Master s Thesis. Configuring robust virtual wireless sensor networks for Internet of Things inspired by brain functional networks

Transcription

1 Master s Thess Ttle Confgurng robust vrtual wreless sensor networks for Internet of Thngs nspred by bran functonal networks Supervsor Professor Masayuk Murata Author Shnya Toyonaga February 10th, 2014 Department of Informaton Networkng Graduate School of Informaton Scence and Technology Osaka Unversty

2 Master s Thess Confgurng robust vrtual wreless sensor networks for Internet of Thngs nspred by bran functonal networks Shnya Toyonaga Abstract In future, wreless sensor networks (WSN) are expected to be ntegrated nto the Internet of thngs and to play an mportant role not only for data collecton but for communcaton nfrastructure. In that stuaton, mult-vendor and heterogeneous WSNs should be federated to make a large scale WSN. As one way to realze the ntegraton of WSNs, vrtualzaton technology n WSN s of great sgnfcance. Although many technques for vrtualzaton of sensor networks have been studed, envronmental changes, such as dverse traffc patterns or addton or removal of vrtual nodes, are not consdered. Snce future WSNs wll face wth a wde varety of requrements, t s crtcally mportant to construct a vrtual sensor network (VSN) whch provdes short delay tme of packet communcaton and a guarantee of network connectvty n a network of arbtrary scale. In ths thess, we propose a method for constructng a VSN nspred by bran functonal networks known for robustness, hgh effcency and adaptve evolvablty. To earn the advantages shown above, we partcularly pay our attenton to modularty and small world property whch bran functonal networks have and we apply them to vrtual topology constructon. Through smulaton experments, compared to a VSN topology constructed by an exstng clusterng technque for achevng small world propertes, our VSN topology s hghly robust n terms of connectvty and average path length. Keywords Wreless sensor networks Vrtual sensor networks Bran functonal networks 1

3 Contents 1 Introducton 5 2 Bran functonal networks Small world property Modular communty structure A method for confgurng vrtual wreless sensor networks usng propertes of bran functonal networks Overvew Modular dvson for a physcal sensor network Confgurng a 1st layer vrtual sensor network by connectng sensor nodes wthn the same module Confgurng an N th layer vrtual sensor network by connectng (N 1)th layer vrtual sensor networks Smulaton experments Bo-nspred technques for achevng small world propertes Evaluaton metrcs Two-layered vrtual sensor networks wthout a long wred connecton Three-layered vrtual sensor networks wth a long wred connecton Concluson and Future Work 35 Acknowledgements 36 Reference 37 2

4 Lst of Fgures 1 Example of herarchcal VSN topology Example of a physcal sensor network Robustness of connectvty aganst random falure when a VSN s constructed by one sensor network Robustness of connectvty aganst targeted attack when a VSN s constructed by one sensor network Robustness of vapl aganst random falure when a VSN s constructed by one sensor network Robustness of vapl aganst targeted attack when a VSN s constructed by one sensor network Robustness of papl aganst random falure when a VSN s constructed by one sensor network Robustness of papl aganst targeted attack when a VSN s constructed by one sensor network Example of a physcal sensor network composed of two sensor networks connected by one wred lnk Robustness of connectvty aganst random falure when a VSN s constructed by two sensor networks wth one wred lnk Robustness of connectvty aganst targeted attack when a VSN s constructed by two sensor networks wth one wred lnk Robustness of vapl aganst random falure when a VSN s constructed by two sensor networks wth one wred lnk Robustness of vapl aganst targeted attack when a VSN s constructed by two sensor networks wth one wred lnk Robustness of papl aganst random falure when a VSN s constructed by two sensor networks wth one wred lnk Robustness of papl aganst targeted attack when a VSN s constructed by two sensor networks wth one wred lnk

5 Lst of Tables 1 Parameter settngs Comparson of VSN constructed by each models n one sensor network Comparson of VSN constructed by each models n two sensor networks connected by one wred lnk

6 1 Introducton Wreless sensor networks (WSN) has a great mportance because of the broad range of ts commercal applcatons such as smart home, health care and ndustral automaton [1]. Furthermore, WSN s recently attractng a great deal of attenton as a requred technology to realze the Internet of Thngs. WSN are expected to be ntegrated nto the Internet of Thngs and to play an mportant role not only for a specfc applcaton such as a data collecton but for communcaton nfrastructure shared by multple applcatons [2, 3]. In that stuaton, sensor nodes whch have varous functons and propertes are deployed n the same area by multple vendors. Vrtualzaton of WSN s one of key solutons for ntegratng such heterogeneous WSNs nto one large WSN and sharng physcal sensor substrate. Vrtualzaton of WSN can be defned as a separaton of a functon for WSN nto two parts, physcal sensor nfrastructure and applcatons workng on aggregated resources. The expected advantages of vrtualzaton of WSN are provdng flexblty, cost effcency, dversty, securty and manageablty [1, 4 6]. Although many researchers have worked on vrtualzaton of WSN, objectves and assumptons of ts use are dfferent and techncal challenges are left to be solved, for example, constructng an arbtrary vrtual sensor network (VSN) wth flexblty, reusablty, resource effcency, securty, prvacy, manageablty, scalablty, programmablty and allowablty of heterogenety [1, 7]. Because envronmental changes, such as dverse traffc patterns or addton or removal of vrtual nodes, are antcpated n vrtualzaton of sensor networks, to construct a VSN wth certan communcaton effcency and connectvty s partcularly mportant. Therefore, we propose an algorthm for constructng a VSN topology wth hgh communcaton effcency and robustness by ntroducng complex network features. In ths thess, we defne two knds of robustness. One s robustness of connectvty and the other s robustness of average path length. Many researchers ntroduce small world propertes, whch s one class of complex network, to sensor networks and show that small number of long-dstance lnks added to a sensor network mprove communcaton effcency drastcally [8, 9]. For that reason, we can construct a VSN topology wth hgh communcaton effcency by ntroducng structural propertes of complex network to sensor networks. Although WSN wth small world propertes has hgh communcaton effcency, t s sad that a topology wth a property of some classes of complex networks s vulnerable aganst targeted attack on nodes wth hgh degree or on long-dstance lnks [10]. To address 5

7 ths problem, we focus on the bran functonal network because t shows hghly robust features and evolves adaptvely dependng on communcaton demands or envronmental changes, whle t has multple features of complex network. The bran functonal network has small world propertes and modular communty structure [11]. Small world propertes are descrbed by hgh effcency and hgh clusterng. These features lead to effcent nformaton dssemnaton globally and locally. Moreover, hghly clusterng structure gves many detour routes from one node to another. Ths leads to robustness n terms of connectvty. The bran functonal network s organzed by a large number of modules, each of whch processes nformaton, such as cogntve, emotonal, perceptual or motor processng nformaton. A network wth modular communty structure can adapt to changes of demands by confgurng a small number of lnks between modules. Therefore, the bran functonal network can negotate trade-offs between wrng cost and communcaton effcency rapdly, resultng n ts evolvablty to changng cogntve demands. Therefore, we propose an algorthm to construct a VSN topology wth small world propertes and modular communty structure for hgh communcaton effcency, robustness and evolvablty. The rest of ths thess s organzed as follows. Secton 2 shows the topologcal propertes of the bran functonal network and advantages by applyng them to WSN. We propose a model for constructng a VSN topology nspred by bran functonal network n Secton 3 and evaluate our proposal n Secton 4. In Secton 5, we conclude ths thess and descrbe future work. 6

8 2 Bran functonal networks In ths secton, we explan topologcal propertes of bran functonal networks and descrbe expected advantages applyng these propertes to wreless sensor networks. A bran functonal network has small world propertes and a modular communty structure. Small world topology has hgh topologcal effcency n local and global areas and robustness. Modular communty structure of a bran functonal network has adaptvty and evolvablty [11 16]. 2.1 Small world property Small world propertes are characterzed by a short average path length and a hgh clusterng coeffcent. In ths thess, we regard path length as a hop count on the shortest path between a par of two nodes. Path length n whole network s quantfed by average path length (APL), defned as AP L = 1 N(N 1) sd(, j), (1) where N s the number of node and sd s the mnmum hop count between node and node j. A short APL means that global communcaton effcency s hgh. Clusterng structure of a network s quantfed by average clusterng coeffcent (CC) defned as,j CC = 1 N 2e k (k 1), (2) where k s a degree of node and e s the number of lnks that exst between neghbor nodes of node. A topology wth hgh CC has many topologcal motfs of a trangle, whch means that the nearest neghbors of a gven node have a hgh probablty to be connected wth each other. Hgh CC means that local communcaton effcency s hgh due to ts densely connected structure n a local regon Long-dstance connectons One of factors contrbutng to global communcaton effcency n a bran functonal network s myelnated long-dstance lnks [11]. An electrc conductvty of a myelnated lnk s hgh. When long-dstance areas are connected by these lnks, communcaton delay between them gets short and these lnks enable a close cooperaton between dfferent functonal areas. 7

9 2.1.2 Hghly clusterng structure A bran functonal network s a spatal network. Ths means that connectng functonal areas s strongly nfluenced by dstance between functonal areas due to wrng and runnng metabolc costs [11]. Therefore, short-length lnks tend to be constructed and mantaned, resultng n a hgh clusterng coeffcent. Because local areas are connected densely, segregated processng and synchronzaton can be done rapdly. 2.2 Modular communty structure A bran functonal network has a modular communty structure n whch nodes wthn the same module are densely connected by short-dstance lnks but sparsely connected to a node n other modules by long-dstance lnks. Moreover, a bran functonal network demonstrates a property of herarchcal modularty. Each module n a bran functonal network s composed of a set of sub-modules and each sub-module s composed of a set of sub-sub-modules [11, 16]. Ths modular communty structure allows a bran functonal network to balance trade-off between effcency and metabolc costs, n other words communcaton delay and connecton dstance, can be rapdly negotated by functonal systems only by confgurng long-dstance nter module lnks [11]. When there s greater demand for cogntve processng, networks adopt a more effcent structure by constructng costly long-dstance lnks, and when cogntve demand s lower, bran networks get more clustered and less costly. Moreover, because connectons between modules are sparse, t seems that bran network can be evolved adaptvely under envronmental changes. In modular systems, each module can confgure ts structure adaptvely, whch has lttle nfluence on outsde of the module. Therefore, modular structure gves whole system evolvablty by segregated confguraton of each module. A wreless sensor network s a spatal network, because t s strongly constraned by physcal dstance. For most of wreless sensor networks densely deployed, a topology of such networks naturally has a regular lattce property and a hgh clusterng coeffcent. Therefore, a wreless sensor network favors segregated processng. Moreover, there are many detour routes from one node to another due to topologcal motfs of a trangle. Ths leads to hgh robustness of connectvty aganst falure of nodes or lnks. When we ntroduce a herarchcal modular structure to wreless sensor networks, t s expected that ts topology can evolve adaptvely to changes of resource or 8

10 traffc demands. Exstence of a long-dstance connecton whch connects two physcally dstant sensor nodes leads to reducton of communcaton delay of a whole network because of shortened average path length. When a physcal long-dstance lnk, such as drectonal beam or long range omndrectonal transmsson, can be assgned to a vrtual lnk, mprovement of communcaton effcency n vrtual networks drectly means that n physcal networks. However, because communcaton capabltes of sensor nodes are constraned, endponts of a vrtual lnk may not be able to communcate wth each other drectly. One of the solutons s that a vrtual lnk s assgned to a path contanng avalable physcal long-dstance lnks. 9

11 3 A method for confgurng vrtual wreless sensor networks usng propertes of bran functonal networks 3.1 Overvew A topology havng hgh modularty enables effcent segregated nformaton processng and local synchronzaton and a topology havng small world propertes enables effcent global communcaton. Therefore, we propose a model whch constructs a VSN topology havng hgh modularty and small world propertes. Consderng a geographcal constrant, we assume that a mnmum unt of a module s a group of sensor nodes dvded by Newman algorthm [17]. We smply call ths mnmum unt of a module as a unt module. We descrbe Newman algorthm n detal n Secton 3.2. We construct a VSN topology by ntegratng these unt modules herarchcally. At the same tme, t has small world propertes n any scale of layer. By repeatng ntegraton of sub-modules wth a new module havng small world propertes, a VSN topology constructed fnally has a hgh modularty and small world propertes. An example of herarchcal VSN s shown n Fgure 1. The frst layer VSN s a network n a unt module whch corresponds to a group of sensor nodes dvded by Newman algorthm. The second layer VSN s a network constructed by connectng unt modules. The thrd layer VSN s a network constructed by connectng sensor networks whch s deployed for dfferent purposes. At frst, we propose an algorthm whch constructs a VSN topology n the frst layer, that s to say ths constructs a small world network n a unt module by addng vrtual long-dstance lnks. In Secton 3.3, we explan the method for constructng a VSN topology n the frst layer n detal. Then, n Secton 3.4, we show the method for constructng a VSN topology n an Nth layer by connectng modules n an (N 1)th layer. 3.2 Modular dvson for a physcal sensor network Newman algorthm s a heurstc algorthm whch dvdes a network n several modules for the maxmzaton of the modularty. The defnton of the modularty, denoted by Q, s as followng. Q = (e a 2 ), (3) 10

12 vrtual 3 rd layer vrtual 2 nd layer vrtual 1 st layer nfra layer sensor node unt module IP gateway Fgure 1: Example of herarchcal VSN topology where s a group ID and e s a rato of edges whose endponts belong to the same group. a s a probablty that at least one of endponts belongs to the group. Then, a 2 that edges whose endponts belong to the same group to all edges. s an expected rato In Newman algorthm, modules are dvded nto two modules recursvely as long as a condton for halt s not satsfed. At frst, we explan the method of the frst dvson n whch a whole network s regarded as one group and dvded nto two groups. For a partcular dvson of the network nto two groups let s = 1 f a node belongs to group 1 and s = 1 f t belongs to group 2. And let A s an adjacency matrx, A j = 1 f node and node j s connected and A j = 0 f node and j s unconnected. The expected number of lnks between node and node j can be descrbed by k k j 2m, where k s a degree of node and m s a total number of lnks embedded n a whole network, that s, m = 1 2 k. Under these assumptons, the modularty can be calculated 11

13 by Equaton (4). Q = 1 2m = 1 4m,j,j (A j k k j 2m )(s s j + 1) 2 (A j k k j 2m )s s j, (4) where (s s j +1) 2 = 1 f node and node j belong to the same group and (s s j +1) 2 = 0 f node and node j belong to dfferent groups. The second equalty follows from the observaton that 2m = k =,j A j. Equaton (4) can convenently be wrtten n matrx form as shown n Equaton (5). Q = 1 4m st Bs, (5) where s s the column vector whose elements are the s. B s a symmetrc matrx whose elements are B j = A j k k j 2m. The am of Newman algorthm s maxmzaton of the modularty Q by choosng a value of the vector s whch means choosng an approprate dvson of the network. By wrtng s as a lnear combnaton of the normalzed egenvectors u x of B, that s s = x a xu x, Equaton (5) can be descrbed as Equaton (6). Q = 1 4m = 1 4m a x u T x B a y u y x y (u T x s) 2 β x, (6) x where β x s an egenvalue of the egenvector u x. Newman assumes that the egenvalues are labeled n decreasng order, β 1 β 2 β n. From Equaton (6), to decde the most approprate s equals to decde the best weght of each egenvalue. Therefore, the most smple method to maxmze Q s to place all of the weght n the term nvolvng the largest egenvalue β 1 by settng s to αu 1. Because there s a constrant that the elements of s must be ±1, Newman maxmzes u T x s by settng s = 1 f the correspondng element of u 1 s postve and s = 1 otherwse. Then, node belongs to group 1 f s = 1 and t belongs to group 2 f s = 1. Decson of module can be realzed by applyng the same algorthm to each dvded group recursvely. However, f ths dvdng procedure s appled to subgraph after smply deletng the lnks between the two parts, the value of modularty n Equaton (4) wll change due to the change of degrees. Instead, Newman uses the alternatve modularty Q to calculate the correct modularty 12

14 and to further dvde a group g of sze n g n two groups. The defnton of Q s Q = 1 2m (1 2 B j (s s j + 1) B j ),j g = 1 4m ( = 1 4m,j g B j s s j B j ),j g,j g (B j δ j B k )s s j,j g k g = 1 4m st B (g) s (7) where δ j s a Kronecker δ-symbol and B (g) s the n g n g matrx wth elements ndexed by the labels, j of nodes wthn group g. An element of B (g) s B (g) j = B j δ j B k. (8) Because Equaton (7) has the same form as Equaton (5), the dvdng algorthm can be appled. By usng Newman algorthm, modular structure can be detected and the modularty Q s maxmzed. However, accordng to ts heurstc manner, n some cases there s a module composed of only one node, whch s unsutable for sensor networks. Therefore, we coordnate Newman algorthm to sut for sensor networks. After dvde a sensor network nto modules by Newman algorthm, node whch belongs to module g checks modules ts neghbor nodes belong to. If there s no neghbor node belongng to module g, then node fnds that t s solated and moves to k g one of the smallest modules ts neghbor nodes belong to. 3.3 Confgurng a 1st layer vrtual sensor network by connectng sensor nodes wthn the same module In ths secton, we explan how to construct a small world network n an ntra-module whch s detected by usng the algorthm descrbed n Secton 3.2. To create a network wth small world propertes, we add a small number of long-dstance lnks, called shortcuts, to ntal regular lattce network. We assume that ntal topology of an ntra-network s the same as the topology of a physcal network, that s to say two nodes whch belong to the same module and are deployed n communcaton range of each other are also connected logcally. Then, we propose a model based 13

15 on [18, 19], n whch vrtual shortcuts are added n consderaton of both constrant of physcal dstance and the preferental attachment rule. In [18], the authors have proposed an enhancng a robustness of scale free network model (ESF) n whch new lnks are added to Barabas Albert model (BA) topology [20] n consderaton of degrees. At frst, a scale free network s constructed by BA model. The number of added lnks s C E 0, where E 0 s the number of lnks embedded n the constructed scale free network and C s a constant value of 0 to 1. Authors defne the probablty of addng a new lnk between unconnected node and node j as k α kj α p ESF (, j) = e a,b Ē kα a kb α, (9) where k s a degree of node, e a,b s a par of nodes and Ē s the set of lnks n the complementary graph. α s a parameter, called enforcng parameter. When α > 0, a new lnk s added preferentally to a node wth hgher degree and the constructed topology s robust on connectvty aganst random falure but vulnerable aganst targeted attack. When α < 0, a new lnk s added preferentally to a node wth lower degree and the constructed topology have an allowable robustness of connectvty aganst both of random falure and targeted attack. Arport network model (Arport model) s proposed n [19]. Arport model can construct a spatal network topology wth scale free property by consderng physcal dstance constrants. Arport model s based on preferental attachment algorthm and ether of two processes descrbed below whch s determned wth probablty Π at each tme step. Probablty Π: addng a new lnk between two nodes already n the network Probablty (1 Π): addng a new node and lnks between t and m nodes already n the network The probablty of addng a lnk between node and node j whch are already n the network s shown n Equaton (10) and the probablty of addng a lnk between a new node and node j s shown n Equaton (11). p Arport (, j) k k j F (d,j ). (10) p Arport (j) k j F (d,j ). (11) k s a degree of node, d,j s a physcal dstance between node and node j and F s a monotonously ncreasng functon. Authors nvestgate two dfferent functonal forms for the 14

16 functon F, whch are F 1(d) = d r and F 2(d) = e d/d x where r and d x are a constant parameter descrbng a cutoff of dstance constrant. In ths thess, we use F 2(d). By mergng two models explaned above, we propose a preferental attachment model based on degree and physcal dstance constrant as p ntra (, j) = e a,b Ē G ntra (k,k j ) F 2(h,j ) G ntra (k a,k b ) F 2(h a,b ), (12) where node and node j belong to the same module M, Ē s the set of lnks n complementary graph of ntra-module network and h,j s the mnmum hop count from node to node j. The reason why we use hop count nstead of physcal dstance s that the same method can be appled to constructng an upper layer VSN topology. The functon G ntra s a strategy of selectng a new lnk preferentally accordng to degrees of endpont nodes. We nvestgate a four dfferent strateges for addng a new lnk n ntra-module network and the name of each strategy ntra s labeled by hh, ll, hl and r. When ntra = hh, a par of two nodes wth hgher degree s selected preferentally for a new lnk, and when ntra = ll, a par of two nodes wth lower degree s selected for a new lnk. When ntra = hl, a node wth hgher degree and another wth lower degree are selected preferentally and connected. When ntra = r, a par of two nodes are selected randomly regardless of ther degrees. Each defnton of G ntra s as follows. G hh (k, k j ) = k k j. (13) G ll (k, k j ) = k 1 k 1 j. (14) G hl (k, k j ) = max(k, k j ) k k j. (15) G r (k, k j ) = 1. (16) The number of added vrtual lnks s C ntra E 0, where E 0 s the number of lnks embedded n the ntal ntra-module network and C ntra s a constant value of 0 to Confgurng an N th layer vrtual sensor network by connectng (N 1)th layer vrtual sensor networks In ths secton, we explan the method to construct an Nth layer VSN topology. Ths problem can be dvded nto two small sub-problems as shown below. 15

17 1. In an Nth layer, regardng an (N 1)th layer VSN as one subnetwork, the frst problem s how to select a par of two subnetworks to be connected. 2. The second problem s how to select an endpont sensor nodes at nfra-layer based on ntersubnetwork lnks n Nth layer. We explan how to solve the frst problem n Secton 3.4.1, and the second problem n Secton Constructng an ntra Nth layer vrtual lnk In ths secton, we propose a method to construct an Nth layer vrtual lnk between (N 1)th layer subnetworks. We regard VSN n an (N 1)th layer as one subnetwork (Sub N 1 ). Proposed method to construct a VSN topology n ntra Nth layer subnetwork s organzed by two steps descrbed below. 1. Constructng an ntal vrtual topology 2. Addng vrtual shortcut lnks to ntal vrtual topology In step 1, ntal vrtual topology s constructed based on physcal connecton. When a par of nodes has physcal lnk and they belong to dfferent (N 1)th layer subnetworks, these (N 1)th layer subnetworks are connected by an Nth layer vrtual lnk. Note that, there s a case that unconnected subgraphs exst because there s no physcal lnk between them. In such a stuaton, the closest subnetworks are connected by an Nth layer vrtual lnk to guarantee ts connectvty. In step 2, new Nth layer vrtual lnks are added to the ntal vrtual topology constructed n step 1 smlar to the proposed model n Secton 3.3. Proposed model s p N ntra(sub N 1, Sub N 1 j ) = where (N 1)th layer subnetwork Sub N 1 and e Sub N 1 a G ntra (k Sub N 1 F 2(h Sub N 1,Sub N 1 b and Sub N 1 j E N k Sub N 1 ) j,sub N 1 ) j Gntra (k Sub N 1 k a Sub N 1 ) b F 2(h Sub N 1 a,sub N 1 ) b, (17) belong to the same Nth layer subnetwork E N s the set of lnks n the complementary graph of the Nth layer ntal vrtual topology. k Sub N 1 Sub N 1 j s a degree of Sub N 1 n graph of Nth layer ntal vrtual topology. and h Sub N 1,Sub N 1 s the mnmum hop count from Sub N 1 to j 16

18 The strategy functon G ntra s the same one shown n Secton 3.3 and we use the same strategy as the strategy to construct a 1st layer VSN topology. The number of added Nth layer vrtual lnks s Cntra N EN 0, where EN 0 s the number of lnks embedded n the Nth layer ntal ntra-subnetwork topology and Cntra N s a constant value of 0 to Constructng a vrtual lnk between under layer vrtual sensor networks based on Nth layer vrtual lnk In ths secton, we explan the method to construct vrtual lnks between the sensor nodes whch belong to dfferent subnetworks based on Nth layer vrtual lnk. We select endponts of an Nth layer vrtual lnk from subnetworks n under layer recursvely. When there s an Nth layer vrtual lnk between Sub N 1 x and Suby N 1, we construct an (N 1)th layer vrtual lnk by selectng endponts from (N 2)th layer subnetworks Sub N 2 and Sub N 2 j Sub N 1 x Sub N 1 y. We assumed that the relatonal operator whose rght operand s an Nth layer subnetwork (Sub N and composes Sub N. The probablty to add a lnk between Sub N 2 vrtual lnk s defned as p N nter(sub N 2, Sub N 2 j ) = where Sub N 1 x Sub N 1 y ) means that ts left operand s a subnetwork n a lower Nth layer Sub N 2 a and Sub N 2 and Sub N 2 j G nter (k Sub N 2 F 2(h Sub N 2 Subx N 1,Sub N 2 b Sub N 1 y as endponts of an Nth layer,k Sub N 2 ) j,sub N 2 ) j G nter (k Sub N 2 a F 2(h Sub N 2 a Sub N 1 x, Subj N 2 Sub N 1 y. The functon G nter s a strategy of selectng endponts Sub N 2 x and Sub N 2 y,k Sub N 2 ) b,sub N 2 ) b, (18) preferentally accordng to ther degrees n (N 1)th layer VSN topology. We nvestgate a four dfferent strateges for addng a new lnk n nter-subnetwork and the name of each strategy nter s labeled by HH, LL, HL and R. When nter = HH, a par of two nodes wth hgher degree s selected preferentally for a new lnk, and when nter = LL, a par of two nodes wth lower degree s selected for a new lnk. When nter = HL, a node wth hgher degree and another wth lower degree are selected preferentally and connected. When nter = R, a par of two nodes s 17

19 selected randomly regardless of ther degrees. Each defnton of G nter s as follows. G HH (k Sub N 2 G LL (k Sub N 2 G HL (k Sub N 2 G R (k Sub N 2, k Sub N 2) = k j Sub N 2, k Sub N 2) = k 1 k 1 j Sub N 2, k Sub N 2 j ) = max(k Sub N 2 k Sub N 2. (19) j Sub N 2 j. (20), k Sub N 2) k j Sub N 2 k Sub N 2. (21) j, k Sub N 2) = 1. (22) j Note that Sub 1 means a module whch s detected by usng the algorthm descrbed n Secton 3.2 and Sub 0 means a sensor node. The number of added vrtual lnks per upper layer lnk s C nter (E SubN 1 x + E SubN 1 y ), where E SubN 1 x s the number of lnks embedded n the (N 1)th layer VSN topology of Sub N 1 x and C nter s a constant value of 0 to 1. However, when N = 2, the value of (E Sub1 x + E Sub 1 y) s relatvely large, accordngly the number of added vrtual lnks between modules s large, resultng n small modularty. Therefore, when N = 2, the number of added vrtual lnks s αc nter (E Sub1 x + E Sub 1 y) where α s a constant value of 0 to 1. By applyng ths algorthm recursvely tll N = 2, we can fnally construct a VSN topology composed of whole sensor nodes. 18

20 4 Smulaton experments In ths secton, we evaluate our proposal through comparson wth Bo-nspred small world network model (Bo-nspred) [21]. We brefly explan Bo-nspred n Secton 4.1. Our proposed model, called bran-nspred confgurng model (BICM), has 16 knds of results by combnaton of 4 strateges of ntra and 4 strateges of nter. Therefore, we dentfy each strategy by two arguments of ntra and nter, such as BICM(ntra,nter). 4.1 Bo-nspred technques for achevng small world propertes Bo-nspred s a model whch acheves small world propertes usng bo-nspred technques n wreless network wth non-unform node densty [21]. The algorthm s composed of two steps, dentfyng clusterng by usng Lateral Inhbton technque and dentfyng nodes that construct long-dstance lnks by usng Flockng technque. The frst step s descrbed n Secton and the second step s descrbed n Secton Authors assume that a long-dstance lnk s realzed by creatng the drectonal beam because a power consumpton s the same as when omndrectonal transmsson Clusterng by usng Lateral Inhbton technque In ths secton, we explan the clusterng algorthm by usng Lateral Inhbton technque. At frst, each node v floods a control packet contaned node ID of cluster head t s assocated (H ), the mnmum hop count from t to H (h v,h ) and the degree of H (k H ). Intally, all the nodes consder themselves as cluster heads and store ther nformaton H = v, h v,h = 0 and k H = k v. When a node w receves a control message, t updates stored nformaton based on stored and receved nformaton. We assume that node w stores nformaton that t belongs to cluster j and s assocated H j. When k Hj < k H and h w,h < g, where g s the maxmum gradent of cluster, node w s assocated H and updates ts stored nformaton to belong to the cluster. Further, when k Hj = k H and h w,h < h w,hj, node w s assocated H and updates ts stored nformaton. When a hop count s also the same, then the node w decdes to update the stored nformaton to the receved nformaton randomly. Then node w broadcasts the updated nformaton after ncrementng the hop count by 1. Ths process s repeated tll all the nodes are assocated the cluster head whch s the maxmum degree wthn g hops. 19

21 4.1.2 Constructng a long-dstance lnk by usng Flockng technque In ths secton, we explan dentfyng nodes that construct long-dstance lnks by usng Flockng technque. In Bo-nspred model, a long-dstance lnk s constructed between a centrod and a perpheral nodes of a cluster to reduce average path length effcently. A centrod node of a cluster s a node wth the maxmum closeness centralty and a perpheral node of a cluster s a node deployed at boundary of the cluster. Closeness centralty s the fracton of shortest dstance between a node to all other nodes n the network of ntra cluster and defned as Closeness(v ) = 1 w v,w C sd(v, w), (23) where sd s the mnmum hop count between two nodes. To dentfy perpheral nodes of cluster, a centrod node c of cluster broadcasts a control message and each node n the cluster gets a hop count to c. Then, the node wth the maxmum hop count to c n those of ts neghbors declares tself as a perpheral node. Each perpheral node v randomly selects the number of antenna elements m whch s a value of 2 to M and determnes a beam length and a beam wdth. A beam length s mr, where r s a communcaton range n omndrectonal mode, and a beam wdth s 2π m 2. Each perpheral node v searches centrod nodes exstng wthn the crcle of radus mr and nomnates them for the endpont of a long-dstance lnk. When a neghborng perpheral node already connected to the centrod node c j, a perpheral node v excludes c j from canddates. Then, node v selects the node to whch the mnmum hop count s the maxmum n canddates and constructs a long-dstance lnk to t. 4.2 Evaluaton metrcs The evaluaton metrcs are small worldness, clusterng coeffcent, average path length n vrtual network, average path length n physcal network, modularty, the total number of vrtual lnks, robustness of connectvty and robustness of average path length. The metrc of small worldness, ω, are proposed n [22]. ω compares network clusterng to an equvalent lattce network and average path length to a random network. Equvalent network means that the degree dstrbuton s the same as that of the orgnal network. ω s defned as ω = L rand L C C latt, (24) 20

22 Table 1: Parameter settngs model parameter value BICM C ntra 0.1 C nter 0.1 α 0.1 Bo-nspred g 4 M 6 where L s average path length and C s clusterng coeffcent of the orgnal network, L rand s average path length of equvalent random network and C latt s clusterng coeffcent of equvalent lattce network. ω s n range [-1,1]. The orgnal network has small world propertes when ω 0, t has a lattce lke property when ω 1 and t has a random lke property when ω 1. When we evaluate APL n the vrtual network (vapl), we assume that nodes connected by a vrtual lnk can communcate wth each other n one hop. When we evaluate APL n the physcal network (papl), we assume that nodes connected by a vrtual lnk communcate wth each other n shortest multhop path of physcal network. Accordng to the method to realze a long-dstance lnk n physcal network, actual APL n physcal network may change. Therefore, vapl ndcates the mnmum APL and papl ndcates the maxmum APL. The metrc of modularty s Q shown n Secton 3.2. We evaluate robustness of connectvty and APL by removng a node one by one. We evaluate the declne n a component sze whch s the number of nodes n the maxmum connected component when we evaluate robustness of connectvty and we evaluate the ncrease n APL when we evaluate robustness of APL. If there s no path from node to node j accordng to removal of nodes, we calculate APL wth regardng the hop count between them as the number of nodes (N). We assume two knds of removal models, random error and targeted attack. The node removed n the next tme step s selected randomly n random error, and the node wth the largest degree s selected to be removed n the next tme step n targeted attack. The parameter settngs are shown n Table 1 and we used OMNeT++ [23] for smulaton experments. 21

23 4.3 Two-layered vrtual sensor networks wthout a long wred connecton In ths secton, we evaluate a vrtual sensor network whch s constructed by one sensor network. In our model, a constructed vrtual sensor network s two-layered. In smulaton, 500 sensor nodes are deployed at random places n the area of 1000m 1000m and the communcaton range s 100m. An example of a physcal sensor network s shown n Fgure 2. We construct a vrtual sensor network based on such a physcal topology and evaluate t. Fgure 2: Example of a physcal sensor network Small world propertes In ths secton, we evaluate a constructed VSN topology and summarze small worldness (ω), CC, vapl, papl, the total number of vrtual lnks and modularty (Q) n Table 2. A VSN constructed by BICM model has small world propertes but relatvely lattce lke propertes. In BICM, a lnk whch has great nfluence on vapl and papl s a lnk between modules. When the strategy nter s HH or HL, vapl of a whole network tends to be small because the long-dstance lnk s constructed at hgh degree nodes. On the contrary, vapl tends to be large when the strategy nter s LL. When the strategy nter s R, vapl tends to be large because a dstance constrant s only consdered. However, when nter = R, papl tends to be small because a constructed vrtual network s smlar to physcal network due to dstance constrants. 22

24 A VSN constructed by Bo-nspred model has the hghest small worldness due to ω 0. Further, although the number of vrtual lnks s the largest, vapl and papl s the smallest of all the models. Ths s due to Flockng technque. The long-dstance lnks are dstrbuted all over the network because each perpheral node does not construct a long-dstance lnk to the centrod node whch s already connected wth ts neghbor node. Moreover, APL reduces drastcally because each perpheral node selects the centrod node to whch the mnmum hop count s the maxmum n the canddates and constructs a long-dstance lnk to t. Table 2: Comparson of VSN constructed by each models n one sensor network ω CC vapl papl # of vrtaul lnks Q BICM(hh,HH) BICM(hh,LL) BICM(hh,HL) BICM(hh,R) BICM(ll,HH) BICM(ll,LL) BICM(ll,HL) BICM(ll,R) BICM(hl,HH) BICM(hl,LL) BICM(hl,HL) BICM(hl,R) BICM(r,HH) BICM(r,LL) BICM(r,HL) BICM(r,R) Bo-nspred

25 the maxmum component sze BICM(hh,HH) BICM(hh,LL) BICM(hh,HL) BICM(hh,R) BICM(ll,HH) BICM(ll,LL) BICM(ll,HL) BICM(ll,R) BICM(hl,HH) BICM(hl,LL) BICM(hl,HL) BICM(hl,R) BICM(r,HH) BICM(r,LL) BICM(r,HL) BICM(r,R) Bo-nspred the number of faled nodes Fgure 3: Robustness of connectvty aganst random falure when a VSN s constructed by one sensor network Robustness of connectvty In ths secton, we evaluate robustness of connectvty aganst random fal and targeted attack. Fgure 3 and Fgure 4 show the declne of a component sze when nodes are removed by random fal and targeted attack respectvely. The declne of component sze of each model s almost same. In BICM, when nodes are removed by targeted attack, a lnk whch has great nfluence on the declne of a component sze s also a lnk between modules. A VSN constructed by the strategy nter = LL or nter = R s hghly robust n terms of connectvty because t keeps a component sze hgh. A VSN constructed by Bo-nspred s hghly robust n terms of connectvty because t s based on lattce regular graph Robustness of average path length In ths secton, we evaluate robustness of vapl and papl aganst random fal and targeted attack. Fgure 5 and Fgure 6 show the ncrease tendency of vapl when nodes are removed by random fal and targeted attack respectvely. In BICM, a lnk whch has great nfluence on robustness of 24

26 the maxmum component sze BICM(hh,HH) BICM(hh,LL) BICM(hh,HL) BICM(hh,R) BICM(ll,HH) BICM(ll,LL) BICM(ll,HL) BICM(ll,R) BICM(hl,HH) BICM(hl,LL) BICM(hl,HL) BICM(hl,R) BICM(r,HH) BICM(r,LL) BICM(r,HL) BICM(r,R) Bo-nspred the number of faled nodes Fgure 4: Robustness of connectvty aganst targeted attack when a VSN s constructed by one sensor network vapl s a lnk between modules. All the VSN constructed by each model have a hghly robust aganst random fal n terms of vapl. A VSN constructed by BICM of the strategy nter = HH or nter = HL or by Bo-nspred has smaller vapl because a long-dstance lnk s constructed to the node wth hgh degree or closeness centralty. However, they are vulnerable of vapl aganst targeted attack due to the same reason. When the nodes are removed by targeted attack, a VSN constructed by BICM of the strategy nter = LL or nter = R has hghly robust n terms of vapl. Fgure 7 and Fgure 8 show the ncrease tendency of papl when nodes are removed by random fal and targeted attack respectvely. All the VSN constructed by each model have a hghly robust of papl aganst random fal. The VSN constructed by BICM of the strategy nter = R or by Bonspred has smaller papl because the both of constructed topologes are almost same as physcal network and almost all paths are shortest paths n the physcal network. When nodes are removed by targeted attack, a VSN constructed by BICM of the strategy nter = LL or nter = R has hghly robust of papl. The VSN constructed by Bo-nspred has the hghest robustness of papl aganst targeted attack because t s based on physcal network. 25

27 vapl BICM(hh,HH) 5 BICM(hh,LL) BICM(hh,HL) BICM(hh,R) 4 BICM(ll,HH) BICM(ll,LL) BICM(ll,HL) 3 BICM(ll,R) BICM(hl,HH) BICM(hl,LL) BICM(hl,HL) 2 BICM(hl,R) BICM(r,HH) BICM(r,LL) 1 BICM(r,HL) BICM(r,R) Bo-nspred the number of faled nodes Fgure 5: Robustness of vapl aganst random falure when a VSN s constructed by one sensor network From the above, the hghly robust model n both vapl and papl s BICM wth the strategy nter = LL. 4.4 Three-layered vrtual sensor networks wth a long wred connecton In ths secton, we evaluate a vrtual sensor network whch s constructed by two sensor networks whch are connected by one wred lnk. In our model, a constructed vrtual sensor network s three-layered. In smulaton, two sensor networks, each of whch s composed of 200 sensor nodes, are embedded n the area of 1000m 1000m. For one of two sensor networks, 200 sensor nodes are deployed at random places n the area of 0m x 400m, 0m y 1000m, and 200 sensor nodes are deployed at random places n the area of 600m x 1000m, 0m y 1000m for the other. One wred lnk s embedded between two sensor networks and sensor nodes of ts endponts are statcally selected. When the wreless communcaton range s 100m, an example of a physcal sensor network s shown n Fgure 9. We construct a VSN based on such a physcal topology and evaluate t. 26

28 vapl BICM(hh,HH) 5 BICM(hh,LL) BICM(hh,HL) BICM(hh,R) 4 BICM(ll,HH) BICM(ll,LL) BICM(ll,HL) 3 BICM(ll,R) BICM(hl,HH) BICM(hl,LL) BICM(hl,HL) 2 BICM(hl,R) BICM(r,HH) BICM(r,LL) 1 BICM(r,HL) BICM(r,R) Bo-nspred the number of faled nodes Fgure 6: Robustness of vapl aganst targeted attack when a VSN s constructed by one sensor network Small world propertes In ths secton, we evaluate a constructed VSN topology and summarze small worldness (ω), CC, vapl, papl, the total number of vrtual lnks and modularty (Q) n Table 3. Table 3 shows the almost same tendency as the propertes of the VSN constructed by one sensor network. Ths mples that mult-layered VSN can be constructed by applyng our proposed algorthm recursvely and ts topology has smlar propertes to those of two-layered VSN. A VSN constructed by BICM model has small world propertes but relatvely lattce lke propertes. In BICM, a lnk between modules has great nfluence on vapl and papl. When the strategy nter s HH or HL, vapl of a whole network tends to be small because a long-dstance lnk s constructed at hgh degree nodes. On the contrary, vapl tends to be large when the strategy nter s LL. A VSN constructed by Bo-nspred model has the hghest small worldness due to ω 0. Further, although the number of vrtual lnks s the largest, vapl and papl s the smallest of all the models accordng to Flockng technque. 27

29 Table 3: Comparson of VSN constructed by each models n two sensor networks connected by one wred lnk ω CC vapl papl # of vrtual lnks Q BICM(hh,HH) BICM(hh,LL) BICM(hh,HL) BICM(hh,R) BICM(ll,HH) BICM(ll,LL) BICM(ll,HL) BICM(ll,R) BICM(hl,HH) BICM(hl,LL) BICM(hl,HL) BICM(hl,R) BICM(r,HH) BICM(r,LL) BICM(r,HL) BICM(r,R) Bo-nspred

30 papl 8 BICM(hh,HH) BICM(hh,LL) 7 BICM(hh,HL) BICM(hh,R) 6 BICM(ll,HH) BICM(ll,LL) 5 BICM(ll,HL) BICM(ll,R) 4 BICM(hl,HH) BICM(hl,LL) 3 BICM(hl,HL) BICM(hl,R) 2 BICM(r,HH) BICM(r,LL) BICM(r,HL) 1 BICM(r,R) Bo-nspred the number of faled nodes Fgure 7: Robustness of papl aganst random falure when a VSN s constructed by one sensor network Robustness of connectvty In ths secton, we evaluate robustness of connectvty aganst random fal and targeted attack. Fgure 10 and Fgure 11 show the declne of a component sze when nodes are removed by random fal and targeted attack respectvely. Note that there are few opportuntes to fal the node whch s the endpont of a wred lnk than other nodes because t s assumed to be suppled energy through wred lnk. Therefore, we assume that the node connected by a wred lnk does not fal. The declne of a component sze of each model s almost same. In BICM, when nodes are removed by targeted attack, a VSN constructed by the strategy nter = LL or nter = R s hghly robust n terms of connectvty because t keeps a component sze hgh. A VSN constructed by Bo-nspred s hghly robust n connectvty because t s based on lattce regular graph. These features are also observed n Secton

31 papl 8 BICM(hh,HH) BICM(hh,LL) 7 BICM(hh,HL) BICM(hh,R) 6 BICM(ll,HH) BICM(ll,LL) 5 BICM(ll,HL) BICM(ll,R) 4 BICM(hl,HH) BICM(hl,LL) 3 BICM(hl,HL) BICM(hl,R) 2 BICM(r,HH) BICM(r,LL) BICM(r,HL) 1 BICM(r,R) Bo-nspred the number of faled nodes Fgure 8: Robustness of papl aganst targeted attack when a VSN s constructed by one sensor network Robustness of average path length In ths secton, we evaluate robustness of vapl and papl aganst random fal and targeted attack. The results show an almost same tendency as the results of a VSN whch s constructed by one sensor network. Fgure 12 and Fgure 13 show the ncrease tendency of vapl when nodes are removed by random fal and targeted attack respectvely. All the VSN constructed by each model have a hgh robustness aganst random fal n terms of vapl. A VSN constructed by BICM of the strategy nter = HH or nter = HL or by Bo-nspred has smaller vapl because a longdstance lnk s constructed to the node wth hgh degree or closeness centralty. However, they are vulnerable of vapl aganst targeted attack due to the same reason. When nodes are removed by targeted attack, a VSN constructed by BICM of the strategy nter = LL or nter = R has hgh robustness of vapl. Fgure 14 and Fgure 15 show the ncrease tendency of papl when nodes are removed by random fal and targeted attack respectvely. All the VSN constructed by each model have a hghly robust of papl aganst random fal. A VSN constructed by BICM of the strategy nter = R or by 30

32 a wred lnk Fgure 9: Example of a physcal sensor network composed of two sensor networks connected by one wred lnk the maxmum component sze BICM(hh,HH) BICM(hh,LL) BICM(hh,HL) BICM(hh,R) BICM(ll,HH) BICM(ll,LL) BICM(ll,HL) BICM(ll,R) BICM(hl,HH) BICM(hl,LL) BICM(hl,HL) BICM(hl,R) BICM(r,HH) BICM(r,LL) BICM(r,HL) BICM(r,R) Bo-nspred the number of faled nodes Fgure 10: Robustness of connectvty aganst random falure when a VSN s constructed by two sensor networks wth one wred lnk 31

33 the maxmum component sze BICM(hh,HH) BICM(hh,LL) BICM(hh,HL) BICM(hh,R) BICM(ll,HH) BICM(ll,LL) BICM(ll,HL) BICM(ll,R) BICM(hl,HH) BICM(hl,LL) BICM(hl,HL) BICM(hl,R) BICM(r,HH) BICM(r,LL) BICM(r,HL) BICM(r,R) Bo-nspred the number of faled nodes Fgure 11: Robustness of connectvty aganst targeted attack when a VSN s constructed by two sensor networks wth one wred lnk Bo-nspred has smaller papl because both of constructed topologes are almost same as physcal network and almost all paths are shortest paths n the physcal network. When nodes are removed by targeted attack, a VSN constructed by BICM of the strategy nter = LL or nter = R has hgh robustness of papl. A VSN constructed by Bo-nspred has the hghest robustness of papl aganst targeted attack because t s based on physcal network. From the above, the hghly robust model n both vapl and papl s BICM wth the strategy nter = LL. When we consder all results, mult-layered VSN constructed by our proposed algorthm has a certan small worldness, communcaton effcency, robustness of connectvty and robustness of APL. Ths suggests that subnetworks observed on arbtrary scale of VSN constructed by our algorthm have smlar propertes. 32

34 vapl BICM(hh,HH) 5 BICM(hh,LL) BICM(hh,HL) BICM(hh,R) 4 BICM(ll,HH) BICM(ll,LL) BICM(ll,HL) 3 BICM(ll,R) BICM(hl,HH) BICM(hl,LL) BICM(hl,HL) 2 BICM(hl,R) BICM(r,HH) BICM(r,LL) 1 BICM(r,HL) BICM(r,R) Bo-nspred the number of faled nodes Fgure 12: Robustness of vapl aganst random falure when a VSN s constructed by two sensor networks wth one wred lnk vapl BICM(hh,HH) 5 BICM(hh,LL) BICM(hh,HL) BICM(hh,R) 4 BICM(ll,HH) BICM(ll,LL) BICM(ll,HL) 3 BICM(ll,R) BICM(hl,HH) BICM(hl,LL) BICM(hl,HL) 2 BICM(hl,R) BICM(r,HH) BICM(r,LL) 1 BICM(r,HL) BICM(r,R) Bo-nspred the number of faled nodes Fgure 13: Robustness of vapl aganst targeted attack when a VSN s constructed by two sensor networks wth one wred lnk 33

35 papl 8 BICM(hh,HH) BICM(hh,LL) 7 BICM(hh,HL) BICM(hh,R) 6 BICM(ll,HH) BICM(ll,LL) 5 BICM(ll,HL) BICM(ll,R) 4 BICM(hl,HH) BICM(hl,LL) 3 BICM(hl,HL) BICM(hl,R) 2 BICM(r,HH) BICM(r,LL) BICM(r,HL) 1 BICM(r,R) Bo-nspred the number of faled nodes Fgure 14: Robustness of papl aganst random falure when a VSN s constructed by two sensor networks wth one wred lnk papl 8 BICM(hh,HH) BICM(hh,LL) 7 BICM(hh,HL) BICM(hh,R) 6 BICM(ll,HH) BICM(ll,LL) 5 BICM(ll,HL) BICM(ll,R) 4 BICM(hl,HH) BICM(hl,LL) 3 BICM(hl,HL) BICM(hl,R) 2 BICM(r,HH) BICM(r,LL) BICM(r,HL) 1 BICM(r,R) Bo-nspred the number of faled nodes Fgure 15: Robustness of papl aganst targeted attack when a VSN s constructed by two sensor networks wth one wred lnk 34

36 5 Concluson and Future Work In ths thess, we propose a model for constructng a VSN topology nspred by bran functonal networks. Our proposed model s organzed by three steps, dvdng sensor networks nto unt modules, constructng a vrtual topology wth small world property n each module and ntegratng multple modules or subnetworks of under layer. We nvestgate combnatons of four strateges ntra for constructng an ntra N th layer vrtual lnks and four strateges nter for confgurng vrtual lnks of under layer based on a vrtual lnk of Nth layer. The results of the smulaton experments show that the strategy nter plays an mportant role for communcaton effcency and robustness of constructed VSN topology. When at least one of the endponts of vrtual long-dstance lnk between modules has hgh degree, global effcency s mproved but robustness aganst targeted attack declnes. When nodes whch are wthn dfferent modules and have low degree are connected by a vrtual long-dstance lnk, global effcency s slghtly low but all of three knds of robustness, n terms of connectvty, vapl and papl, aganst targeted attack are hgh. Comparng wth a VSN topology constructed by Bo-nspred, a VSN topology constructed by our model has a hgh robustness of vapl aganst targeted attack. In ths thess, we analyze only statc propertes of vrtual topology composed of all sensor nodes. Therefore, we need to consder the followngs n future work. At frst we need consder the method to realze a vrtual lnk n physcal network. The packet forwarded along a vrtual lnk should be conveyed wth short delay. For example, creatng drectonal beam, ncreasng omndrectonal transmsson range or forwardng by mult hop wth prorty wll do. Secondly, when there are multple demands for constructng VSNs whch compete for resources such as energy, memory or bandwdth, we need nvestgate the model constructng resource effcent VSN topologes. Thrdly, we want to construct a protocol for confgurng a VSN topology adaptvely accordng to envronmental changes, such as dverse traffc patterns, addton or removal of vrtual nodes or modules. Due to modular communty structure, small adjustment of a few numbers of vrtual lnks between modules wll acheve that. 35

37 Acknowledgements Ths thess would not accomplsh wthout a lot of great supports of several people. Frst, I would lke to express my sncere grattude to my supervsor, Professor Masayuk Murata of Osaka Unversty, for hs contnuous support and valuable advce throughout my studes, and provdng me ths precous study opportunty n hs laboratory. Furthermore, I show my deepest apprecaton to Assstant Professor Dach Komnam of Osaka Unversty. He devoted a great deal of tme for me and gave me an excellent gudelne of my research and consderable supports. Moreover, I would lke to apprecate to Professor Naok Wakamya, Assocate Professor Shn ch Arakawa and Assstant Professor Yuch Ohsta of Osaka Unversty for benefcal comments and suggestons on ths study. In addton, I heartly thank Ms. Kazama, Ms. Negta and Ms. Yabk secretares dong a lot of help, and the encouragement at tmes. Furthermore, I would lke to express sncere apprecaton to my senor assocates, Mr. Takuya Iwa, Ms. Naom Kuze. I receved a lot of advces from them and they kndly provded consultaton for me. Fnally, I would lke to thank all the members of the Advanced Network Archtecture Laboratory at the Graduate School of Informaton Scence and Technology, Osaka Unversty, for support and meanngful dscusson about my research and hearty encouragement. 36

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