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Articles 2401 - 2430 of 3960
Full-Text Articles in Numerical Analysis and Scientific Computing
Application Of Recursive Least Square Method In Identication Of Dehydrogenation Reator, Guoyou Li, Ningning Gao, Wenhua Xia
Application Of Recursive Least Square Method In Identication Of Dehydrogenation Reator, Guoyou Li, Ningning Gao, Wenhua Xia
Journal of System Simulation
Abstract: The current production methods of styrene at home and abroad are mainly dhydrogenation of ethylbenzene which accounts for more than 90% of styrene production capacity in the world. To save energy, it was needed to optimize the system and its premise was to know the mathematical model of ethylbenzene dehydrogenation reactor. Due to the complexity of the reactor internal structure, mechanism modeling was more difficult to establish objective and accurate mathematics models. To solve this problem, it was used recursive least squares to conduct parameter identification. On the basis of actual plant data, ethylbenzene dehydrogenation reactor mathematical model was …
Simulation Research Of Maglev Train During Uphill And Downhill Process, Songqi Li, Kunlun Zhang, Guoqing Liu, Chen Yin
Simulation Research Of Maglev Train During Uphill And Downhill Process, Songqi Li, Kunlun Zhang, Guoqing Liu, Chen Yin
Journal of System Simulation
Abstract: In the low speed EMS maglev test line experiments in Zhuzhou, it was found that vehicles are prone to hit the tracks, when the maglev train travels uphill or downhill through the tracks with slopes. This seriously affected the safety and comfort of the vehicle. In order to study the problem, a single low speed EMS maglev train carriages-track model with four degrees of freedom was built. It simulated and analyzed dynamic behaviors of the vehicle going uphill on different track curves, under different vehicle -track parameters. The simulation results show that the vehicle parameters, vehicle speed, and the …
Modeling Method Based On Reachable Set For Safety Path In Autonomous Vehicle Obstacle Avoidance, Cao Kai, Xiaoxiao Huang, Yu Yun, Liu Chun
Modeling Method Based On Reachable Set For Safety Path In Autonomous Vehicle Obstacle Avoidance, Cao Kai, Xiaoxiao Huang, Yu Yun, Liu Chun
Journal of System Simulation
Abstract: In view of problem in all possible uncertain behavior of vehicle unable existed by the traditional path planning algorithm, a modeling method was proposed which deemed a moving vehicle as a hybrid system switching dynamically between continuous and discrete mode, modeled an optimal trajectory for vehicle obstacle avoidance by using a single security target location, and built a safe state reachable set based on the trajectory beam of multiple security target locations. On this basis, the condition of the inevitable collision of vehicle was analyzed, and the optimal control problem with loose constraints for the vehicle obstacle avoidance was …
Numerical Simulation For Influence Of Baffle Length On Hydraulic Characteristics In Radial Sedimentation Tanks, Wenli Wei, Zewei Zhang, Yunfei Hong, Yuling Liu
Numerical Simulation For Influence Of Baffle Length On Hydraulic Characteristics In Radial Sedimentation Tanks, Wenli Wei, Zewei Zhang, Yunfei Hong, Yuling Liu
Journal of System Simulation
Abstract: The VOF (volume of fluid) method was applied to track the free water surface, and the RNG turbulent model was used to close the two-phase flow time-averaged equations. The influence of inlet vertical baffle with different lengths on hydraulic characteristics in radial sedimentation tank was simulated and analyzed. The control equations were discretized using the finite volume method. Velocity and pressure were solved using the PISO (Pressure-Implicit with Splitting of Operators) algorithm. The research results show that: the long length feed flow baffle model has a smaller recirculation zone, better velocity field distribution than short length baffle, and the …
Research Of Visualization Of Road Guide Sign Panel Based On Combination Of Guiding Information, Zhongming Niu, Huang Min, Yuan Yuan, Li Min
Research Of Visualization Of Road Guide Sign Panel Based On Combination Of Guiding Information, Zhongming Niu, Huang Min, Yuan Yuan, Li Min
Journal of System Simulation
Abstract: In order to realize the intelligent management of road guide signs, a method of visualization of road guide sign panel based on the flexible combination of guiding information was proposed. As a consequence of analysis for structures of guide sign panel, the message on the guide sign panel was decomposed into guiding information, and then visualization function was proposed. The panel style was determined by the physical and logical topology of guiding intersection dynamically with the help of guide sign system database. Then the composition of geography information and guiding information was utilized in the process of visualization …
Simulation-Based An Exploratory Analysis Of Drone Air Strike On Saudi Oilfields, Jiajun Zhang, Xiaochao Qian, Jinpeng Zhou, Xuanling Wang, Zhifeng Lu
Simulation-Based An Exploratory Analysis Of Drone Air Strike On Saudi Oilfields, Jiajun Zhang, Xiaochao Qian, Jinpeng Zhou, Xuanling Wang, Zhifeng Lu
Journal of System Simulation
Abstract: The incident of air strike in Sandi Arabia in September 2019 is taken as an example,A rapid analysis method for crisis events based on simulation is proposed. Combining the simulation with the exploratory analysis, the uncertainty of crisis events is comprehensively analyzed and dealt with. According to the public information of the incidents details from Sandi Arabia, Yemen, the combat situation of the air strike is replayed based on the wargaming. The rationality and authenticity of the details in the event statement is verified and can also provide reference to the development and combat research of the “Low, Small …
Multi-Tank Adaptive Scheduling Algorithm And Simulation For Ship Stability Realization, Xiong Yong, Xuanzhuo Liang, Zhang Jia
Multi-Tank Adaptive Scheduling Algorithm And Simulation For Ship Stability Realization, Xiong Yong, Xuanzhuo Liang, Zhang Jia
Journal of System Simulation
Abstract: Aiming at the influence of the oil tank on the floating state and stability of the ship, the multi-tank adaptive dispatching control algorithm to maintain the stability of the ship is studied. The automatic floating state adjustment simulation system of the ship is realized by the WinCC (Windows Control Center) configuration software. For the system architecture, the Boolean logic table is used to construct the connection relationships of the oil tanks, pumps and pipelines, and the amount of oil exchange between the cabins is calculated according to the floating equation, and the balance of the floating state in the …
Simulation-Based Effectiveness Evaluation For System-Of-System Under Multi-Equipment Collaboration, Ma Ning, Shenglin Lin
Simulation-Based Effectiveness Evaluation For System-Of-System Under Multi-Equipment Collaboration, Ma Ning, Shenglin Lin
Journal of System Simulation
Abstract: Complex coordination exists among the various equipment in the system-of-system (SoS) operational process. The influence relationship among the various indexes is ignored in the traditional effectiveness evaluation methods. Aiming at this, a new effectiveness evaluation approach for the SoS is proposed. Numerous evaluation data is analyzed, based on the association rules mining, to obtain the influence among the effectiveness indexes. The networked evaluation index system is constructed, and the effectiveness integration evaluation is realized based on the analytic network process. The feasibility and validity of the proposed method are verified by evaluating the effectiveness of an air defense SoS.
Identification Method For Fractional-Order Systems Based On Haar Wavelet Operational Matrix, Yuanlu Li, Li Teng, Baoying Liu
Identification Method For Fractional-Order Systems Based On Haar Wavelet Operational Matrix, Yuanlu Li, Li Teng, Baoying Liu
Journal of System Simulation
Abstract: Studies have shown that the dynamical systems can be more accurately described by the fractional-order systems because its order can be any number. That’s why the fractional-order systems are being paid more and more attention. However, how to create a fractional-order system is still in the exploratory stage. Considering the nonlocal features of the fractional differentiation, a method for the fractional-order system identification is proposed by taking the Haar wavelet operational matrix. The proposed method can reduce the dimension of the operational matrix by abandoning the high frequency coefficients of the input and output signals so that the buffer …
Virtual-Point-Light Sampling Algorithm Based On Indirect Illumination Clustering Of Visible Scene Region, Chen Sheng, Chunyi Chen, Qiwei Xing, Chaozhi Yang
Virtual-Point-Light Sampling Algorithm Based On Indirect Illumination Clustering Of Visible Scene Region, Chen Sheng, Chunyi Chen, Qiwei Xing, Chaozhi Yang
Journal of System Simulation
Abstract: Focusing on the accuracy of indirect illumination calculation, an improved view-sensitive virtual point light (VPL) sampling method is proposed. The visible shading points are clustered according to the positions and normal vectors. The product of the contribution of VPLs on the representative visible shading points and the number of VPLs belonging to the same class is calculated, and the sum of the products is treated as the estimation of the indirect illumination which constructs the cumulative distribution function (CDF). On the basis of the CDF, the VPLs of calculating the indirect illumination on every visible shading point are selected. …
Augmented Reality Interactive Media System For Ancient Buildings Based On Servomotor, Xingquan Cai, Zhe Yang, He Xin, Chen Chao
Augmented Reality Interactive Media System For Ancient Buildings Based On Servomotor, Xingquan Cai, Zhe Yang, He Xin, Chen Chao
Journal of System Simulation
Abstract: Augmented reality is usually limited to the screen devices, and is difficult to realize the stereoscopic dynamic interaction of multiplayer. A large screen interactive display method based on the servo motor is prsented. The serial communication program to control the scanning reciprocating mode of the servo is designed. By using the edge detection methods and deep normal texture processing, the line draft of the ancient buildings is rendered. By combining the hardware and presentation application modules, the user interaction capabilities and seasonal effects is added to the showcase application modules. The experimental results show that the interactive media system …
Adaptive Differential Crisscross Optimization Algorithm For Dynamic Economic Emission Dispatch Considering Wind Power, Panpan Mei, Lianghong Wu, Hongqiang Zhang, Huiying Wang
Adaptive Differential Crisscross Optimization Algorithm For Dynamic Economic Emission Dispatch Considering Wind Power, Panpan Mei, Lianghong Wu, Hongqiang Zhang, Huiying Wang
Journal of System Simulation
Abstract: Because of the randomness and fluctuation of the wind power, the large scale wind power integration makes the economic emission dispatch of power systems more complicated. By fusing the advantages of the differential evolution algorithm with the parameter self-adaption and crisscross optimization, a hybrid intelligent optimization algorithm called ADE-CSO is proposed to solve the dynamic economic emission dispatch considering wind power integration. A constraint handling technology is introduced to satisfy the feasibility of the power balance and ramp limits. To demonstrate the effectiveness of the proposed algorithm, a typical test case of five generator bus system is conducted and …
Classification Of Chest X-Ray Disease Based On Convolutional Neural Network, Huang Xin, Fang Yu, Mengdan Gu
Classification Of Chest X-Ray Disease Based On Convolutional Neural Network, Huang Xin, Fang Yu, Mengdan Gu
Journal of System Simulation
Abstract: The artificial intelligence technology can effectively assist the chest X-ray diagnosis. On the basis of the analysis of Chinese reports of chest X-rays, a labeling method of the thoracic disease classification for the chest abnormal parts is proposed and a dataset of the thoracic disease classification labels is complied. The thoracic disease classification is evaluated through four kinds of convolutional neural networks, AlexNet, VGGNet, ResNet and DenseNet and through three kinds of training methods, direct training, ImageNet pre-training and Chest X-14 pre-training. The result shows that the more complicated convolutional neural network with the more parameters, the better performance …
Study On Evacuation Cellular Automaton Model Considering Avoidance Behavior, Yinghua Song, Zhang Yu, Feizhou Huo, Lü Wei, Yaping Ma
Study On Evacuation Cellular Automaton Model Considering Avoidance Behavior, Yinghua Song, Zhang Yu, Feizhou Huo, Lü Wei, Yaping Ma
Journal of System Simulation
Abstract: To study the avoidance behavior in the evacuation process, a cellular automaton model considering avoidance behavior is established. The model divides the evacuees into avoiders and transferees, and reflects the avoidance behavior by changing the selected probability of evacuees. The impact of the avoidance behavior on the efficiency and evacuation process in different personnel ratios and different initial positions is analyzed. The results show that the avoidance behavior can optimize the evacuation sequence, improve the evacuation efficiency and reduce the risk of evacuation process. The evacuation time is significantly reduced when the probability of avoidance exceeds the thread value, …
Crowd Evacuation Model Based On Improved Pso Algorithm, Changhua Li, Chenggong Bi, Zhijie Li
Crowd Evacuation Model Based On Improved Pso Algorithm, Changhua Li, Chenggong Bi, Zhijie Li
Journal of System Simulation
Abstract: Aiming at the poor local optimization ability and easy premature convergence of the particle swarm optimization (PSO) algorithm in evacuation simulation, a crowd evacuation model based on the improved PSO algorithm is proposed. On the basis of the original model, factors such as the forward driving force, exclusion driving force and panic degree of evacuees are introduced. According to the environmental factors and crowd movement, evacuees' direction is dynamically adjusted, and tends to the ideal exit under the optimal exit selection mechanism. The parametric simulation experiment of evacuation efficiency is carried out for the physical factors such as the …
Research On Modeling Technology For Hard Cutting Process, Caixu Yue, Liu Xin, Jiang Nan, Xianli Liu, Genghuang He, Lingxiang Li
Research On Modeling Technology For Hard Cutting Process, Caixu Yue, Liu Xin, Jiang Nan, Xianli Liu, Genghuang He, Lingxiang Li
Journal of System Simulation
Abstract: The hard cutting has the features of the high maching flexibility, economical efficiency and environmental friendliness, and is widely used in automobile industry, bearing industry, hydraulic industry, etc. The simulation modeling not only plays an important role in predicting the performance of the hard machining and optimizing machining parameters, but also better reflects the nature of the machining and provides the theoretical guidance to the actual machining. The simulation modeling methods of the hard cutting at home and abroad are introduced, and the chip formation, cutting force, cutting temperature, tool wear and machined surface quality are summarized, and the …
Spatiotemporal Saliency Detection Of Infrared Videos Based On Gestalt-Guided Optimization, Wang Xin, Chunyan Zhang, Ning Chen
Spatiotemporal Saliency Detection Of Infrared Videos Based On Gestalt-Guided Optimization, Wang Xin, Chunyan Zhang, Ning Chen
Journal of System Simulation
Abstract: A spatiotemporal saliency detection method based on Gestalt optimization is proposed. A method based on the multi-scale local sparse representation and local contrast measure is proposed to compute the spatial saliency in the infrared videos. A multi-frame symmetric difference approach is adopted to detect the temporal saliency. To get the initial spatiotemporal saliency map, a scheme based on the mutual-consistency is designed to fuse the spatial and temporal saliency maps adaptively. A Gestalt-guided optimization method is designed to calculate the final spatiotemporal saliency map. Experimental results show that the proposed method can effectively detect the spatiotemporal saliency of infrared …
A Discrete Krill Herd Algorithm For The No-Wait Flow Shop Scheduling Problem, Changping Liu, Zhenfu Jian, Wenhan Fu
A Discrete Krill Herd Algorithm For The No-Wait Flow Shop Scheduling Problem, Changping Liu, Zhenfu Jian, Wenhan Fu
Journal of System Simulation
Abstract: A discrete krill herd algorithm (DKH) is proposed to solve the no-wait flow shop scheduling problem (NWFSP) with the makespan criterion. Based on the characteristics of the optimization mechanism, the notion of “virtual food” in krill herd algorithm and the influenced crossover rules between krill individuals are defined. The concept and calculation method of the individual distance are redefined to measure the neighborhood range to realize the information exchange. The local search strategies of random swap, inverse and insert operator are employed to enhance the local search ability of DKH, and the multiple initialization strategies are redesigned to promote …
3d Reconstruction Of Uav Sequence Image Based On Motion Structure Graph, Yuhao Wu, Xuefeng Cao, Jinchao Peng, Lianrui Xu
3d Reconstruction Of Uav Sequence Image Based On Motion Structure Graph, Yuhao Wu, Xuefeng Cao, Jinchao Peng, Lianrui Xu
Journal of System Simulation
Abstract: UAV sequence image has the characteristics of high overlap and strong topological connection. Aiming at the inefficient and unstable in processing the large-scale UAV images of the existing incremental 3D reconstruction algorithm, a 3D reconstruction method based on motion structure graph is proposed. The image matching index is established by using the geolocation information and IMU data to improve the image matching efficiency, and the random motion consistency algorithm is used to calculate the relative motion; motion structure graph is used to represent the "association" between images, and closed-loop detection algorithm is used to eliminate the false edges. Under …
Intelligent Evaluation Of Simulation Training For Aerial Ammunition Technical Support, Xu Gang, Zhang Lei, Tian Lei
Intelligent Evaluation Of Simulation Training For Aerial Ammunition Technical Support, Xu Gang, Zhang Lei, Tian Lei
Journal of System Simulation
Abstract: Quantitative evaluation is an important part of the simulation training of the Aviation Ammunition technical support. In order to realize the automatic evaluation of the simulation training, intelligent evaluation technology is introduced, and a prediction model based on Sigmoid regression is proposed. On the basis of analyzing the linear relationship of the sample data of the performance indicators, a subset of the characteristic indicators is selected as the input of the prediction mathematical model. In order to avoid the gradient descent method falling into the local solution problem, the gradient descent + PSO algorithm is presented. After testing the …
Modeling And Simulation Of Quadrotor Uav With Vector Thrust Based On Backstepping, Zhou Nan, Wang Liang, Jianliang Ai
Modeling And Simulation Of Quadrotor Uav With Vector Thrust Based On Backstepping, Zhou Nan, Wang Liang, Jianliang Ai
Journal of System Simulation
Abstract: Combined with characteristics of the traditional quadrotor and the quad tilt-wing UAV, a quadrotor UAV with the vector thrust (VTQ) is proposed. This UAV has the ability of vertical take-off and landing and hovering, as well as the high maneuverability of the traditional quad tilt-wing UAV. It has the ability of completing the diversified tasks by being specified the desired yaw angle and pitch angle. Control system adopts the method of the layered design. The upper layer is the position control system, the lower layer is the attitude control system, and the control laws are both designed by the …
Dynamics Modeling And Simulation Of Gait Rehabilitation Robot Based On Lie Groups And Lie Algebras Theory, Bingjing Guo, Jianhai Han, Xiangpan Li, Yan Lin
Dynamics Modeling And Simulation Of Gait Rehabilitation Robot Based On Lie Groups And Lie Algebras Theory, Bingjing Guo, Jianhai Han, Xiangpan Li, Yan Lin
Journal of System Simulation
Abstract: A pneumatic-driven gait rehabilitation robot based on rigid mechanism and flexible driver is designed. To explore the dynamic characteristics of the human-robot harmony system constructed by patients and the exoskeleton robot, the dynamic models of human, robot and human-robot system in different gait phases are established based on Lie group and Lie algebra theory. The driving and energy characteristics of three rehabilitation training modes of passive, active assistance and resistance are analyzed. The robot joint driven moment and the human active moment are simulated to verify the Lie group and Lie algebraic modeling method and the dynamic model. It …
Simulation Optimization Of Initial Fire Evacuation Schemes For Vertical Ship Lift, Chen Shu, Xi Yan, Jianping Wang, Menghan Shang, Li Zhi
Simulation Optimization Of Initial Fire Evacuation Schemes For Vertical Ship Lift, Chen Shu, Xi Yan, Jianping Wang, Menghan Shang, Li Zhi
Journal of System Simulation
Abstract: In order to improve the efficiency of fire evacuation in the initial stage of the vertical ship lift and reduce the evacuation time, the structure and evacuation channel of the vertical ship lift are analyzed to identity the vertical evacuation path. The vertical evacuation time is determined by comparing the evacuation time of stairs and elevator based on the docking rules of cargos. Aiming at the shortest vertical evacuation time the evacuation time of the different docking elevations is simulated to obtain the optimal evacuation plan. The results show that, when the distance between the docking elevation and the …
Study Of Parallelized Graph Clustering Algorithm Based On Spark, Dongjiang Liu, Jianhui Li
Study Of Parallelized Graph Clustering Algorithm Based On Spark, Dongjiang Liu, Jianhui Li
Journal of System Simulation
Abstract: The parallelized graph clustering algorithm is researched. A new parallelized graph clustering algorithm is proposed based on Spark. As the top operation of Spark occupies a lot of memory space, a new algorithm which is used to substitute the top operation is proposed to reduce the memory consumption. By improving bottom up hierarchical clustering algorithm, the speed of the proposed algorithm is improved. A new data filtering method based on the feature of graph data is proposed. By the method, the running time and memory space comsuption is reduced greatly. The reason of the high efficiency of this filtering …
A Multi-Strategy Differential Evolution Algorithm Combined With Neighborhood Search, Can Sun, Xinyu Zhou, Mingwen Wang
A Multi-Strategy Differential Evolution Algorithm Combined With Neighborhood Search, Can Sun, Xinyu Zhou, Mingwen Wang
Journal of System Simulation
Abstract: The difficulties of designing a multi-strategy differential evolution (DE) algorithm are how to select the mutation strategies and allocate these strategies. A multi-strategy DE algorithm combined with the neighborhood search operator is proposed. The population is divided into three subpopulations according to the fitness values, and each subpopulation employs a different mutation strategy and parameter settings to complement the search ability, to balance the exploration and exploitation ability of the whole population. The subpopulation with the best fitness values employs the neighborhood search operator to exploit possible benefit information to guide the search. Extensive experiments are carried out on …
Cae Modeling And Fault Simulation For Instantaneous Action Mechanism With High Power And Heavy Load, Teng Lin, Tang Tang, Qiaojie Li, Chen Ming
Cae Modeling And Fault Simulation For Instantaneous Action Mechanism With High Power And Heavy Load, Teng Lin, Tang Tang, Qiaojie Li, Chen Ming
Journal of System Simulation
Abstract: A FEM simulation of a high voltage circuit breaker under actual conditions is proposed to solve the high-frequency vibration and mechanical failure problems caused by the realistic factors such as the clearance and structural elasticity of the breaker. Its operating characteristic under the high power pulse load is analyzed and the influence of the spring stiffness and dimension error on the breaker’s motion characteristics was predicted. On the basis of the dependency of the breaker’s mechanical characteristics on potential faults, critical parameters and design defects are established. The new FEM of the a high-voltage circuit breaker will replace the …
Holiday Highway Traffic Flow Prediction Method Based On Deep Learning, Xiaofeng Ji, Yicheng Ge
Holiday Highway Traffic Flow Prediction Method Based On Deep Learning, Xiaofeng Ji, Yicheng Ge
Journal of System Simulation
Abstract: Accurately predicting highway traffic holiday flow can provide important data for the emergency management of highway. The LSTM-SVR prediction model is established by using the theoretical framework of deep learning. The BP neural network is used to process the sample data, and the data features captured by LSTM are input into the SVR regression layer to realize the traffic flow prediction. Before and after the “Eleventh” Golden Week, the LSTM-SVR model was verified by using the traffic monitoring data of the intermodulation station in Lijiang City and the prediction results were compared with the others. It is found that …
Attribute Proxy Re-Encryption For Ciphertext Storage Sharing Scheme On Blockchain, Xiaohong Zhang, Lanlan Sun
Attribute Proxy Re-Encryption For Ciphertext Storage Sharing Scheme On Blockchain, Xiaohong Zhang, Lanlan Sun
Journal of System Simulation
Abstract: In order to implement the information storage sharing service safely and efficiently, a blockchain storage sharing scheme supporting the attribute proxy re-encryption and keyword retrieval is proposed. By the nodes classification and ciphertext storage separation, the anti-collusion attack is better implemented. The smart contract design of the information transaction is introduced and the information sharing parties can communicate spontaneously without the participation of the central organization. By the attribute-based proxy re-encryption algorithm, the information owner can share the information with other users without re-encrypting, uploading, and downloading information, and relieves the burden of the high-frequency access of the cloud …
Perfect Recovery (2,N) Color Visual Cryptography Scheme, Xianhuan Zhang, Zhengxin Fu, Ouyang Dan, Bin Yu
Perfect Recovery (2,N) Color Visual Cryptography Scheme, Xianhuan Zhang, Zhengxin Fu, Ouyang Dan, Bin Yu
Journal of System Simulation
Abstract: Based on XOR operation and combining the characteristic of computer display technology, a perfect recovery (2,n) color visual cryptography scheme was proposed. Sharing algorithm of color secret image was designed on the basis of constructing row vectors${{V}_{1}},{{V}_{2}},\cdots ,{{V}_{n}}$. Through computing shares by XOR operation and dealing with recovery image, the secret image was recovered. The experimental results show that the scheme on the basis of keeping the simplicity in the reconstruction phase of visual cryptography can realize the secret image perfect recovery with low pixel expansion for price. Each participant only needs to carry a share …
Optimization Sensing Slot Under Transmission Collision Of Primary User And Secondary User In Cognitive Radio System, Chen Song, Nae Zheng, Wang Sheng
Optimization Sensing Slot Under Transmission Collision Of Primary User And Secondary User In Cognitive Radio System, Chen Song, Nae Zheng, Wang Sheng
Journal of System Simulation
Abstract: In the cognitive radio system, that the primary user (PU) has collision with the secondary user (SU) when the secondary user (SU) was detected properly was considered. The queuing theory was introduced and the PU’s appearance pattern was described by M/M/1 model. Considering the length of the transmitting slot, detection probability and transmitting collision, the function of spectrum usage and transmitting time were established based on the PU’s appearance pattern. The existence of the maximum value of spectrum usage in the definition domain of the transmitting time was proved by theoretical derivation in some condition. The simulation results provide …