node in a wireless network has two disincentives for forwarding for others: energy expenditure (real cost) and possible delays for it ..."
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Cited by 36 (2 self)
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Abstract—The assumption that all nodes cooperate to relay packets for each other may not be realistic for commercial wireless ad hoc networks. An autonomous (selfish) node in a wireless network has two disincentives for forwarding for others: energy expenditure (real cost) and possible delays for its own data (opportunity cost). We introduce a mechanism that “fosters cooperation through bribery ” in the context of forwarding in ad hoc networks. Using a microeconomic framework based on game theory, we design and analyze a pricing algorithm that encourages forwarding among autonomous nodes by reimbursing forwarding. Taking a joint networkcentric and usercentric approach, the revenue maximizing network and utility (measured in bitsperJoule) maximizing nodes interact through prices for channel use, reimbursements for forwarding, transmitter power control, as well as forwarding and destination preferences. In a threenode (twosources, oneaccesspoint) network, the network converges to an architecture that induces forwarding only when the network geometries are such that forwarding is likely to increase individual benefits (network revenue and node utilities). For other geometries, the network converges to architectures that do not favor forwarding. We then generalize to a multinode network, where it is seen that the nodes ’ willingness to forward decrease for large ratios of the average internodal distance to the smallest distance between the access point and any source node. Pricing with reimbursement generally improves the network aggregate utility (or aggregate bitsperJoule), as well as utilities and revenue compared with the corresponding pricing algorithm without reimbursement. Index Terms—Cooperation, incentive for forwarding, noncooperative game, pricing, revenue maximization, Stackelberg game, utility. I.