Model Design of Wireless Sensor Network based on Scale-Free Network TheoryABSTRACThe key issue of researches on wireless sensor networks is to balance the energy costs across the whole network and to enhance the robustness in order to extend the survival time of the whole sensor network. As a special complex network limited especially by the environment, sensor network is much different from the traditional complex networks, such as Internet network, ecological network, social network and etc. It is necessary to introduce a way of how to study wireless sensor network by complex network theory and analysis methods, the key of which lies in a successful modeling which is able to make complex network theory and analysis methods more suitable for the application of wireless sensor network in order to achieve the optimization of some certain network characteristics of wireless sensor network. Based on generation rules of traditional scale-free networks, this paper added several restrictions to the improved model. The simulation result shows that improvements made in this paper have made the entire network have a better robustness to the random failure and the energy costs are more balanced and reasonable. This improved model which is based on the complex network theory proves more applicable to the research of wireless sensor network.ey-words: Wireless sensor network; Complex network; Scale-free networkI. INTRODUCTIONn recent years, wireless sensor networks have attracted more and more related researchers for its advantages. Sensor nodes are usually low-power and non-rechargeable. The integrity of the original networks will be destroyed and other nodes will have more business burden for data transmission if the energy of some certain nodes deplete. The key issue of sensor network research is to balance the energy consumption of all sensor nodes and to minimize the impact of random failure of sensor nodes or random attacks to sensor nodes on the entire network [1].omplex network theory has been for some time since first proposed by Barabasi and Albert in 1998, but complex network theory and analysis method applied to wireless sensor networks research is seriously rare and develops in slow progress. As a special complex network limited especially by the environment, sensor network is much different from the traditional complex network, and the existing complex network theory and analysis methods can not be directly applied to analyze sensor networks. Based on scale-free network theory (BA model) [2], (1) this paper added a random damage mechanism to each sensor node when deployed in the generation rule; (2) considering the real statement of wireless sensor networks, a minimum and maxinum restriction on sensor communication radius was added to each sensor node; (3) in order to maintain a balanced energy comsuption of the entire network, this paper added a limited degree of saturation value to each sensor node. This improved scale-free model not only has the mentioned improvements above, but also has lots of advantages of traditional scale-free networks, such as the good ability to resist random attacks, so that the existing theory and analysis methods of complex network will be more suitable for the researches of wireless sensor network.II. PROGRESS OF RELATED RESEARCHailin Zhu and Hong Luo have proposed two complex networks-based models for wireless sensor networks [3], the first of which named Energy-aware evolution model (EAEM) can organize the networks in an energy-efficient way, and can produce scale-free networks which can improve the networks reliance against random failure of the sensor nodes. In the second model named Energy-balanced evolution model (EBEM), the maximum number of links for each node is introduced into the algorithm, which can make energy consumption more balanced than the previous model (EAEM).HEN Lijun and MAO Yingchi have proposed a topology control of wireless sensor networks under an average degree constraint [4]. In the precondition of the topology connectivity of wireless sensor networks, how to solve the sparseness of the network topology is a very important problem in a large number of sensor nodes deployed randomly. They proved their proposed scheme can decrease working nodes, guarantee network topology sparseness, predigest routing complexity and prolong network survival period.EI Ming and LI Deshi have proposed a research on self-organization reliability of wireless sensor network[5], which aiming on the two situations: deficiency of WSN nodes and under external attack, analyzes the error tolerance ability of different topologies of WSN, and eventually obtains optimized self—organized topological models of WSN and proposes a refined routing algorithm based on WSN.III. IMPROVED SCALE-FREE MODEL FOR WSNecause of the limited energy and the evil application environment, wireless sensor networks may easily collapse when some certain sensor nodes are of energy depletion or destruction by the nature, and even some sensor nodes have been damaged when deployed. There is also a restriction on maxinum and mininum communication radius of sensor nodes rather than the other known scale-free networks such as Internet network, which has no restriction on communication radius. To have a balanced energy consumption, it is necessary to set up a saturation value limited degree of each sensor node [6].n response to these points, based on the traditional scale-free model, this paper has made the following improvements in the process of model establishment:1) A large number of researches have shown that many complex networks in nature are not only the result from internal forces, but also the result from external forces which should not be ignored to form an entire complex network. Node failure may not only occour by node energy depletion or random attacks to them when sensor networks are in the working progress, but also occour by external forces, such as by the nature, when deployed. In this paper, a mechanism of small probability of random damage has been added to the formation of sensor networks.2) Unlike Internet network where two nodes are able to connect directly to each other and their connection are never limited by their real location, sensor network, two nodes in which connect to each other by the way of multi-hop, so that each node has a maximum of length restriction on their communication radius. To ensure the sparse of the whole network, there must also be a minimum of length restriction on their communication radius. In this paper, a length restriction on communication radius of sensor nodes has been proposed in the improved model.3) In sensor network, if there exists a sensor node with a seriously high degree, whoseenergy consumption is very quickly, it will be seriously bad. The whole sensor network would surely collapse if enough energy were not supported to the certain node. To avoid this situation, this paper has set up a saturation value limited degree of each sensor node. By adding the mentioned restrictions above to the formation of the scale-free model, the new improved model will be more in line with the real statement of sensor network. Complex network theory and analysis methods will be more appropriate when used to research and analyze the sensor network.IV. DESCRIPTION OF THE IMPROVED ALGORITHMhe specific algorithm of the improved model formation are described as follows :1) A given region (assumed to be square) is divided into HS*HSbig squares (named as BS);2) Each BS (assumed to be square) is divided into LS*LS small squares (named as SS), and each SS can have only one node in its coverage region;3) m0 backbone nodes are initially generated as a random graph, and then a new node will be added to the network to connect the existing m nodes with m edges at each time interval. (m< m0, mis a quantity parameter);4) The newly generated node v, has a certain probability of Peto be damaged directly so that it will never be connected with any existing nodes;5) The newly generated node vconnects with the existing node i, which obeyes dependent-preference rule and is surely limited by the degree of the certain saturation value .6) The distance div between the newly generated node v connects and the existing node i shall be shorter than the maximum dmax of the communication radius of sensor nodes.bove all, the probability that the existing node i will be connected with the newly generatednode v can be shown as follows:n order to compute it conveniently, here assumed that few nodes had reached the degree of saturation value kimax . That is, N is very minimal in Eqs.1) so that it can be ignored here. And in Eqs.iN j 1ak Kjπ=≈∑ 0N=m 1t +- (2)ith The varying rate with time of ki, we get:0m 112i i i i t jj k amk amk m t mt m k δπδ+-====-∑ (3)hen t→∞,ondition: k i (t i )=m, we get the solution: i 2,i t k t aββ=（t ）=m （）(4) he probability that the degree of node I is smaller than k is:(5)he time interval when each newly generated node connected into the network is equal, so that probability density of t i is a constant parameter:01(t )i P m t=+1/β we replace it into Eqs. (5), then we get:11111{k (t)k}P{t }1(t )i m t k i i i t m t P P k ββββ=<=>=-∑ (6)1101(t m )m t k ββ-+ So we get: 110(k (t)k)21(k).i P m t P k m t kββδδ<==+ (7) When t →∞, we get:2(k)2m r P k -= (8) In which 12=1+=1+a γβ, and the degree distribution we get and the degree distribution of traditional scale-free network are similar. Approximately, it has nothing to do with the time parameter t and the quantity of edges m generated at each time interval.max P{d d }iv ≤could be calculated by the max in um restriction dmax on communication radius of each sensor node and the area of the entire coverage region S, that ismax P{d d }iv ≤=2Sd π Then we replace max P{d d }iv ≤=2S d π and a=max P{d d }iv ≤(1-P )e into Eqs. and eventually we get: 22S 21122(k)2m 2e a P km k π----==（1-P ）d .V. SIMULATIONhis paper used Java GUI mode of BRITE topology generator to generate the topology, and parameter settings were as follows:) N=5000means the quantity of the sensor nodes at the end of theopology generation.) m=m0 =1means the quantity of the new generated edges by the new generated node at each time interval.) HS=500S means the given region was divided into HS*HS big squares.) .LS=50 LS means each big square was divided into LS*LS small squares.d=10) minis the mininum restriction on communication radius of each sensor node.d=128) maxis the maxinum restriction on communication radius of each sensor node.) PC=1C means wether preferential connectivity or not.) .IG=1G means wether incremental grouth or not.) e P=0.01, m=1his means that any newly generated node has 1% chance to be node failure and the newly generated node if normal only connect with one existing node .hen we got each degree of the sensor network nodes from BRITE topology generator. To analyze the degree distribution, we use Matlab to calculate datas and draw graph. As can easily be seen from Fig. 1, the distribution of degree k subjected approximately toPower-Law distribution. However, the value of γ is no longer between 2 and 3, but a very large value, which is caused by the random damage probability P e to new generated nodes when deployed and the max in um of communication radius d max of each sensor node. It can be easily seen that the slope of P(k) is very steep and P(k) rears up because sensor node has a limited degree of saturation value by 180. The existence of 0 degree nodes is result from the random damage to new generated nodes when deployed.ig. 1 Degree distribution of Improved Modelompared with the degree distribution produced by traditional scale-free network as is shown in Fig. 2, the generation rule proposed in this paper has produced a degree distribution in a relatively low value as is shown in Fig. 1; there are some nodes of 0 degree as is shown in Fig. 1 on the left for the random damage rule; as is shown on the right in Fig. 1, there are no nodes with higher degree than the quantity of 180 while there are some nodes whose degree are of higher degree than the quantity of 180.Fig. 2 Degree distribution of traditional Scale-free Model VI. CONCLUSIONhis paper has added a random damage to new generated nodes when deployed; considering multi-hop transmission of sensor network, this paper has proposed a maximum restriction on the communication radius of each sensor node; in order to improve the efficiency of energy comsumption and maintain the sparsity of the entire network, this paper has also added a minimum restriction on the communication radius of each sensor node to the improved model; to balance the energy comsuption of the entire network, this paper has proposed a limited degree of saturation value on each sensor node.n this paper, an improved scale-free network model was proposed to introduce the theory of traditional scale-free network and analysis methods into the researches of wireless sensor networks more appropriately, which would be more approximate to the real statement of wireless sensor networks.REFERENCES[1] R. Albert, H. Jeong and A.-L. Barabasi. Error and attack tolerance of complex networks. Nature, 2000; 406: 378-382.[2] Albert R, Barabasi A. Statistical mechanics of complex networks. Rev Mod Phys 2002; 74: 47–97..[3] Zhu HL, Luo H. Complex networks-based energy-efficient evolution model for wireless sensor networks. Chaos, Solitons and Fractals; 2008: 1-4.[4] Chen LJ, Mao YC. Topology Control of Wireless Sensor Networks Under an Average Degree Constraint. Chinese Journal of computers 2007; 30: 1-4.[5] Lei M, Li DS. Research on Self-Organization Reliability of Wireless Sensor Network . Complex system and complexity science ; 2005, 2: 1-4.[6] Chen LJ, Chen DX. Evolution of wireless sensor network . WCNC 2007; 556: 3003–7.[7] Peng J, Li Z. An Improved Evolution Model of Scale-Free Network . Computer application. 2008 , 2; 1: 1-4.基于无范围网络理论的无线传感器网络模型设计张戌源通信工程部通信与信息工程学院上海，中国摘要线传感器网络的研究的关键问题是是平衡整个网络中的能源成本并且为了延长整个传感器网络的生存时间要增强鲁棒性。