Social-aware Dynamic Router Node Placement in Wireless Mesh Networks

Transcription

1 Social-aware Dynamic Rouer Node Placemen in Wireless Mesh Neworks Chun-Cheng Lin Pei-Tsung Tseng Ting-Yu Wu Der-Jiunn Deng ** Absrac The problem of dynamic rouer node placemen (dynrnp) in wireless mesh neworks (WMNs) is concerned wih deermining a dynamic geographical placemen of mesh rouers o serve mobile mesh cliens a differen imes, so ha boh nework conneciviy (i.e., he greaes opology subgraph componen size) and clien coverage (i.e., he number of he served mesh cliens) are maximized. Mesh cliens are wireless devises associaed wih users, and in real world, he users wih same ineress or some social relaionship have higher chance o gaher and move ogeher geographically, i.e., hey form a communiy, and he WMN wih muliple communiies can be regarded as a social nework. Therefore, his paper invesigaes he so-called social-aware WMN-dynRNP problem assuming ha mesh rouers should be aware of he social communiy srucure of mesh cliens o dynamically adjus heir placemen o improve nework performance. To cope wih his problem, his paper proposes a social-based paricle swarm opimizaion approach, which addiionally includes a social-supporing vecor o direc low-loading mesh rouers o suppor he heavy-loading mesh rouers in he same opology subgraph componen (communiy), so as o dynamically adop o he social communiy behavior of mesh cliens. As compared wih he previous approach, our experimenal resuls C.-C. Lin P.-T. Tseng T.-Y. Wu Deparmen of Indusrial Engineering and Managemen, Naional Chiao Tung Universiy, Hsinchu 300, Taiwan s: cclin321@ncu.edu.w, jacky.p@gmail.com, ingyuwu777@gmail.com * D.-J. Deng (Corresponding auhor) Deparmen of Compuer Science and Informaion Engineering, Naional Changhua Universiy of Educaion, Changhua 500, Taiwan djdeng@cc.ncue.edu.w

2 2 C.-C. Lin, P.-T. Tseng, T.-Y. Wu, D.-J. Deng show ha he proposed approach is capable of effecively reducing number of he unserved mesh cliens and increasing nework conneciviy in dynamic social scenarios. Keywords Social nework wireless mesh nework rouer node placemen communiy movemen paricle swarm opimizaion 1 Inroducion Wireless mesh nework (WMN) has been a popular wireless communicaions echnology. Differen from oher communicaions echnologies, e.g., GSM, saellie, 3G, and WLAN, WMNs combine characerisics of WLANs and ad hoc neworks, and enjoy meris of high ransmission bandwidh, low cos, and high mobiliy. They have various applicaions and provide las-few-miles soluions [1], [2], e.g., home broadband neworks, communiy neworks, enerprise nework conneciviy, building auomaion, wireless mulimedia sensor nework [3], [4], ec. WMNs are robus as nodes in he nework have self-organizing and self-configuring abiliy, i.e., he WMN sysem can find oher alernaive rouing pahs for hose disconneced mesh nodes [5]. This paper considers he WMNs composed of mesh rouers and mesh cliens. Mesh cliens are wireless devices associaed wih users; mesh rouers are access poins ha consiue he backbone of WMNs, and have he gaeway funcion o connec o he ouside Inerne. A opology graph can be esablished as follows. Each mesh rouer provides a circular radio coverage region, and he mesh cliens wihin he radio coverage region can connec o he Inerne via muli-hop communicaion. Two mesh rouers can communicae wih each oher if heir radio coverage re-

3 Social-aware Dynamic Rouer Node Placemen in Wireless Mesh Neworks 3 gions are overlapped. As illusraed in Figure 1, he connecion from a mesh rouer o he Inerne is represened by a black solid line segmen; he connecion beween a mesh rouer and a mesh clien is represened by a red doed line segmen; he connecion beween wo mesh rouers is represened by a green dashed line segmen. Noe ha if a mesh clien exiss in he overlapping range of radio coverage regions of wo mesh rouers, i chooses an arbirary mesh rouer o communicae. Inerne Mesh clien Mesh rouer Inerne Wired link Wireless link for backbone Wireless link for serving cliens Fig.1. Illusraion of a WMN opology. This paper is concerned wih he problem of rouer node placemen (RNP) in WMNs [6], and his line of research has moved from saic WMN scenarios [7], [8], [9], [10], [11] o he dynamic WMN scenarios [12]. Noe ha he RNP problem has been sudied in oher fields of opimizaion (e.g., faciliy planning and logisics), and he geographic concern in wireless neworks has as well, e.g., [13]. In recen years, he RNP problem has been applied o wireless neworks, e.g., sensor placemen in wireless sensor neworks [14], gaeway placemen in WMNs [15], ec. In WMNs, a bad-qualiy RNP could lead o unavoidable wireless inerference as well as load unbalancing, in which some mesh rouers have unexpeced high service loading while he ohers have a lower uilizaion rae [16]. The ob-

4 4 C.-C. Lin, P.-T. Tseng, T.-Y. Wu, D.-J. Deng jecive of he WMN-RNP problem in his paper is o maximize he WMN connecively and he clien coverage [17], which are size of he greaes opology subgraph componen and number of he covered mesh cliens, respecively. Since he WMN-RNP problem has been shown o be NP-hard [14], [15], [18], i is commonly resolved by meaheurisic algorihms. A lo of previous works exised for saic WMN-RNP problems. Oda e al. [7] proposed a geneic algorihm approach, and esed he influences of differen muaion and selecion schemes on differen WMN sizes. Xhafa e al. [8] proposed a simulaed annealing approach, and hen Xhafa e al. [9] proposed a abu search approach o avoid he soluion search from falling ino local opimal soluions. Chang e al. [10] proposed a hill-climbing algorihm. Our previous work in [11] furher proposed a simulaed annealing approach wih momenum erms for he saic WMN-RNP problem wih mesh clien prioriy consrain. Insead of considering he saic WMN scenario, our anoher previous work in [12] sared o invesigae he meaheurisic algorihms for dynamic WMN-RNP problems (WMN-dynRNP for shor), in which mesh cliens and mesh rouers have mobiliy; mesh cliens move heir posiions a differen imes; mesh rouers adjus heir deploymens accordingly o adap he WMN opology change. The work in [12] furher proposed a paricle swarm opimizaion (PSO) approach for he WMN-dynRNP problem, and derived a heoreical convergence analysis. This paper focuses on he so-called social-aware dynamic rouer node placemen in WMNs (social-aware WMN-dynRNP for shor). In pracice, some mesh cliens may form a social communiy relaionship, in which he mesh cliens wih similar ineres may have a high chance o gaher or move ogeher and frequenly communicae wih each oher direcly or indirecly, so ha hey form a social nework [19]. As a resul, his paper exends our previous work in [12] for he WMN-dynRNP problem o a more pracical social nework scenario in which some mesh

5 Social-aware Dynamic Rouer Node Placemen in Wireless Mesh Neworks 5 cliens in he WMN form a communiy srucure, so ha he mesh cliens in he same communiy gaher and move ogeher; addiionally, each mesh rouer is resriced o serve only a resriced number of mesh cliens (which were never considered before). Hence, he placemen of mesh rouers should be aware of he communiy srucure o be adjused a differen imes. Some previous works also made heir exension in he similar way on differen opics. For insance, Kim e al. [20] and Song e al. [21] simulaed he movemen behavior of real-human communiies o conduc he relaed analysis on heir respecive problems. To solve he social-aware WMN-dynRNP problem, if we coninue using he original PSO approach in [12], hen many mesh cliens could no be served, because each single mesh rouer could no serve dense mesh cliens due o heir communiy srucure. Addiionally, if he placemen of mesh rouers is no adjused accordingly in ime o fi he communiy srucure, performance could become worse as some communiies move o heir new locaions a he nex ime sep. From he lieraure, los of previous works also applied characerisics of social neworks o enhance he communicaion process among nodes, especially used for designing rouing proocols and algorihms, e.g., [22], [23], [24], [25], [26]. Therefore, his paper also considers he facor of social communiy o improve he original PSO approach in [12] o propose he so-called social-based PSO approach, which includes an addiional social-supporing vecor where mesh rouers in he same communiy can communicae wih and suppor each oher o make a rapid adjusmen for possible communiy movemen behaviors of mesh cliens. By doing so, low-loading mesh rouers end o move o be closer o he heavy-loading mesh rouers in he same communiy, so ha hose unserved mesh cliens wihin he radio coverage regions of heavy-loading mesh rouers have higher chance o be served a laer ime seps. To evaluaion performance of he proposed approach, we consider he experimenal daase in [12] wih wo or hree

6 6 C.-C. Lin, P.-T. Tseng, T.-Y. Wu, D.-J. Deng communiies of mesh cliens and heir moving rajecories. Experimenal resuls show ha in he dynamic scenario, he proposed social-based PSO approach is capable of effecively decreasing he oal number of unserved mesh cliens, and increasing nework conneciviy. The organizaion of his paper is saed as follows. Secion 2 describes he social-aware WMN-dynRNP problem in deail. Secion 3 proposes a social-based PSO approach for he social-aware WMN-dynRNP problem. Secion 4 gives he experimenal design and resuls. Finally, Secion 5 gives he conclusion of his work. 2 Problem Descripion This secion describes he problem of social-aware WMN-dynRNP mahemaically. 2.1 Describing he Concerned Problem For a WMN consising of mesh rouers and mesh cliens deployed in a recangular area, consider a more pracical scenario where some of he mesh cliens may gaher and move ogeher geographically o form a communiy, so ha he WMN wih muliple communiies consiues a social nework wih a communiy srucure. Alhough a communiy srucure underlies he disribuion of mesh cliens, i canno be realized and deermined due o is complexiy and uncerainy. If he placemen of mesh rouers can be aware of he communiy srucure of mesh cliens o be adjused dynamically, he performance would be increased. Hence, his paper invesigaes he so-called social-aware WMN-dynRNP problem, in which he RNP is capable of being aware of he social communiy movemen behavior of mesh cliens o dynamically deermine heir placemen a differen imes, so as o maximize he nework conneciviy

7 Social-aware Dynamic Rouer Node Placemen in Wireless Mesh Neworks 7 and he clien coverage. Especially, he mesh rouers in he same opology subgraph componen should be able o suppor each oher o balance he service loading. Hence, he concerned problem is described as follows: Social-aware dynamic rouer node placemen in WMNs (Social-aware WMN-dynRNP): Consider a WMN deployed in a 2D recangular area wih size W H, consising of n mesh rouers and m mesh cliens. Suppose ha each mesh rouer can serve only a resriced number of mesh cliens; and mesh cliens form a communiy srucure. A each ime sep, each mobile mesh clien can arbirarily change is posiion in he deploymen area; some of he mesh cliens form a communiy and he mesh cliens of he same communiy could gaher and move ogeher. The problem is o be aware of he social communiy behavior of mesh cliens o deermine placemen of mesh rouers a each ime sep, and he objecive of his problem is o maximize boh he nework conneciviy and he clien coverage simulaneously. 2.2 Noaions This paper coninues using he noaions in [12], excep for hose used in he service capaciy consrain of each mesh rouer. All he noaions used hroughou his paper is given in Table 1. A he -h ime sep, he WMN wih n mesh rouers and m mesh cliens deployed on a 2D area of size W H can be represened as U = R C in which R = {r 1, r 2,, r n } is se of mesh rouers and C = {c 1, c 2,, c m } is se of mesh cliens. For i {1, 2,.., n}, each mesh rouer r i is associaed wih a circular radio coverage region wih radius i. Noe ha he subscrip used in U and C is because mesh cliens could swich off heir nework access a differen

8 8 C.-C. Lin, P.-T. Tseng, T.-Y. Wu, D.-J. Deng ime seps in he dynamic scenario. Table 1 Noaions used in his paper. Variable Meaning W Widh of he recangular deploymen area H Lengh of he recangular deploymen area Index of ime sep n Number of mesh rouers m Number of mesh cliens r i The i-h mesh rouer, for i {1, 2,, n} c i The i-h mesh clien, for i {1, 2,, m} R = {r 1, r 2,, r n } Se of mesh rouers C = {c 1, c 2,, c m } Se of mesh cliens a he -h ime sep U = R C Se of mesh nodes a he -h ime sep i Radius of he circular radio coverage range of mesh rouer r i Number of he mesh cliens served by mesh rouer r i a he -h ime sep i max Upper bound of i D (c i ) Posiion of mesh clien c i C on he deploymen area a he -h ime sep D (R) = {D (r 1 ),, Se of posiions of all mesh rouers on he deploymen area a he -h ime sep D (r n )} i The circle cenered a D (r i ) wih radius i E Se of he links a he -h ime sep G = (U, E ) The nework opology graph a he -h ime sep G 1 2 h G G... G There are h subgraph componens 1 2 h G, G,..., G in G ( G ) Nework conneciviy of opology graph G ( G ) Clien coverage of opology graph G X ( x, x,..., x ) Posiion of paricle k on he soluion space, for placemen a he -h ime sep k k1 k2 k(2 n) Vk vk1 vk2 vk(2 n) V max (,,..., ) Velociy of paricle k, for placemen a he -h ime sep Maximal velociy Ineria weigh o conrol influence of he velociy a he previous ieraion f ( X k ) Finess of paricle k, for placemen a he -h ime sep G,k Topology graph according o he placemen represened by X k The bes posiion found by paricle k so far, for placemen a he -h ime sep P k P * The bes posiion found by all paricles so far Si ( sk1, sk2,..., sk(2 n) ) Social-supporing vecor of paricle k a he -h ieraion, for placemen a he -h ime sep In wha follows, we esablish a opology graph based on he mesh nodes in U and he following wo ypes of links. Firs, consider he links beween mesh rouers and mesh cliens. Noe ha each mesh rouer has a radio coverage region. Differen from he previous works, his paper assumes ha each mesh rouer serves only a resriced

9 Social-aware Dynamic Rouer Node Placemen in Wireless Mesh Neworks 9 number of mesh cliens. Hence, if a mesh clien is locaed wihin he radio coverage region of some mesh rouer, and he mesh rouer does no exceed is resriced number of serving mesh cliens, hen he mesh clien can be linked o he mesh rouer. As for communicaion beween wo mesh cliens, if wo mesh cliens are linked o he same mesh rouer, hey can communicae wih each oher via he mesh rouer. On he oher hand, if wo mesh cliens are linked o wo differen mesh rouers ha belong o he same opology subgraph componen, hey can communicae wih each oher via muli-hop communicaion. Tha is, if wo mesh cliens belong o wo differen subgraph componens, or no boh of hem are linked o any mesh rouers, hey canno communicae. Addiionally, we assume a heerogeneous WMN scenario where he radio coverage region of each mesh rouer is of a differen size. Second, consider he links beween mesh rouers. If he radio coverage regions of wo mesh rouers are overlapped, he wo mesh rouers are linked and hen belong o he same opology subgraph componen. Noe ha he mesh rouers in he same opology subgraph componen can be aware of exisence of each oher, and hence, should be able o help and suppor each oher, from he viewpoin of social communiy cooperaion behavior. One of he main differences of his work from he previous works is o consider ha each mesh rouer serves only a resriced number of mesh cliens. Throughou he res of his paper, le i denoe number of he mesh cliens served by mesh rouer r i a he -h ime sep, and max denoe is upper bound, i.e., i max. Addiionally, o be consisen wih he pracice, i is assumed ha each mesh rouer can only be aware of wheher i. max 2.3 Modeling he Social-aware WMN-dynRNP Problem

10 10 C.-C. Lin, P.-T. Tseng, T.-Y. Wu, D.-J. Deng Afer defining noaions and definiions of mesh rouers and mesh cliens, his subsecion describes he dynamic scenario of he social-aware WMN-dynRNP problem, in which mesh rouers and mesh cliens have mobiliy; mesh cliens can change heir posiions a differen imes; some of he mesh cliens belong o a communiy, and he mesh cliens wihin he same communiy could gaher and move ogeher. Afer mesh cliens change heir posiions, he placemen of mesh rouers in he social-aware WMN-dynRNP problem aims o be aware of he social communiy behavior of mesh cliens o be adjused periodically. Suppose ha he period o deermine placemen of mesh rouers is beween wo ime seps. Hence, a each ime sep, mesh cliens may form a differen communiy srucure, and he placemen of mesh rouers should base on he communiy srucure o be adjused o maximize he nework performance. The dynamic scenario can be described as follows. A he -h ime sep, he posiion of each mesh clien c i C on he 2D deploymen area is denoed by D (c i ) R 2. Based on he posiion disribuion of mesh cliens a each ime sep, posiions of mesh rouers on he deploymen area are deermined and denoed by D (R) = {D (r 1 ), D (r 2 ),, D (r n )}. Noe ha he circle cenered a D (r i ) wih radius i is denoed by i. Wih he posiions of mesh rouers and mesh cliens, we can esablish a opology graph G = (U, E ), in which U = R C ; E is se of he links wih wo following ypes: Firs, for each pair of mesh rouers r i, r j R, if i j, hen (r i, r j ) E ; second, for each i j mesh clien c i C and each mesh rouer r j R, if D ( c ), hen (c i, r j ) E. Noe ha he nework opology graph G may no be conneced, i.e., G includes muliple subgraph componens. Suppose ha h subgraph componens 1 2 h,,..., G G G exis in G, so ha 1 2 h... G G G G where i, j {1,

11 Social-aware Dynamic Rouer Node Placemen in Wireless Mesh Neworks 11 2,, h}, i j, G i j G. To increase he nework connecively of he WMN opology, size of he greaes subgraph componen should be maximized so ha i can serve as he backbone of he nework o connec all mesh cliens. However, a large greaes subgraph componen size does no imply ha i serves a large number of mesh cliens, so we should also consider o serve mesh cliens as many as possible. The social-aware WMN-RNP problem considers o maximize he following wo erms: nework conneciviy and clien coverage, as described in [12]. To make he placemen of mesh rouers consiue a backbone for he whole nework, he nework conneciviy a he -h ime sep is defined as he size of he greaes subgraph componen among he h componens 1 2 h,,..., G G G in G, as expressed as follows: ( G ) max { G }. i {1,..., h} i If (G ) is larger, hen more mesh nodes are conneced. Specifically, if (G ) = m + n, hen i implies ha all mesh nodes are conneced. If only he nework conneciviy is concerned, he mesh cliens covered by oher subgraph componens may be negleced. Hence, he second erm of our problem objecive is o maximize he clien coverage a he -h ime sep expressed as follows: ( G ) d ( c ), i i {1,..., m} where d (c i ) is defined as follows: 1, if mesh clien ci a he -h ime sep is served; d( ci) 0, oherwise.

12 12 C.-C. Lin, P.-T. Tseng, T.-Y. Wu, D.-J. Deng 3 The Proposed Social-based PSO Approach for he Social-aware WMN-dynRNP Problem This secion firs gives he overview of he proposed social-based PSO approach o he social-aware WMN-dynRNP problem, and hen he main componens of he approach. 3.1 Algorihm of he Social-based PSO Approach Paricle swarm opimizaion (PSO) [27], [28] is a meahurisic algorihm ha ieraively searches he global soluion by imiaing a number of paricles (agens) ha search an opimal soluion (in erms of finess values) on he soluion landscape space. Each paricle has is own posiion (a candidae soluion on he soluion space) a each ieraion, and flies o a new posiion a a velociy a he nex ieraion. The velociy is updaed a each ieraion according o he bes posiion found by each paricle so far (i.e., he individual bes experience of each paricle) as well as he bes posiion found by all paricles so far (i.e., he global bes experience). Afer a number of ieraions, he final soluion is generaed if almos all paricles arrive a he same posiion (soluion). The proposed social-based PSO approach o he social-aware WMN-dynRNP problem is based on our previous approach o he WMN-dynRNP problem in [12]. The main difference of he proposed approach from [12] is o include a social-supporing vecor in he velociy updaing formula which makes low-loading mesh rouers end o suppor he heavy-loading mesh rouers in he same opology subgraph componen. The algorihm of he proposed social-based PSO approach o deermine he placemen of mesh rouers a he -h ime sep is given as follows (see also he flowchar of he algorihm in Figure 2):

13 Social-aware Dynamic Rouer Node Placemen in Wireless Mesh Neworks 13 1) If ime sep index = 0, hen le each paricle k s iniial posiion 0 X k be a random posiion (soluion) wihin he soluion landscape space, and each paricle k s iniial velociy 0 V k be a random velociy wihin he feasible range; else (i.e., > 0), le each paricle k s posiion X k and velociy V k be heir respecive values a he previous ieraion (i.e., 1 X k and k 1 V, respecively). Le he bes posiion P k found by each paricle k so far be equal o X k. k 2) Evaluae each paricle k s finess value f ( X ). According o hose finess values, find he posiion wih he bes finess value, and le i be he bes posiion found by all paricles so far, denoed by P *. 3) Repea he following seps unil he maximal number of ieraions is reached. a) Use each paricle k s social-supporing vecor S k o updae is velociy V k and posiion X k according o Equaions (1) and (2), respecively. Noe ha he wo vecors mus saisfy heir respecive range consrains. k b) Evaluae each paricle k s finess value f ( X ). According o hose new finess values, updae he bes posiions found by each paricle k and all paricles so far, i.e., P k and P *, respecively. c) Updae each paricle s social-supporing vecor S k. The above algorihm is explained as follows. Noe ha each paricle s posiion represens a candidae soluion of he concerned problem, i.e., he placemen of mesh rouers on he deploymen area. A Sep 1) of he algorihm, since he concerned problem is o deermine he placemen of mesh rouers a differen imes, wo cases for he iniial posiion of each paricle are considered according o he curren ime sep. If he iniial ime sep (i.e., = 0) is con-

14 14 C.-C. Lin, P.-T. Tseng, T.-Y. Wu, D.-J. Deng cerned, hen he iniial soluion and velociy of each paricle are se randomly wihin he resriced ranges; else (i.e., he posiions and velociies a he previous ime sep exis), he wo vecors are se o inheri heir respecive values a he previous ime sep. Begin rue Time sep = 0? false Randomize each paricle k s iniial posiion and velociies For each paricle k, ; Iniialize oher parameers Updae each paricle k s velociy and posiion Evaluae each paricle k s finess value Updae each paricle k s previous bes posiion Updae he global bes posiion P * Increase ieraion number Compue each paricle k s social-supporing vecor The maximal ieraion number is achieved? false loop unil he maximal number of ieraions is achieved. In he loop, Sep a) updaes each paricle s posiion and verue End Fig. 2. Flowchar of he proposed social-aware PSO approach. A Sep 2), he finess value is used o evaluae he performance of each paricle according o is posiion (i.e., placemen of mesh rouers), and hen he bes posiion found by all paricles so far is recorded. Nex, Sep 3) repeas a

15 Social-aware Dynamic Rouer Node Placemen in Wireless Mesh Neworks 15 lociy according o Equaions (1) and (2), which will be explained laer. Noe ha Equaion (1) includes a social-supporing vecor, which is he main difference from he previous work. Nex Seps b) and c) updae each paricle s bes posiions respecively found by is own, all paricles, and is social-supporing vecor. 3.2 Main Componens of he Social-based PSO Approach Based on he social-based PSO algorihm deailed in he previous subsecion, his subsecion gives he main componens of he algorihm Soluion Represenaion The soluion represenaion in his work is he same as [12]. Posiion of each paricle represens a placemen of mesh rouers (i.e., (x, y)-coordinaes of n mesh rouers) on a 2D deploymen area of size W H, whose boom-lef corner is placed a he origin of he xy plane. Hence, for each paricle k, posiion of paricle k a he -h ime sep is encoded as Xk xk1 xk2 xk(2 n) (,,..., ), in which ( xk(2i 1), xk(2 i) ) is he (x, y)-coordinae of mesh rouer r i, i {1, 2,, n}; 0 xk(2i 1) W; 0 x k(2 i) H. Le P and P * denoe he bes posiions found of each paricle k and all paricles k so far, respecively. Also le f(x) be he finess value of posiion X. Hence, f ( X ), f ( P ), and f(p * ) are he finess k k values of X k, P k, and P *, respecively Updaing he Paricle Velociy and Posiion

16 16 C.-C. Lin, P.-T. Tseng, T.-Y. Wu, D.-J. Deng A each ieraion, each paricle k a he -h ime sep moves is posiion X a a velociy Vk ( vk1, vk2,..., vk(2 n) ) k wih V max v i V max, i {1, 2,, 2n}, where V max max{w, H}. Before movemen, velociy V i is updaed according o he following formula: V V w e P X w e P X w e S, (1) * k k 1 1 ( k k) 2 2 ( k) 3 3 k where V k denoes he updaed velociy wih four sources: he original velociy V k, he direcion oward he bes posiion P k found by paricle k so far, he direcion oward he bes posiion P * found by all paricles so far, and he social-supporing vecor S k of paricle k, which will be explained laer; parameer is he ineria weigh o conrol he influence of V k ; parameers w 1, w 2, and w 3 are used o conrol he scales of he laer hree erms in his formula; e 1, e 2, and e 3 are hree random floaing numbers beween 0 and 1. Noe ha was proposed firs in [29], and in general, i decreases linearly from 0.9 o 0.4 as number of ieraions grows. Then, he work in [30] proposed a random ineria weigh. Since he dynamical posiions of mesh cliens canno be prediced in he concerned problem, he random ineria coefficien is more suiable for our approach. Afer updaing he velociy V k, he new posiion sep can be obained by he following formula: X k of paricle k a he -h ime k k k X X V. (2) Finess Evaluaion Finess value is used o evaluae performance of a paricle s posiion, and he PSO approach aims o ieraively improve he finess value of each paricle. The finess evaluaion in his work is he same wih [12], which aims o simulaneously maximize he nework conneciviy and he clien coverage as follows:

17 Social-aware Dynamic Rouer Node Placemen in Wireless Mesh Neworks 17 ( Gk, ) ( Gk, ) f( Xk ) (1 ) n m m k where f ( X ) is he finess value of he posiion X k of paricle k a he -h ime sep; G,k is he opology graph according o he placemen of mesh rouers represened by k X ; ( G k, ) and ( G k, ) are he nework conneciviy and he clien coverage based on G k,, respecively; he denominaor of each erm is used for normalizaion; is a floaing number beween 0 and 1, which is used for balancing he wo erms. Noe ha he previous works in [7], [8], [9], [10] were wo-sage mehods for saic RNP problems, which maximize he firs erm and hen he second erm. The concerned problem focuses on a dynamic scenario, which is generally resolved by simulaneously maximizing he wo erms [11], [12] Social-Supporing Vecor In he social-aware WMN-dynRNP problem, each mesh rouer serves only a resriced number of mesh cliens. Recall ha i denoes he number of mesh cliens served by mesh rouer r i a he -h ime sep, and max denoes he maximal number of mesh cliens ha each mesh rouer can serve. Hence, we have i. max Given a placemen of mesh rouers, consider he case where a lo of mesh cliens are locaed densely wihin he radio coverage region of a mesh rouer (i.e., one dense communiy may exis in his region), and he oal number of hose mesh cliens is greaer han max. In his case, he mesh rouer is aware ha a communiy of mesh cliens exiss in he neighborhood of he coverage region, bu has no enough capaciy o serve all of hose mesh cliens. To make use of he awareness, he proposed social-based PSO approach includes a social-supporing vecor S i in he velociy updaing formula of V i in Equaion (1), which makes he mesh rouers in he same opology subgraph componen

18 18 C.-C. Lin, P.-T. Tseng, T.-Y. Wu, D.-J. Deng end o suppor he mesh rouer ha is aware of a dense communiy. Noe ha he reason why we only make use of he mesh rouers in he same opology subgraph componen is ha he oher componens canno communicae wih he concerned componen and hence canno suppor i. Le Si sk1 sk2 sk(2 n) (,,..., ) where ( sk(2i 1), sk(2 i) ) is he movemen of mesh rouer r i for supporing oher mesh rouers for each i {1, 2,, n}. The algorihm of calculaing S is saed as follows: k 1) Consider each mesh rouer, say r i, ha does no serve any mesh clien. 2) Arbirarily selec a mesh rouer r j ha serves no less han max mesh cliens in he same opology subgraph componen wih mesh rouer r i (i.e., i is aware ha a communiy may exis in is neighborhood). 3) The enries ( sk(2i 1), sk(2 i) ) for mesh rouer r i in he social-supporing vecor S k are calculaed as follows: k(2i 1) k(2 i) k(2 j 1) k(2 j) k(2i 1) k(2 i) ( s, s ) ( x, x ) ( x, x ). Tha is, mesh rouer r i will end o move closer o he posiion of mesh rouer r j. 4) Afer considering all he mesh rouers a Sep 1), he final social-supporing vecor S k is obained. Noe ha each pair (0, 0) in his vecor means ha is corresponding mesh rouer does no suppor any mesh rouer. Noe ha in Sep 1) of he above algorihm, if here is no mesh rouer ha does no serve any mesh clien, hen no social suppor is generaed from he remaining seps of he algorihm. However, i is hard o decide wheher o move some mesh rouer ha has served some number of mesh cliens, because hose served mesh cliens may lose connecion of he mesh rouer. Hence, i would be of ineres o design a cos funcion ha evaluaes wheher o move a mesh rouer ha has served some number of mesh cliens.

19 Social-aware Dynamic Rouer Node Placemen in Wireless Mesh Neworks 19 To clarify he above algorihm, a simple numerical example is given as follows. Consider he opology graph G a he -h ime sep as illusraed in Figure 3(a), in which here are 6 mesh rouers r 1, r 2,, r 6 and 12 mesh cliens c 1, c 2,, c 12 ; he links beween mesh rouers and mesh cliens are marked by red doed line segmens; he links beween mesh rouers are marked by green dashed line segmens. Suppose ha each mesh rouer serves a mos hree mesh cliens (i.e., max = 3). Hence, mesh rouers r 4 and r 6 in Figure 3(a) serve no less han 3 mesh cliens, i.e., each of hem is aware ha a communiy may exis in is neighborhood. (a) (b) Fig. 3. A numerical example for illusraing he social-supporing vecor. Sep 1) of he above algorihm finds he mesh rouers ha do no serve any mesh cliens, i.e., r 2, r 3, and r 5. Since here is no heavy-loading mesh rouer in he opology subgraph componen ha mesh rouer r 2 belong o, i suffices o consider mesh rouers r 3 and r 5. Suppose ha Sep 2) of he above algorihm selecs mesh rouers r 6 and r 4 respecively for mesh rouers r 3 and r 5. Le (x i, y i ) denoe he (x, y)-coordinae of mesh rouer r i for each i {1, 2,, 6}. Hence, Sep 3) of he above algorihm calculaes he enries for mesh r 3 and r 5 in he social-supporing vecor as

20 20 C.-C. Lin, P.-T. Tseng, T.-Y. Wu, D.-J. Deng (x 6 x 3, y 6 y 3 ) and (x 4 x 5, y 4 y 5 ), respecively. Hence, Sep 4) of he above algorihm obains he final social-supporing vecor as follows: S k = (0, 0, 0, 0, x 6 x 3, y 6 y 3, 0, 0, x 4 x 5, y 4 y 5, 0, 0). 3.3 Complexiy analysis of he proposed algorihm In order o analyze he space and ime complexiy of he proposed algorihm, some noaions are concerned as follows. Recall ha n and m denoe numbers of mesh rouers and mesh cliens, respecively. Le be number of paricles applied in he social-based PSO algorihm, and be number of ieraions of he main loop of he algorihm. Consider o analyze he space complexiy of he proposed social-based PSO algorihm. The proposed algorihm works on paricles. Each paricle keeps a posiion vecor X, a velociy vecor k V k, is previous bes posiions P, k and is social-supporing vecor S i ; and he whole paricle swarm keeps he global bes soluion P *. Also, each vecor is of lengh 2n. Hence, he space complexiy of recording all paricles daa srucures is O( (4 2n ) + 2 n) = O( n). To evaluae finess of each paricle, he graph opology of each paricle (Subsecion 2.3) is recorded for convenience of compuaion. Each graph opology consiss of links beween mesh rouers and mesh cliens (sored in O(m n) space) and links beween mesh rouers (sored in O(n 2 )). Hence, he oal space complexiy of he algorihm is O( n + (m n + n 2 )) = O( (m + n) n). Consider o analyze he ime complexiy of he main algorihm (Subsecion 3.1). Iniializaion of all parameers in Sep 1) is done in ime O( n) because lengh of each parameer vecor is a mos 2n and some parameers are se a mos imes for all paricles. A Sep 2), o evaluae finess of each paricle, a opology graph corresponded o he

21 Social-aware Dynamic Rouer Node Placemen in Wireless Mesh Neworks 21 posiion of each paricle is esablished in O((m + n) n) ime as analyzed in he above space complexiy analysis. Since nework conneciviy ( G k, ) and clien coverage ( G k, ) can be compued linearly in side of he opology (Subsecion 2.3), he finess value of a paricle can be compued in O((m + n) n) ime. Therefore, Sep 2) is done in O( (m + n) n) ime. Before analyzing Sep 3) of he algorihm in Subsecion 2.3, consider o analyze he algorihm of calculaing a social-based supporing vecor in Subsubsecion Sep 1) considers each mesh rouer r i, and hence, his algorihm has n ieraions. For each ieraion, Sep 2) finds he neighboring mesh rouer r j in O(n) ime, because he daa srucure of he graph opology has recorded he adjacency relaionship of links during esablishing opology. Sep 3) is done in O(1) ime. Sep 4) jus oupus he final resul. Hence, he oal ime complexiy of he algorihm of calculaing a social-based supporing vecor in Subsubsecion is O(n 2 ). Now consider Sep 3) of he main algorihm in Subsecion 2.3. Subsep a) updaes all paricles velociies and posiions in O( n) ime. Subsep b) is done in O( (m + n) n) ime as he analysis for Sep 2). Since a social supporing vecor is calculaed in O(n 2 ) ime, Subsep c) calculaed all paricles social supporing vecors in O( n 2 ) ime. As a resul, Sep 3) of he main algorihm considers ieraions, so is done in O( ( n + (m + n) n + n 2 )) = O( (m + n) n) ime. Wih he above ime complexiy analysis, he proposed social-based PSO algorihm is compued in O( (m + n) n) ime.

22 22 C.-C. Lin, P.-T. Tseng, T.-Y. Wu, D.-J. Deng 4 Experimenal Design and Resuls Performance of he proposed social-based PSO approach o he social-aware WMN-dynRNP problem is evaluaed in his secion, and compared wih he previous PSO approach in [12]. This secion firs describes he experimenal daa and he experimenal design on dynamic scenarios, and hen gives he experimenal resuls under various scenarios. 4.1 Experimenal Daa We coninue using he experimenal daases in [12], including he following hree differen-scale nework cases, each of which has 10 insances: Small-scale case: Consider a deploymen area (i.e., W = H = 32). The problem is o place 16 mesh rouers wih circular radio coverage regions wih radii ~ U(3, 6) o serve 48 mesh cliens. Middle-scale case: Consider a deploymen area. The problem is o place 32 mesh rouers wih circular radio coverage regions wih radii ~ U (4 2 2,8 2 2) o serve 96 mesh cliens. Large-scale case: Consider a deploymen area. The problem is o place 64 mesh rouers wih circular radio coverage regions wih radii ~ U(7, 14) o serve 192 mesh cliens. The simulaion is implemened in C++ programming language, and he parameer seings are given in Table 2, in which mos of he parameer values coninue using hose in [12]. Noe ha he seing of he value has been discussed in our previous work in [12], which was decided by no only los of experimenal rials bu also visualizaion of he WMN configuraions (see also Fig. 4 in [12]). The work

23 Social-aware Dynamic Rouer Node Placemen in Wireless Mesh Neworks 23 in [12] found ha a oo large value leads o a deploymen where mesh rouers are oo dense in some regions so ha number of he served cliens is small; while a oo small value canno lead o a large opology componen. Hence, he value is se o 0.3 finally. Also noe ha number of he ieraions beween wo ime seps in he dynamic scenario is 30, i.e., mesh cliens change a each ime sep (a each 30 ieraions), and he placemen of mesh rouers is adjused o adap o his change. Table 2 Parameer seing. Parameer Value Number of ieraions in he saic scenario 90 Number of ieraions beween wo ime seps in he dynamic scenario 30 The oal number of ieraions in he dynamic scenario for small-scale nework case The oal number of ieraions in he dynamic scenario for middle-scale nework case The oal number of ieraions in he dynamic scenario for large-scale nework case The farhermos disance o which a mesh clien can move in he dynamic scenario 3 The maximal number of mesh cliens ha a mesh rouer can serve (i.e., max ) 3 The weighing parameer ha conrols he wo erms in he objecive 0.3 Parameer w 1 in Equaion (1) 2 Parameer w 2 in Equaion (1) 2 Parameer w 3 in Equaion (1) 1 The maximal velociy V max of each paricle 0.1 W The oal number of paricles Experimenal Design of Dynamic Scenarios for Social Communiies To es wheher he proposed approach can cope wih he dynamic behavior of social communiies of mesh cliens, we design hree dynamic scenarios wih social communiy behavior in he experimens: simplified dynamic scenario, generalized saic scenario, and generalized dynamic scenario, in which he erm simplified means ha each mesh clien belongs o a communiy; he erm generalized means ha excep for hose mesh cliens ha belong o communiies, he ohers are scaered on he deploymen area; he erm saic means ha all mesh cliens are saic, while he

24 24 C.-C. Lin, P.-T. Tseng, T.-Y. Wu, D.-J. Deng erm dynamic means ha each mesh clien could move is posiion or swich is nework access as ime goes. For simpliciy, we only consider he hree scenarios, bu hey suffice o analyze performance of he proposed approach. Addiionally, wo or hree communiies are considered in each scenario. Hence, considering 3 nework scales (i.e., small, middle, large), 2 possible communiy numbers (i.e., 2 or 3), and 3 scenarios (i.e., simplified dynamic, generalized saic, and generalized dynamic scenarios), here are = 18 combinaions of experimenal seings in oal. The number of mesh cliens in each communiy in differen-scale nework cases is given in Table 3. Table 3 The number of mesh cliens in each communiy in differen-scale nework cases. Small-scale nework case Num. of Communiies 2 2 (simplified) 3 3 (simplified) Num. of mesh cliens in Communiy # Num. of mesh cliens in Communiy # Num. of mesh cliens in Communiy # Oher scaered mesh cliens Toal mesh cliens Middle-scale nework case Num. of Communiies 2 2 (simplified) 3 3 (simplified) Num. of mesh cliens in Communiy # Num. of mesh cliens in Communiy # Num. of mesh cliens in Communiy # Oher scaered mesh cliens Toal mesh cliens Large-scale nework case Num. of Communiies 2 2 (simplified) 3 3 (simplified) Num. of mesh cliens in Communiy # Num. of mesh cliens in Communiy # Num. of mesh cliens in Communiy # Oher scaered mesh cliens Toal mesh cliens In wha follows, he dynamic design of communiies is explained in deail. Consider wo ypes of mesh cliens: he mesh clien of ype 1 mus belong o some communiy and hence move ogeher wih he communiy; he mesh clien of ype 2 does no belong o any communiy and hence can move arbirarily on is own. Hence, he simplified scenario is defined o include only he firs ype of mesh cliens, while he generalized scenario is defined o include

25 Social-aware Dynamic Rouer Node Placemen in Wireless Mesh Neworks 25 boh of he wo ypes of mesh cliens. For example, a generalized scenario is illusraed in Figure 4, which includes wo communiies and some scaered mesh cliens on he deploymen area. Nex, consider he communiy movemen in he dynamic scenario. Take Figure 4 for an example in he generalized dynamic scenario wih wo communiies, in which he moving rajecory of each communiy is shown. Fig. 4. The moving rajecories of wo communiies. Fig. 5. The moving rajecories of hree communiies. Our dynamic design for his example includes four social communiy behaviors: firs, he wo communiies move o gaher ogeher and hence are merged ino a single super communiy (i.e., he rajecories shown by doed

26 26 C.-C. Lin, P.-T. Tseng, T.-Y. Wu, D.-J. Deng curves in Figure 4); hen, he super communiy moves ogeher for a while (i.e., he rajecories shown by solid curves in Figure 4); hen, he super communiy is divided ino he original wo communiies ha keep moving on heir own (i.e., he rajecories shown by dashed curves in Figure 4); finally, all he mesh cliens in he wo respecive communiies are disbanded (i.e., hey do so a he arrow marks in Figure 4). Those social communiy behaviors are obained by imiaing he human behaviors in real world. Figure 5 is an example in he generalized dynamic scenario wih hree communiies, in which he hird communiy moves from he upper-righ corner o he lower-lef corner and finally is disbanded. Alhough our dynamic design for communiy movemen is arificial, some noable works on social neworks (e.g., see [31]) also applied arificial dynamics in heir dynamic design. In fac, invesigaing real-world dynamic races in he dynamic design suffices o form anoher full paper (including user survey and behavior validaion) and is complicaed. I is ou of he scope of his paper. Hence, a fuure line of he research is o invesigae wheher he proposed approach can handle real-world dynamic races in he dynamic design in he fuure work. 4.3 Experimenal Resuls in he Simplified Dynamic Scenario The purpose o conduc he experimens in he simplified dynamic scenario (i.e., each mesh clien belongs o a communiy) is o obain he basic es for wheher our proposed social-based PSO approach can make more efficien and effecive adjusmen for such a communiy srucure han he previous PSO approach in [12]. Noe ha here is no previous work ha is direcly relaed o his work excep for [12], and hence, only he work in [12] is compared experimenally wih his work. We conduc he experimens of hree differen-scale daases in he simplified dynamic

27 Social-aware Dynamic Rouer Node Placemen in Wireless Mesh Neworks 27 scenario wih wo or hree communiies by using our proposed approach and he previous approach in [12]. Noe ha each daase conains 10 insances, and each saisical value is obained by averaging 20 imes of running he experimens on he 10 insances. Afer comparing all experimenal saisics (he bes finess value, he average finess value, he wors finess value, and he sandard deviaion of finess values), our proposed approach always performs beer han he previous approach. Comparisons of he bes, average, and wors finess values using our and he previous approaches in he simplified dynamic scenario are given in Figure 6(a) (c), respecively, in which he horizonal axis liss all differen-scale cases and wo possible communiy numbers (denoed by C). From Figure 6, our proposed approach performs beer han he previous approach in erms of he hree saisics of finess values in all cases small (C = 2) small (C = 3) middle (C = 2) middle (C = 3) large (C = 2) large (C = 3) small (C = 2) small (C = 3) middle (C = 2) middle (C = 3) large (C = 2) large (C = 3) small (C = 2) small (C = 3) middle (C = 2) middle (C = 3) large (C = 2) large (C = 3) previous our previous our previous our (a) Bes finess (b) Average finess (c) Wors finess Fig. 6. Comparison of he finess values using our and he previous approaches in he simplified dynamic scenario. To analyze he reason why our proposed approach performs beer in he simplified dynamic scenario, we find ha he previous approach in [12] does no uilize he social relaionship of mesh rouers in he same opology sub-

28 28 C.-C. Lin, P.-T. Tseng, T.-Y. Wu, D.-J. Deng graph componen, and hence requires more ieraions o adjus is placemen of mesh rouers o adap o he communiy srucure of mesh cliens; furhermore, before finishing he adjusmen o adap o he communiy srucure, some communiies may move o heir nex posiions a he nex ime sep in he dynamic scenario, and hence, he performance of he previous approach becomes worse. On he oher hand, our proposed new social-based approach includes a social-supporing vecor o make effecive adjusmen o adap o he communiy srucure. 4.4 Experimenal Resuls in he Generalized Saic Scenario The experimenal resuls in he previous subsecion have shown ha our proposed approach performs beer in he simplified dynamic scenario. However, in real world, aside from communiies, scaered mesh cliens exis on he deploymen area (i.e., hey do no belong o any communiy). Hence, his paper furher analyzes he experimenal resuls in a generalized scenario. Noe ha alhough his paper focuses on he dynamic scenario, i is of ineres in his subsecion o firs analyze wheher our proposed approach also performs beer in he generalized saic scenario. The comparisons of he bes, average, and wors finess values using our and he previous approaches in he generalized saic scenario are given in Figure 7(a) (c), respecively. From Figure 7, he difference of all finess saisics using our and he previous approaches looks almos no differen. Hence, he independen-sample -es is conduced o es wheher performance of he wo approach has remarkable difference. In he es, we selec he experimenal seing wih he mos represenaive average finess value and he mos complex daase (i.e., he large-scale nework case and hree communiies). Under he 95% confidence inerval, he p-value of he -es is > Tha is, he average finess values using he wo approaches

29 Social-aware Dynamic Rouer Node Placemen in Wireless Mesh Neworks 29 do no have remarkable difference. As a resul, we conclude ha our social-based PSO approach mainly focuses on he dynamic scenario, and hence, he experimenal resuls in his subsecion confirm ha even if scaered mesh cliens exis on he deploymen area, our approach sill keeps as good performance as he original PSO approach, so ha we can furher analyze he experimenal resuls in he generalized dynamic scenario small (C = 2) small (C = 3) middle (C = 2) middle (C = 3) large (C = 2) large (C = 3) small (C = 2) small (C = 3) middle (C = 2) middle (C = 3) large (C = 2) large (C = 3) small (C = 2) small (C = 3) middle (C = 2) middle (C = 3) large (C = 2) large (C = 3) previous our previous our previous our (a) Bes finess (b) Average finess (c) Wors finess Fig. 7. Comparison of he finess values using our and he previous approaches in he generalized saic scenario. 4.5 Experimenal Resuls in he Generalized Dynamic Scenario From he experimenal resuls in he wo previous subsecions, we have known ha our approach performs beer in he simplified dynamic scenario, and performs similar o he previous approach in he generalized saic scenario. This subsecion furher analyzes he performance in he generalized dynamic scenario. Comparisons of he bes, average, and wors finess values using our and he previous approaches in he generalized dynamic scenario are given in Figure 8(a) (c), respecively. From Figure 8, i can be observed ha our pro-

30 30 C.-C. Lin, P.-T. Tseng, T.-Y. Wu, D.-J. Deng posed approach performs beer han he previous approach in erms of all finess saisics. To analyze his, we find ha since each of he majoriy of he mesh cliens in he generalized dynamic scenario belong o a cerain communiy, mesh cliens can suppor each oher by using our social-based approach, and hence an efficien and effecive readjusmen can be achieved small (C = 2) small (C = 3) middle (C = 2) middle (C = 3) large (C = 2) large (C = 3) previous our small (C = 2) small (C = 3) middle (C = 2) middle (C = 3) large (C = 2) large (C = 3) previous our small (C = 2) small (C = 3) middle (C = 2) middle (C = 3) large (C = 2) large (C = 3) previous our (a) Bes finess (b) Average finess (c) Wors finess Fig. 8. Comparison of he finess values using our and he previous approaches in he generalized dynamic scenario. 5 Conclusion and Fuure Work This paper focuses o include he social-awareness of mesh rouers o he placemen of dynamic rouer node placemen in WMNs (WMN-dynRNP), in which mesh cliens may belong o a communiy, and hence move and gaher ogeher; addiionally, each mesh rouer can serve only a resriced number of mesh cliens. To cope wih his problem, his paper has proposed a social-based PSO approach, which includes a social-supporing vecor in he formula of updaing he velociy of each paricle. This vecor makes low-loading mesh rouers end o suppor he heavy-loading mesh rouers in he same opology subgraph componen, and hence, he mesh cliens wihin he radio coverage re-

31 Social-aware Dynamic Rouer Node Placemen in Wireless Mesh Neworks 31 gions of hose heavy-loading mesh rouers may have higher chance o be served by oher mesh rouers. The experimenal resuls are compared wih our previous approach o he basic WMN-dynRNP problem in [12]. Firs, in he simplified dynamic scenario (in which each mesh clien belongs o a communiy, i.e., here is no scaered mesh cliens), our proposed approach obviously performs beer han he previous approach o make effecive adjusmen o adap he dynamic change of communiies. Nex, we consider he generalized saic scenario in which scaered mesh cliens are added, and we find ha our approach performs no significanly differen from he previous approach, bu our approach sill can ensure o keep he soluion qualiy. Las, he experimenal resuls in he generalized dynamic scenario show ha our proposed social-based approach can perform beer o adjus he mesh rouer placemen according o he social communiy behavior of mesh cliens, under differen problem scales. In he fuure work, more exension on he social behaviors of mesh cliens could be made, and he daa in a real-world deploymen area can be applied. Especially, i is of ineres o invesigae wheher he proposed approach can handle real races of communiies in he dynamic design. Addiionally, deailed parameer analysis of he proposed algorihm would be also ineresing. For he soluion solvabiliy, a cos funcion may be considered during he process of calculaing he social-supporing vecor, so ha mesh rouers could move o he direcion wih he mos benefi o suppor he oher mesh rouers so as o achieve beer soluions. Acknowledgemens The auhors hank he anonymous referees for commens ha improved he conen as well as he presenaion of his paper. This work has been suppored in par by MOST E MY2 and NSC