The energy efficiency(EE) for the full-duplex massive multi-input multi-output(MIMO) system is investigated. Given the transmit powers of both the uplink and the downlink, the closed-form solutions of the optimal ...The energy efficiency(EE) for the full-duplex massive multi-input multi-output(MIMO) system is investigated. Given the transmit powers of both the uplink and the downlink, the closed-form solutions of the optimal number of antennas and the maximum EE are achieved in the high regime of the signal-to-noise ratio(SNR). It is shown that the optimal number of antennas and the maximum EE gets larger with the increase in user numbers. To further improve the EE, an optimization algorithm with low complexity is proposed to jointly determine the number of antennas and the transmit powers of both the uplink and the downlink. It is shown that, the proposed algorithm can achieve the system performance very close to the exhaustive search.展开更多
In this paper, we propose an energy-efficient power control scheme for device-to-device(D2D) communications underlaying cellular networks, where multiple D2D pairs reuse the same resource blocks allocated to one cellu...In this paper, we propose an energy-efficient power control scheme for device-to-device(D2D) communications underlaying cellular networks, where multiple D2D pairs reuse the same resource blocks allocated to one cellular user. Taking the maximum allowed transmit power and the minimum data rate requirement into consideration, we formulate the energy efficiency maximization problem as a non-concave fractional programming(FP) problem and then develop a two-loop iterative algorithm to solve it. In the outer loop, we adopt Dinkelbach method to equivalently transform the FP problem into a series of parametric subtractive-form problems, and in the inner loop we solve the parametric subtractive problems based on successive convex approximation and geometric programming method to obtain the solutions satisfying the KarushKuhn-Tucker conditions. Simulation results demonstrate the validity and efficiency of the proposed scheme, and illustrate the impact of different parameters on system performance.展开更多
In order to achieve higher system energy efficiency (EE),a new coordinated multipoint (CoMP)-transmission-based scheme selection energy saving (CTSES)algorithm is proposed for downlink homogeneous cellular netwo...In order to achieve higher system energy efficiency (EE),a new coordinated multipoint (CoMP)-transmission-based scheme selection energy saving (CTSES)algorithm is proposed for downlink homogeneous cellular networks.The problem is formulated as an optimization of maximizing system EE,under the constraints of the data rate requirement and the maximum transmit power.The problem is decomposed into power allocation and alternative scheme selection problems.Optimal power allocation is calculated for CoMP-JT (joint transmission)and CoMP-CS (coordinated scheduling) transmissions,and the scheme with higher EE is chosen. Since the optimal problem is a nonlinear fractional optimization problem for both CoMP transmission schemes, the problem is transformed into an equivalent problem using the parametric method. The optimal transmit power and optimal EE are obtained by an iteration algorithm in CoMP-JT and CoMP-CS schemes.Simulation results show that the proposed algorithm offers obvious energy-saving potential and outperforms the fixed CoMP transmission scheme.Under the condition of the same maximum transmit power limit,the empirical regularity of user distribution for scheme choice is presented, and using this regularity, the computational complexity can be reduced.展开更多
In this paper, proportional fairness(PF)-based energy-efficient power allocation is studied for multiple-input multiple-output(MIMO) non-orthogonal multiple access(NOMA) systems. In our schemes, statistical channel st...In this paper, proportional fairness(PF)-based energy-efficient power allocation is studied for multiple-input multiple-output(MIMO) non-orthogonal multiple access(NOMA) systems. In our schemes, statistical channel state information(CSI) is utilized for perfect CSI is impossible to achieve in practice. PF is used to balance the transmission efficiency and user fairness. Energy efficiency(EE) is formulated under basic data rate requirements and maximum transmitting power constraints. Due to the non-convex nature of EE, a two-step algorithm is proposed to obtain sub-optimal solution with a low complexity. Firstly, power allocation is determined by golden section search for fixed power. Secondly total transmitting power is determined by fractional programming method in the feasible regions. Compared to the performance of MIMO-NOMA without PF constraint, fairness is obtained at expense of decreasing of EE.展开更多
The resource allocation for device-to-device(D2D)multicast communications is investigated.To achieve fair energy efficiency(EE)among different multicast groups,the max-min fairness criterion is used as the optimizatio...The resource allocation for device-to-device(D2D)multicast communications is investigated.To achieve fair energy efficiency(EE)among different multicast groups,the max-min fairness criterion is used as the optimization criterion and the EE of D2D multicast groups are taken as the optimization objective function.The aim is to maximize the minimum EE for different D2D multicast groups under the constraints of the maximum transmit power and minimum transmit rate,which is modeled as a non-convex and mixed-integer fractional programming problem.Here,suboptimal resource allocation algorithms are proposed to solve this problem.First,channel assignment scheme is performed to assign channel to D2D multicast groups.Second,for a given channel assignment,iterative power allocation schemes with and without loss of cellular users’rate are completed,respectively.Simulation results corroborate the convergence performance of the proposed algorithms.In addition,compared with the traditional throughput maximization algorithm,the proposed algorithms can improve the energy efficiency of the system and the fairness achieved among different multicast groups.展开更多
Cognitive radio is considered as an efficient way to improve the spectrum efficiency. As one of its key technologies,spectrum handoff can guarantee the transmission continuity of secondary users(SUs). In this paper,we...Cognitive radio is considered as an efficient way to improve the spectrum efficiency. As one of its key technologies,spectrum handoff can guarantee the transmission continuity of secondary users(SUs). In this paper,we address a new and more generalized spectrum handoff problem in cognitive radio networks(CRNs),by considering simultaneously energy efficiency,multiple spectrum handoffs and multiple channels. Furthermore,effects of the primary users'(PUs')arrival and service rate on the target channel sequence selection are also considered. In order to obtain the energy-efficient target channel sequence,we firstly analyze the energy consumption and the number of delivered bits per hertz in the spectrum handoff process,and formulate a ratio-type energy efficiency optimization problem,which can be transformed into a parametric problem by utilizing fractional programming. Then,we propose an algorithm combining dynamic programming with bisection(DPB)algorithm to solve the energy efficiency optimization problem. Our simulation results verify that the designed target channel sequence has better performance than the existing algorithms in terms of energy efficiency.展开更多
How to achieve transmissions in an energy-efficient way in multi-hop decode and forward(DF) relay cognitive radio sensor networks(CRSNs) is important since sensor nodes in CRSNs are usually battery powered. This paper...How to achieve transmissions in an energy-efficient way in multi-hop decode and forward(DF) relay cognitive radio sensor networks(CRSNs) is important since sensor nodes in CRSNs are usually battery powered. This paper aims to maximize energy efficiency(EE) by joint optimizing sensing time and power allocation in multi-channels & multihops DF relay CRSNs under constraints on outage probability and sensing performance. First, we design a channel selection scheme for sensing according to the available probabilities of multi channels. Second, we analyze the expected throughput and energy consumption and formulate the EE problem as a concave/concave fractional program. Third, coordinate ascent and Charnes-Cooper Transformation(CCT) methods are used to transform the nonlinear fractional problem into an equivalent concave problem. Subsequently, the closed form of outage probability is derived and the convergence rate of the iterative algorithm is analyzed. Finally, simulation results show that the proposed scheme can achieve effective EE.展开更多
An energy effi cient resource allocation scheme in timesharing multiuser system with a hybrid energy harvesting transmitter is studied in this paper. Specially, the operation energy of system is supplied by constant e...An energy effi cient resource allocation scheme in timesharing multiuser system with a hybrid energy harvesting transmitter is studied in this paper. Specially, the operation energy of system is supplied by constant energy and energy harvesting, which harvests energy from external environment. Our goal is to maximize the energy effi ciency of timesharing multiuser systems by considering jointly allocation of transmission time and power control in an off-line manner. The original nonconvex objective function is transformed into convex optimization problem via the fractional programming approach. Then, we solve the convex problem by Lagrange dual decomposition method. Simulation results show that the proposed energy efficient resource allocation scheme has a better performance than the scheme which decomposes optimization problem into two parts(power allocation, time allocation) to solve iteratively.展开更多
Most of the networks are generally less energy efficient and most of the time resources are underutilized. Even resources of busy networks are also underutilized and thus networks show energy inefficient management sy...Most of the networks are generally less energy efficient and most of the time resources are underutilized. Even resources of busy networks are also underutilized and thus networks show energy inefficient management system. This paper focuses on how to obtain minimum resources for the current situation of the network to maintain connectivity, power saving and quality of service. Four different models are proposed in this perspective with different purposes and functions. These models determine the minimum resources under certain constrains. Two types of services namely, "minimum bandwidth" and "trivial file transfer" are considered. For "minimum bandwidth" service, minimum edge, minimum delay and minimum change models are proposed. Here data rate switch and enable/disable of edges are placed in these models for power saving strategy. Another model, multi flow is proposed for "trivial file transfer" service. It is proposed for transferring files through multiple flows in multiple paths from source to destination. All models except multi flow model are mixed integer programming optimization problem.展开更多
Building envelope is the sole interface with outdoors that can lie in the level of integrating control strategies to enhance occupant's comfort and building performance. However, in the literature, there is still ...Building envelope is the sole interface with outdoors that can lie in the level of integrating control strategies to enhance occupant's comfort and building performance. However, in the literature, there is still a lack of multi-purpose control strategies which can balance diverse and antagonistic aspects of occupant comfort while keeping the building energy consumption under control. Therefore, this research proposed an integrated simulation-based workflow using EnergyPlus and Python-based package, OpyPlus, to adjust a roller shade for single occupied office space in a hot and arid climate. The developed system aims to improve both occupant's visual and thermal comfort considering daylight level, potential glare at occupant's field of view, view to outdoor satisfaction, and Fanger PMV method, and then, managing the HVAC system in favor of enhancing building energy efficiency. Furthermore, the controller's performance was compared to multiple fixed controls and another multi-agent control scenario from visual and thermal comfort and energy performance perspectives. The developed control system could perform effectively to provide a glare-free view and higher thermally comfortable indoor environment by 99% for the occupant across the year, while improving the heating and cooling loads. The research provides novel insights and potential future integrations for facade designers and building operators.展开更多
We consider the problem of nearly optimal energy efficiency in massive(Multiinput Multi-output) MIMO systems. Considering the correlated channel in practice, we derive the ergodic expression with zero-forcing precodin...We consider the problem of nearly optimal energy efficiency in massive(Multiinput Multi-output) MIMO systems. Considering the correlated channel in practice, we derive the ergodic expression with zero-forcing precoding and analyze the simplified antennas selection method. Aiming at optimizing the energy efficiency, the closed form expressions of the nearly optimal number of transmit antennas and transmit power are given under the circuit consumption model. The joint solution of the number of transmit antennas and transmit power was replaced to only solve transmit power. Based on the expression only related with transmit power, we give an energy efficiency optimization algorithm. The simulation results show that the proposed algorithm can achieve nearly optimal energy efficiency with fast convergence speed.展开更多
In Non-Orthogonal Multiple Access(NOMA),the best way to fully exploit the benefits of the system is the efficient resource allocation.For the NOMA power domain,the allocation of power and spectrum require solving the ...In Non-Orthogonal Multiple Access(NOMA),the best way to fully exploit the benefits of the system is the efficient resource allocation.For the NOMA power domain,the allocation of power and spectrum require solving the mixed-integer nonlinear programming NP-hard problem.In this paper,we investigate user scheduling and power allocation in Multi-Cell Multi-Carrier NOMA(MCMC-NOMA)networks.To achieve that,we consider Weighted Sum Rate Maximization(WSRM)and Weighted Sum Energy Efficiency Maximization(WSEEM)problems.First,we tackle the problem of user scheduling for fixed power using Fractional Programming(FP),the Lagrange dual method,and the decomposition method.Then,we consider Successive Pseudo-Convex Approximation(SPCA)to deal with the WSRM problem.Finally,for the WSEEM problem,SPCA is utilized to convert the problem into separable scalar problems,which can be parallelly solved.Thus,the Dinkelbach algorithm and constraints relaxation are used to characterize the closed-form solution for power allocation.Extensive simulations have been implemented to show the efficiency of the proposed framework and its superiority over other existing schemes.展开更多
The improvement of energy efficiency has played an important role in the global low-carbon economy and the sustainable development process.There are many methodologies for estimating energy efficiency in academia.This...The improvement of energy efficiency has played an important role in the global low-carbon economy and the sustainable development process.There are many methodologies for estimating energy efficiency in academia.This article introduces four frontier methods for energy efficiency evaluation:nonparametric data envelopment analysis(DEA),parametric linear programming,stochastic frontier analysis(SFA),and the meta-frontier approach.The advantages and disadvantages of these methods are discussed.Finally,suggestions for model selection in energy efficiency measurement are offered.展开更多
基金supported by the National Natural Science Foundation of China(61371188)the Research Fund for the Doctoral Program of Higher Education(20130131110029)+2 种基金the Open Fund of State Key Laboratory of Integrated Services Networks(ISN14-03)the China Postdoctoral Science Foundation(2014M560553)the Special Funds for Postdoctoral Innovative Projects of Shandong Province(201401013)
文摘The energy efficiency(EE) for the full-duplex massive multi-input multi-output(MIMO) system is investigated. Given the transmit powers of both the uplink and the downlink, the closed-form solutions of the optimal number of antennas and the maximum EE are achieved in the high regime of the signal-to-noise ratio(SNR). It is shown that the optimal number of antennas and the maximum EE gets larger with the increase in user numbers. To further improve the EE, an optimization algorithm with low complexity is proposed to jointly determine the number of antennas and the transmit powers of both the uplink and the downlink. It is shown that, the proposed algorithm can achieve the system performance very close to the exhaustive search.
基金supported by National Natural Science Foundation of China (No.61501028)Beijing Institute of Technology Research Fund Program for Young Scholars
文摘In this paper, we propose an energy-efficient power control scheme for device-to-device(D2D) communications underlaying cellular networks, where multiple D2D pairs reuse the same resource blocks allocated to one cellular user. Taking the maximum allowed transmit power and the minimum data rate requirement into consideration, we formulate the energy efficiency maximization problem as a non-concave fractional programming(FP) problem and then develop a two-loop iterative algorithm to solve it. In the outer loop, we adopt Dinkelbach method to equivalently transform the FP problem into a series of parametric subtractive-form problems, and in the inner loop we solve the parametric subtractive problems based on successive convex approximation and geometric programming method to obtain the solutions satisfying the KarushKuhn-Tucker conditions. Simulation results demonstrate the validity and efficiency of the proposed scheme, and illustrate the impact of different parameters on system performance.
基金The National Science and Technology Major Project(No.2013ZX03001032-004)the National High Technology Research and Development Program of China(863 Program)(No.2014AA01A702)+1 种基金Jiangsu Province Science and Technology Support Program(No.BE2012165)Foundation of Huawei Corp.Ltd
文摘In order to achieve higher system energy efficiency (EE),a new coordinated multipoint (CoMP)-transmission-based scheme selection energy saving (CTSES)algorithm is proposed for downlink homogeneous cellular networks.The problem is formulated as an optimization of maximizing system EE,under the constraints of the data rate requirement and the maximum transmit power.The problem is decomposed into power allocation and alternative scheme selection problems.Optimal power allocation is calculated for CoMP-JT (joint transmission)and CoMP-CS (coordinated scheduling) transmissions,and the scheme with higher EE is chosen. Since the optimal problem is a nonlinear fractional optimization problem for both CoMP transmission schemes, the problem is transformed into an equivalent problem using the parametric method. The optimal transmit power and optimal EE are obtained by an iteration algorithm in CoMP-JT and CoMP-CS schemes.Simulation results show that the proposed algorithm offers obvious energy-saving potential and outperforms the fixed CoMP transmission scheme.Under the condition of the same maximum transmit power limit,the empirical regularity of user distribution for scheme choice is presented, and using this regularity, the computational complexity can be reduced.
基金supported by the National Natural Science Foundation of China (No. 61671252)
文摘In this paper, proportional fairness(PF)-based energy-efficient power allocation is studied for multiple-input multiple-output(MIMO) non-orthogonal multiple access(NOMA) systems. In our schemes, statistical channel state information(CSI) is utilized for perfect CSI is impossible to achieve in practice. PF is used to balance the transmission efficiency and user fairness. Energy efficiency(EE) is formulated under basic data rate requirements and maximum transmitting power constraints. Due to the non-convex nature of EE, a two-step algorithm is proposed to obtain sub-optimal solution with a low complexity. Firstly, power allocation is determined by golden section search for fixed power. Secondly total transmitting power is determined by fractional programming method in the feasible regions. Compared to the performance of MIMO-NOMA without PF constraint, fairness is obtained at expense of decreasing of EE.
基金Projects(61801237,61701255)supported by the National Natural Science Foundation of ChinaProject(SBH17024)supported by the Postdoctoral Science Foundation of Jiangsu Province,China+2 种基金Project(15KJB510026)supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions,ChinaProject(BK20150866)supported by the Natural Science Foundation of Jiangsu Province,ChinaProjects(NY215046,NY217056)supported by the Introduction of Talent Fund of Nanjing University of Posts and Telecommunications,China
文摘The resource allocation for device-to-device(D2D)multicast communications is investigated.To achieve fair energy efficiency(EE)among different multicast groups,the max-min fairness criterion is used as the optimization criterion and the EE of D2D multicast groups are taken as the optimization objective function.The aim is to maximize the minimum EE for different D2D multicast groups under the constraints of the maximum transmit power and minimum transmit rate,which is modeled as a non-convex and mixed-integer fractional programming problem.Here,suboptimal resource allocation algorithms are proposed to solve this problem.First,channel assignment scheme is performed to assign channel to D2D multicast groups.Second,for a given channel assignment,iterative power allocation schemes with and without loss of cellular users’rate are completed,respectively.Simulation results corroborate the convergence performance of the proposed algorithms.In addition,compared with the traditional throughput maximization algorithm,the proposed algorithms can improve the energy efficiency of the system and the fairness achieved among different multicast groups.
基金Heilongjiang Province Natural Science Foundation(Grant No.F2016019);National Natural Science Foundation of China(Grant No.61571162);Major National Science and Technology Project(2015ZX03004002004); China Postdoctoral Science Foundation(Grant No.2014M561347).
文摘Cognitive radio is considered as an efficient way to improve the spectrum efficiency. As one of its key technologies,spectrum handoff can guarantee the transmission continuity of secondary users(SUs). In this paper,we address a new and more generalized spectrum handoff problem in cognitive radio networks(CRNs),by considering simultaneously energy efficiency,multiple spectrum handoffs and multiple channels. Furthermore,effects of the primary users'(PUs')arrival and service rate on the target channel sequence selection are also considered. In order to obtain the energy-efficient target channel sequence,we firstly analyze the energy consumption and the number of delivered bits per hertz in the spectrum handoff process,and formulate a ratio-type energy efficiency optimization problem,which can be transformed into a parametric problem by utilizing fractional programming. Then,we propose an algorithm combining dynamic programming with bisection(DPB)algorithm to solve the energy efficiency optimization problem. Our simulation results verify that the designed target channel sequence has better performance than the existing algorithms in terms of energy efficiency.
基金supported by the National Nature Science Foundation of China. (Grant No. 61771410)
文摘How to achieve transmissions in an energy-efficient way in multi-hop decode and forward(DF) relay cognitive radio sensor networks(CRSNs) is important since sensor nodes in CRSNs are usually battery powered. This paper aims to maximize energy efficiency(EE) by joint optimizing sensing time and power allocation in multi-channels & multihops DF relay CRSNs under constraints on outage probability and sensing performance. First, we design a channel selection scheme for sensing according to the available probabilities of multi channels. Second, we analyze the expected throughput and energy consumption and formulate the EE problem as a concave/concave fractional program. Third, coordinate ascent and Charnes-Cooper Transformation(CCT) methods are used to transform the nonlinear fractional problem into an equivalent concave problem. Subsequently, the closed form of outage probability is derived and the convergence rate of the iterative algorithm is analyzed. Finally, simulation results show that the proposed scheme can achieve effective EE.
基金supported in part by the National Natural Science Foundation of China(61471115)in part by the 2016 Science and Technology Joint Research and Innovation Foundation of Jiangsu Province(BY2016076-13)
文摘An energy effi cient resource allocation scheme in timesharing multiuser system with a hybrid energy harvesting transmitter is studied in this paper. Specially, the operation energy of system is supplied by constant energy and energy harvesting, which harvests energy from external environment. Our goal is to maximize the energy effi ciency of timesharing multiuser systems by considering jointly allocation of transmission time and power control in an off-line manner. The original nonconvex objective function is transformed into convex optimization problem via the fractional programming approach. Then, we solve the convex problem by Lagrange dual decomposition method. Simulation results show that the proposed energy efficient resource allocation scheme has a better performance than the scheme which decomposes optimization problem into two parts(power allocation, time allocation) to solve iteratively.
文摘Most of the networks are generally less energy efficient and most of the time resources are underutilized. Even resources of busy networks are also underutilized and thus networks show energy inefficient management system. This paper focuses on how to obtain minimum resources for the current situation of the network to maintain connectivity, power saving and quality of service. Four different models are proposed in this perspective with different purposes and functions. These models determine the minimum resources under certain constrains. Two types of services namely, "minimum bandwidth" and "trivial file transfer" are considered. For "minimum bandwidth" service, minimum edge, minimum delay and minimum change models are proposed. Here data rate switch and enable/disable of edges are placed in these models for power saving strategy. Another model, multi flow is proposed for "trivial file transfer" service. It is proposed for transferring files through multiple flows in multiple paths from source to destination. All models except multi flow model are mixed integer programming optimization problem.
文摘Building envelope is the sole interface with outdoors that can lie in the level of integrating control strategies to enhance occupant's comfort and building performance. However, in the literature, there is still a lack of multi-purpose control strategies which can balance diverse and antagonistic aspects of occupant comfort while keeping the building energy consumption under control. Therefore, this research proposed an integrated simulation-based workflow using EnergyPlus and Python-based package, OpyPlus, to adjust a roller shade for single occupied office space in a hot and arid climate. The developed system aims to improve both occupant's visual and thermal comfort considering daylight level, potential glare at occupant's field of view, view to outdoor satisfaction, and Fanger PMV method, and then, managing the HVAC system in favor of enhancing building energy efficiency. Furthermore, the controller's performance was compared to multiple fixed controls and another multi-agent control scenario from visual and thermal comfort and energy performance perspectives. The developed control system could perform effectively to provide a glare-free view and higher thermally comfortable indoor environment by 99% for the occupant across the year, while improving the heating and cooling loads. The research provides novel insights and potential future integrations for facade designers and building operators.
基金supported by the Natural Science Foundation of China(61201135)State 863 Project(2014AA01A704)111 Project(B08038)
文摘We consider the problem of nearly optimal energy efficiency in massive(Multiinput Multi-output) MIMO systems. Considering the correlated channel in practice, we derive the ergodic expression with zero-forcing precoding and analyze the simplified antennas selection method. Aiming at optimizing the energy efficiency, the closed form expressions of the nearly optimal number of transmit antennas and transmit power are given under the circuit consumption model. The joint solution of the number of transmit antennas and transmit power was replaced to only solve transmit power. Based on the expression only related with transmit power, we give an energy efficiency optimization algorithm. The simulation results show that the proposed algorithm can achieve nearly optimal energy efficiency with fast convergence speed.
基金supported by the National Science Foundation of P.R.China (No.61701064)the Chongqing Natural Science Foundation (cstc2019jcyj-msxmX0264).
文摘In Non-Orthogonal Multiple Access(NOMA),the best way to fully exploit the benefits of the system is the efficient resource allocation.For the NOMA power domain,the allocation of power and spectrum require solving the mixed-integer nonlinear programming NP-hard problem.In this paper,we investigate user scheduling and power allocation in Multi-Cell Multi-Carrier NOMA(MCMC-NOMA)networks.To achieve that,we consider Weighted Sum Rate Maximization(WSRM)and Weighted Sum Energy Efficiency Maximization(WSEEM)problems.First,we tackle the problem of user scheduling for fixed power using Fractional Programming(FP),the Lagrange dual method,and the decomposition method.Then,we consider Successive Pseudo-Convex Approximation(SPCA)to deal with the WSRM problem.Finally,for the WSEEM problem,SPCA is utilized to convert the problem into separable scalar problems,which can be parallelly solved.Thus,the Dinkelbach algorithm and constraints relaxation are used to characterize the closed-form solution for power allocation.Extensive simulations have been implemented to show the efficiency of the proposed framework and its superiority over other existing schemes.
基金financial support provided by the National Natural Science Foundation of China (Grant Nos.41461118 & 91746112)the National Social Science Foundation of China (Grant No.15ZDA054)
文摘The improvement of energy efficiency has played an important role in the global low-carbon economy and the sustainable development process.There are many methodologies for estimating energy efficiency in academia.This article introduces four frontier methods for energy efficiency evaluation:nonparametric data envelopment analysis(DEA),parametric linear programming,stochastic frontier analysis(SFA),and the meta-frontier approach.The advantages and disadvantages of these methods are discussed.Finally,suggestions for model selection in energy efficiency measurement are offered.