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无线传感器网络模型设计


Model Design of Wireless Sensor Network based on Scale-Free Network Theory ABSTRACT
The key issue of researches on wireless sensor networks is to balance the energy costs across the whol

e 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. Key-words: Wireless sensor network; Complex network; Scale-free network

I. INTRODUCTION
In 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]. Complex 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 RESEARCH
Hailin 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). CHEN 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. LEI 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 WSN
Because 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]. In 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, whose energy 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 ALGORITHM
The 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. Above all, the probability that the existing node i will be connected with the newly generated node v can be shown as follows:

In 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.

??

ak i

? Kj
j?1

N

N=m0 ? t ? 1 (2)

With The varying rate with time of ki, we get:

? ki amk amki (3) ? m? i ? m ?t ?1 i ? ?t 2mt ? m

?
j ?1

0

kj

When t→∞,
t ? 2 condition: ki (ti)=m, we get the solution: k (4) ( i t)=m( ), ? ? ti a

The probability that the degree of node I is smaller than k is:
P{k i (t) ? k} ? P{t i ? m1 ? t } k1 ?
(5)

The time interval when each newly generated node connected into the network is equal, so that probability density of ti is a constant parameter:
P(t i ) ? 1 1/β m0 ? t

we replace it into Eqs. (5), then we get:

m1 ? t P{k i (t) ? k} ? P{t i ? 1 ? } ? 1 ? k

m1 ? t k1 ? ti ?1

? P(t )
i

(6)

1?

m1 ? t So we get: k1 ? (t ? m0 )
(7)

? P(ki (t) ? k) 2m1 ? t 1 P(k) ? ? . ?k m0 ? t k 1 ?
When t →∞, we get:

P(k) ? 2m2 k ?r
In which ? =1+
1

(8)

2 =1+ , and the degree distribution we get and the degree distribution of ? a

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.

P{div ? dmax } 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 is ?d2 2 ?d Then we replace P{div ? dmax } = S and a= P{div ? dmax } (1-Pe ) into P{div ? dmax } = S

Eqs. and eventually we get: P(k) ? 2m k
2

?1?

2 a

? 2m k
2

2S ?1? (1-Pe)? d2

.

V. SIMULATION

This paper used Java GUI mode of BRITE topology generator to generate the topology, and parameter settings were as follows: 1) N=5000 N means the quantity of the sensor nodes at the end of the topology generation. 2) m=m0 =1 M means the quantity of the new generated edges by the new generated node at each time interval. 3) HS=500 HS means the given region was divided into HS*HS big squares. 4) .LS=50 LS means each big square was divided into LS*LS small squares. 5) dmin =10

dmin is the mininum restriction on communication radius of each sensor node.
6) dmax =128

dmax is the maxinum restriction on communication radius of each sensor node.
7) PC=1 PC means wether preferential connectivity or not. 8) .IG=1 IG means wether incremental grouth or not. 9) Pe =0.01, m=1 This 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 .

Then 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 to

Power-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 dmax 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.

Fig. 1 Degree distribution of Improved Model Compared 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. CONCLUSION
This 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. In 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

1

摘要
无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。 作为一个特殊的复杂网络特别是由于环 境的限制,传感器网络很不同于传统的复杂的网络,例如 Internet 网络,生态网络, 社交网络等。 这就有必要来介绍一种通过复杂网络理论和分析方法如何研究无线传感 器网络的方式,其中的关键在于能够作出一个成功的建模,它能够使复杂网络理论和 分析方法更适合无线传感器网络的应用, 以达到根据某些特定无线传感器网络的特点 进行优化。 基于传统的无尺度的网络生成规则, 本文对改进后的模型增加了一些限制。 仿真结果表明,在本文中进行的改进,使整个网络对随机故障有一个更好的鲁棒性并 且能源成本更平衡和合理。 这种基于复杂网络理论的改进模型证明更适用于无线传感 器网络的研究。 关键词:无线传感器网络,复杂网络,无尺度网络

2

引言
近年来,由于无线传感器网络的优点,吸引了越来越多的相关研究人员 。传感 器节点通常是低功率和非可再充电的。如果某些节点的能量消耗完,原来网络的完整 性将被破坏并且其他 进行数据传输的节点,会有更多的业务负担。 传感器网络的研 究的关键问题是是平衡所有的传感器节点能源消耗和把传感器节点随机错误影响或 者是对整个网络的传感器节点随机攻击降到最低。 复杂网络理论,自从 Barabasi 和 Albert 在 1998 年提出已经有一段时间了,但应 用于无线传感器网络的复杂网络理论和分析方法研究严重稀缺并且开发进展缓慢。 作 为一个尤其是环境的限制特殊的复杂的网络, 传感器网络是远远不同于传统的复杂网 络并且现有的复杂网络理论和分析法不能直接应用到分析传感器网络上。 基于无标度 网络理论(BA 模型)[2], (1)本文中当部署在生成规则时添加到每个传感器节点随 机损伤机制 (2)考虑到无线传感器网络的实际声明,传感器通信半径参数最大和最 小限制 添加到每个传感器节点; (3)为了维持整个网络平衡的的能源消耗率,本文 每个传感器节点加入了和度值的限度。这对无尺度模型改善不仅提到是以上的改善, 而且还具有传统的无标度网络大量的优点,如很好的抵抗随机的攻击的能力,从而使 现有的复杂网络的理论和分析方法,将是更适合于无线传感器网络的研究。

3

相关的研究进展
海林朱和香罗提出了两种复杂的基于网络的无线传感器网络模型 [3],第一个名 叫能量感知的演化模型(EAEM)可以以高效节能的方式组织网络,并能产生无尺度 网络,它可以提高网络抵御传感器节点随机失误的可靠性。第二个模型命名为能量均 衡演化模型(EBEM) ,为每个节点的最大链接数被引入算法,它可以使能源消费比 以前的型号更均衡(EAEM) 。 陈立军和毛驰提出了拓扑无线传感器网络控制下平均程度约束条件 [4]。在无线 传感器网络拓扑连通性的前提下,在大量的随机部署的传感器节点中,如何解决稀疏 性网络的拓扑结构是一个非常重要的问题。他们证明了自己的方案可以减少工作节 点,保证网络拓扑稀疏,简化路由的复杂性和延长网络的生存期。 雷鸣和李德氏提出了自组织无线传感器网络的可靠性的研究 [5],这针对两种情 况:缺乏 WSN 节点和外部的攻击下,分析了不同拓扑结构的无线传感器网络错误的 耐受能力,并最终获得优化自组织的无线传感器网络的拓扑模型,并提出了基于无线 传感器网络的精制路由算法。

4

改进的无标度模型的 WSN
由于能量有限和恶劣的应用环境,某些传感器节点的能量耗尽或被自然力损坏, 无线传感器网络会很容易遭到破坏,甚至还有一些传感器节点被部署时已经损坏。还 设有一个限制最大限度和最低限度的传感器节点的通信半径, 而不是其它已知的无标 度网络,如互联网络,它没有限制通信半径。为了有一个平衡的能源消耗,有必要设 置一个传感器的有限度的饱和度值[6]。 为了回答这些要点, 根据传统的无标度模型, 模型建立的过程中本文已做出以 下改进: (1)大量的研究表明,许多在本质上是复杂的网络不仅是内力,也是外部势力 的结果。形成一个完整的复杂网络时,这不应被忽略。在传感器网络工作的进展中, 节点故障不仅可能出现在节点的能量消耗或他们遭受随机攻击时, 也出现在外力情况 下,如当部署时的自然力。本文一种小概率的随机损伤机制已被添加到传感器网络的 形成中。 (2)不同于互联网网络,其中能够直接连接到彼此两个节点,它们的连接永远 不会受到真实位置的限制,无线传感器网络,两个相连的节点由多跳(multi-hop)的 方式彼此连接,使每个节点在通信半径上都有一个最大长度的限制。为了确保全网络 的稀疏性,还必须是有一个最小长度的通信半径限制。在本文中,改进后的模型中。 传感器节点的通信半径长度的限制,已经提出来了。
(3)在无线传感器网络,如果存在一个传感器很高的节点,其能源消耗是非常

快, 它会严重不利。 如果没有足够的能量支持某个节点, 整个传感器网络一定会崩溃, 。 为了避免这种情况,本文在每个传感器节点建立了一个饱和值限度。通过加入上述提 到的限制形成无尺度的模式,改进后的新模型将更加符合传感器网络的真实陈述。复 杂网络理论和分析方法将更加适合用来研究和分析传感器网络。

5

改进算法说明
具体算法改进模型形成描述如下: 给定的区域(假设是正方形) (1)分为 HS* HS 正方形(命名为 BS); (2)每个 BS(假设是正方形)分为 LS* LS 小正方形(命名为 SS) ,并且每个 SS 中在其覆盖区域只能有一个节点;
(3)M0 骨干节点最初作为一个随机产生的图形,然后一个新的节点将被添加到

网络以 每次有 m 条边连接现有的 m 个节点的时间间隔。 (M0 M,m 是一个量参数); (4)对新生成的节点 v,具有一定的直接被损坏概率 P,这样它会永远不与任何 现有的节点连接; (5)新生成的节点 v 与现有的连接节点 i 连接,服从依赖优先规则,肯定是被 确定的目标饱和度值 k 限制; (6)d 和新生成的节点 V 连接并且与现存的节点 I 之间的距离将比传感器通信 半径最大距离 dmax 更短。 总之,现有节点的概率,我将连接与新生成的节点 v 可以表示为 如下:

为了计算方便, 这里假设几个节点已经达到了饱和值达到。 所以上式可以被写为:

??

ak i

? Kj
j?1

N

N=m0 ? t ? 1

随着 ki 随时间的变化率,我们得到:

? ki amk amki ? m? i ? m ?t ?1 i ? ?t 2mt ? m

?
j ?1

0

kj

( i t) 当 t 趋近无穷大时,根据初始条件, k =m,我们的到结论:

6

t ? 2 k ( i t)=m( ), ? ? ti a

节点 i 的度比 k 小的概率是:
P{k i (t) ? k} ? P{t i ? m1 ? t } k1 ?

每个新生成的节点时的时间间隔连接到网络中是相等的, 从而使概率密度是一个 恒定的参数:
P(t i ) ? 1 我们把它带进式中,我们得到: m0 ? t

P{k i (t) ? k} ? P{t i ?

m1 ? t } ? 1? k1 ?

m1 ? t k1 ? ti ?1

? P(t )
i

1?

m1 ? t k1 ? (t ? m0 )

P(k) ?

? P(ki (t) ? k) 2m1 ? t 1 ? . ?k m0 ? t k 1 ?

P(k) ? 2m2 k ?r
在 ? =1+

2 =1+ 和度分布获取和传统的无标度网络的度分布是相似的。它具有与时无关参数 t ? a

1

和米的边的数量在每个时间产生的时间间隔。

P{div ? dmax } 可以通过以下计算,量子限制每个传感器节点的通信半径最大 D 和
区域的整个覆盖区域 S。 P{div ? dmax } =
?1? 2 a

?d2
S

,我们将上式代入 a= P{div ? dmax } (1-Pe )

我们最终得到 P(k) ? 2m k
2

? 2m k
2

2S ?1? (1-Pe)? d2



7

仿真
本文使用的 Java GUI 模式布里特拓扑生成器来生成的拓扑结构和参数设定为如 下所示: (1)N=5000 N 表示的数量的传感器节点的结尾拓扑生成。 (2)m=m0=1 m 表示由新生成的边的数量新生成的节点在每个时间间隔。 (3)HS=500 HS 是指给定的区域被分成 HS* HS 大正方形。 (4)LS=50 LS 意味着每个大广场被分为 LS* LS 小正方形。 (5) dmin =10 dmin 是最低限度的限制,通信半径。 (6) dmax = 128 (7)PC=1 (8)IG=1

dmax 是每个传感器节点参数最大通信半径的限制。

PC 意味连接与否。 IG 意味着生长或减少。

(9) Pe =0.01, m =1 这意味着,任何新产生的节点有 1%的几率出现节点故障并且新生成的节点如果只正 常连接一个现有的节点。 然后,我们得到了布里特拓扑生成的传感器网络节点的每一个度。为了分析度 分布,我们利用 Matlab 计算数据,画图形。可以很容易从图 1 中看出,k 的度分布大 概服从约幂律分布。然而,γ 的值不再是在 2 和 3 之间,而是一个非常大的值,这是 由部署时带给新生成的节点随机损伤概率 P,和每个传感器节点的通信半径 d。 不难看出,P(K)是非常陡峭的斜坡和 P(K)后轮传感器节点,因为有一个有 限的饱和度值 180。0 度的节点的存在导致了新生成的节点在部署时的随机损伤。

8

图一度分布的改进模型 相对于传统的无标度网络所产生的度分布如图 2 所示, 本文提出的生成规则产生 的度分布在一个相对较低的值,如图 1 所示。另外还有一些节点为 0 度,如图 1 随 机破坏规则的左侧图 1 的右侧,没有比 180 更高的数量较高的节点 180,而另外一个 还有一些节点的度比 180 的数量更高。

图 2 传统的无标度模型的度分布
9

结论
本文在节点部署时添加了一个随机产生的损害,考虑到传感器网络的多跳 传输,本文提出了一个对每个传感器节点的通信半径最大的限制,为了提高能量消耗 的利用率和保持整个网络的稀疏性,本文对改进模型中,每个传感器节点添加了通信 半径的最小限制,以平衡整个网络的能量消耗率,本文提出了 AA 每个传感器节点上 有限度的饱和值。 本文提出了一种改进的无标度网络模型,建议引入传统的无标度理论和分析 方法来更适当的研究传感器网络, 这会使无线传感器网络更接近真实的陈述规范性引 用。

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文献参考
[1]阿尔伯特,H.郑某,A.-L.鲍劳巴希.错误和攻击性复杂的网络,自然,2000,406;378-382. [2]伟业 R,鲍劳巴希 A.统计力学的复杂网络.牧师国防部物理 2002,74;47-97. [3]朱凯,罗 H.基于复杂网络高效节能的演变模型的无线传感器网络.混沌,孤子和分形;2008 年:1-4. [4] 陈 LJ, 毛 泽 东 黄 牌 . 无 线 传 感 器 网 络 的 拓 扑 控 制 根 据 平 均 度 约 束 . 中 国 计 算 机 学 报,2007,30;1-4. [5]雷男,李德生.无线自组织可靠性研究传感器网络.复杂系统与复杂性科学,2005,2;1-4. [6]陈利军,陈 DX.无线传感器网络的演进. WCNC2007;556;3003-7. [7]彭京,李祯一种改进的无标度网络演化模型.计算机应用. 2008 年,21;1-4.

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