Improving the Connectivity of Heterogeneous Multi-Hop Wireless Networks

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1 Improving the Connectivity of Heterogeneous Multi-Hop Wireless Networks Te-Hoon Kim, Dvid Tipper, nd Prshnt Krishnmurthy Grdute Networking nd Telecommunictions Progrm University of Pittsburgh, Pittsburgh PA, USA Emil: tk11@pitt.edu, {dtipper, prshnt}@sis.pitt.edu Abstrct Heterogeneous conditions cn occur in multi-hop wireless networks due to vriety of fctors such s vritions in trnsmission power nd signl propgtion environments. Directed links cn occur when the environment nd/or the nodes re heterogeneous. In this pper, we exmine the network connectivity for heterogeneous multi-hop wireless networks nd propose n lgorithm to identify the connectivity of the network. We follow this with numericl study of the connectivity in rndom topologies. Lstly, we propose two schemes for constructing dditionl links to enhnce the connectivity of the network. Our proposed schemes identify the links to be improved or creted vi cluster bsed pproch. Index Terms Connectivity, heterogeneous multi-hop wireless networks I. INTRODUCTION Multi-hop wireless networks re expected to become n importnt prt of the communictions lndscpe. Exmples include wireless mesh networks (WMNs) [1], vehiculr d-hoc networks (VANETs) [2], nd mobile d-hoc networks (MANETs) [3]. In multi-hop wireless networks, the nodes must cooperte to dynmiclly estblish routes using wireless links nd routes my involve multiple hops with ech node cting s router. In mny multi-hop network scenrios the nodes cn move rbitrrily or the interference cn chnge dynmiclly resulting in topology chnges. Multi-hop wireless networks lso inherit the trditionl problems of wireless communictions, which when combined with mobility nd lck of infrstructure mkes their design nd development chllenging [1-3]. A bsic problem in mny multi-hop wireless networks is mintining connectivity. A network is connected if ll nodes hve communiction pth to ech other. Similrly, network is k-connected if there re k-disjoint pths between every pir of nodes. Mintining connectivity is difficult due to the unstructured nture of the topology nd the occurrence of link nd node filures due to interference, mobility, rdio chnnel effects nd bttery life [1-3]. Mny reserchers hve studied multi-hop wireless network connectivity determining conditions under which connectivity [3, 8] nd k-connectivity [9-11] cn be inferred probbilisticlly or ssured symptoticlly. The focus hs lrgely been on wht combintion of node density nd power rnge re required to provide k-node connectivity in specific deployment scenrio for homogenous network. A mjor wekness of this work is the ssumption of homogeneous () Different Tx power levels (b) Non-uniform Tx rnge Fig. 1. Directionl links in heterogeneous wireless networks network context where nodes hve identicl properties nd inhbit uniform environment (e.g., identicl trnsmission power, bttery life, rdio propgtion rnges, ntenns, etc.). Mesurement studies [12] hve shown tht mny of the ssumptions in the homogeneous context re inccurte. In prticulr it ws noted tht rel networks cn hve directionl links. For exmple, if ech node hs different trnsmission power, then their trnsmission rnge differs nd directionl link cn result s shown in Figure 1(). Similrly, in Figure 1(b) directionl link results from nodes hving non-identicl signl propgtion due to differences in the locl environment (e.g., trees, buildings, etc.). In this pper, we look t how one cn develop techniques to improve the connectivity of sprse heterogeneous multi-hop wireless networks without incresing the node density. Our pproch is to determine the topologicl connectivity criticl points tht need to be improved to ttin/mintin t lest 1-connectivity. We propose novel lgorithm for determining the connectivity bsed on results from lgebric grph theory. Using the criticl points identified by our connectivity lgorithm, we propose two techniques to improve the connectivity of the network by djusting the trnsmission power of nodes round criticl point in order to crete dditionl links in the network. The rest of the pper is orgnized s follows. In Section II, we propose n lgorithm to determine the connectivity of heterogeneous networks. Numericl results utilizing the proposed lgorithm to study the effects of network density on the connectivity re given. Then, we propose two network link modifiction schemes in Section III to improve the network connectivity without chnging the node density. Simultion results illustrting the effectiveness nd trdeoffs of the proposed connectivity improvement schemes re lso given. Lstly, we present our conclusions in Section IV.

2 A C E G B D F H () 1-Connected (b) Disconnected Fig. 2. Smple 8 node heterogeneous network topologies () Adjusted 1-Connected (b) Adjusted Disconnected Fig. 3. Adjusted network topologies corresponding to Fig. 2 II. HETEROGENEOUS NETWORK CONNECTIVITY A distinguishing chrcteristic of homogeneous networks is tht the set of multi-hop pths between pir of nodes re the sme in ech direction, while this my not be the cse in heterogeneous network. For exmple, in the network of Figure 2 (), the pth from node A to H is A C D F H wheres the pth from H to A is H G E C D B A (i.e., PATH A H PATH H A ). Another effect of directed links in the topology is tht communictions my be one wy. For exmple in the network of Figure 2 (b), nodes A, B, C, nd D cn receive dt from E, F, G, nd H through the links E C nd F D. However, the opposite direction is not vilble such tht A, B, C, or D, cn communicte with E, F, G, or H. Given tht directionl links cn occur in heterogeneous networks we define the connectivity between pir of nodes s requiring tht they be bi-communicble. Specificlly we hve the following. Definition 1. Bi-communicble: A pir of nodes is bi-communicble if nd only if both nodes cn receive informtion from ech other. Note tht bi-communicble doesn t require tht pths between the nodes in question hve the sme set of intermedite nodes. This definition indictes tht node i nd j re connected if nd only if node i cn receive dt sent by j nd vice vers. Bsed on this connectivity definition, we introduce modified definition of link between two nodes in network. Definition 2. Vlid Link: A pir of nodes i nd j hve vlid link if nd only if direct link exists in both directions or t lest one direct link in either direction exists nd t lest one multi-hop pth in the other direction is vilble. Bsed on Definitions 1 nd 2 we define prtition of the network s follows. Definition 3. Prtitioned Network: A network is considered prtitioned if one or more nodes do not hve bi-directionl connectivity to the rest of the nodes in the network. Hence network is 1-connected if nd only if ll pirs of nodes hve t lest one pth between them in both directions. Here we propose n lgorithm for network node to test the overll connectivity of the topology when directed links exist in the network. A. Connectivity Test Consider n rbitrry multi-hop wireless network of N nodes. Let G = (V, E), be the grph of the topology where V is the set of nodes nd E is the set of links. The grph G cn be represented by the N x N djcency mtrix A( t time t, 11( = 21( A( M N1( N1 M L L L 1N 2 N NN M (1) where 1,,. The link connectivity ij ( between two nodes depends on their rdio rnge nd cn be determined by nodes loclly through the exchnge of ``Hello or probing pckets. For now we ssume homogeneous network scenrio where ll links re bidirectionl (i.e., ij (=1 ji (=1). Thus, A( is symmetric mtrix. Let d i ( denote the degree of node i N t time t (i.e., d i ( equls the number of neighbor nodes of i). We define D s the digonl mtrix consisting of the degree of ech node (i.e., D( = dig(d i ()). The Lplcin mtrix L( of grph is defined in terms of the djcency mtrix A( nd nodl degree mtrix D( s L = D( A(. (2) The eigenvlues λ = [λ 1, λ 2,... λ Ν ] of L( form the Lplcin spectrum of the grph. The eigenvlues λ nd their ssocited eigenvectors X = [x 1, x 2, x N ] cn be computed from L λ using number of well known efficient numericl methods. In lgebric grph theory [13] it hs been shown tht zero is lwys n eigenvlue of L nd the number of zero eigenvlues is equl to the number of connected components of the network N CL. Thus the network is connected (i.e., t lest 1-connectivity) if the Lplcin mtrix of the topology hs single zero eigenvlue (i.e., if second smllest eigenvlue is positive N CL = 1). Here we pply this result in constructing test for connectivity in heterogeneous multi-hop wireless networks. The djcent mtrix cn be obtined by use of the topology informtion periodiclly gthering by proctive routing protocol or rective routing protocol tht exchnge locl connectivity periodiclly. The possible existence of directed links in the topology mens tht one cn not directly pply the result. In order to force the djcency mtrix A( to hve symmetric form we pply Definition 2 bove in determining the link connectivity. Specificlly, we require ll links to be vlid links nd modify the link connectivity in logiclly djusted topology djcency mtrix to reflect this. For exmple, the smple topologies of Figure 2 fter djustment will hve the corresponding logicl topologies shown in Figure 3. Note, tht fter djustment of the network topology the resulting is symmetric nd one cn pply test on the Lplcin eigenvlues to determine the network connectivity. The connectivity test procedure is given in lgorithmic form below. Heterogeneous Connectivity Test Algorithm (h-cta) Step 1 : Identify ny directed links in the topology from the djcency mtrix A(. If none, set = A( nd go to step 3. Step 2 : Form djusted djcency mtrix contining only vlid links. Specificlly, for ech link i j such tht ij ji,

3 , 1 1, 1 Otherwise, where is the djusted djcent mtrix. Step 3 : Compute the eigenvlues of the Lplcin mtrix L =, where is the degree mtrix corresponding to Step 4 : Determine the number of zero eigenvlues mong the Lplcin spectrum. If N CL = 1 then the network is connected, otherwise it is prtitioned into N CL components networks. For network of N nodes nd E links of which K re directed, it cn be shown tht the time complexity of h-cta is O(K(E+N logn)+n 2 ). The lgorithm cn be implemented t ny network node hving djcency mtrix informtion However, if the network is prtitioned ccording to Definition 3, ll nodes cnnot exchnge connectivity informtion. For exmple, in the network of Figure 2 (b) cluster 2 (i.e., CL 2 = { E, F, G, H}) cnnot receive connectivity informtion of cluster 1 (i.e., CL 1 = {A, B, C, D}) while cluster 1 cn receive nd obtin the connectivity informtion of cluster 2. Since the nodes in cluster 1 cn obtin the globl djcency informtion, ny node in cluster 1 cn execute h-cta to determine the overll connectivity. In Section III we show node with in cluster such s 1 in Figure 2(b) cn find which link should be improved so tht the cluster 2 cn receive the connectivity informtion of cluster 1. If there exists other wekly connected clusters, the cluster tht cn receive the most informtion cn do initite the h-cta procedure to determine which links need to be dded to provide connectivity. A network such s Figure 2(b) is termed wekly connected nd this is our focus in the pper. Once is found, k-connectivity my be lso exmined by the lgebric connectivity. However, it is out of scope in this pper. B. Numericl Study We utilized the h-cta lgorithm to study the connectivity of heterogeneous multi-hop wireless network topologies. Here we discuss typicl results for the cse of rndom topologies. Using the ns2 simultor, we generted rndom topologies with different number of nodes (i.e., 5, 75, nd 1) in network re of m 2. The nodes were independently distributed ccording to uniform [-15] rndom vrible in the network re. We dopted bseline prmeters from 82.11b equipment (i.e., verge trnsmit power P T = 15dBm, receiver sensitivity threshold P RSST = -9 dbm). The bsic trnsmission rnge ws determined using simple pth loss model dbm dbm 1 log (3) where α is the pth loss exponent nd d is the distnce between pir of nodes in meters. A pth loss exponent of α = ws used, which results in circulr coverge re with rdius 25 meters. A heterogeneous network ws creted by vrying either the trnsmission power or propgtion model for ech node or both fctors. Ech node i selects its trnsmission power P Ti ccording to uniform [13.5dBm dBm] rndom vrible. The resulting mximum trnsmission rnge R is uniform between 231m nd 27.5m. Non-uniform signl propgtion between nodes ws modeled using the Qusi-Unit Disk Grph (Q-UDG) model. In the Qusi-UDG model, link exists between two nodes if the inter-nodl distnce d is less thn βr, where R is the mximum trnsmission rnge of the node nd β is the Q-UDG fctor ( β 1). For distnces d greter thn R, there is no connectivity. However, for βr d R, the link will exist with probbility (R - d)/(r-βr). We selected different β prmeter vlues of.5,.75,.85 nd 1. to show how irregulr propgtion ffects the connectivity. Figure 4 shows 95% confidence intervls on the P(connected network) determined with h-cta versus the node density for two cses of node power ssignment: () homogenous with P Ti = 15dBm t ech node i nd (b) heterogeneous with P Ti drwn from uniform [13.5dBm dBm] rndom vrible for ech node. Ech point in Figure 4 is determined from 4 independent simultion runs. From Figure 4(), notice tht for the cse of homogeneous network (i.e., fixed P T = 15dBm, β = 1.) the network is connected (i.e., P(connected network) = 1) for ll node densities considered. In contrst, the P(connected network) is lmost zero for ll network densities for both homogeneous (4()) nd heterogeneous power ssignments (4(b)) when β =.5. This is becuse the verge trnsmission rnge is only meters. However, the network connectivity increses s β increses. For exmple, in Figure 4() the probbility of connectivity for 1 node network is estimted from the simultion s.43with β =.5,.226 with β =.75, P(Connected Network) () Rndom networks with homogeneous trnsmission power P(Connected Network) Rndom (β =.5) Rndom (β =.75) Rndom (β =.85) Rndom (β = 1.) Rndom (β =.5) Rndom (β =.75) Rndom (β =.85) Rndom (β = 1.) (b) Rndom networks with heterogeneous trnsmission power Fig. 4. Probbility of connectivity in rndom network topologies

4 nd.54 with β =.85. Similrly for fixed β the network connectivity increses with the node density, for exmple in Figure 4 () with β =.85, the probbility of connectivity is.63 t 5 nodes,.1145 t 75 nodes, nd.54 t 1 nodes. In compring homogeneous power ssignment with heterogeneous ssignment (i.e., 4() vs. 4(b)) we see tht only for the β = 1 cse does the power ssignment result in significnt difference in the connectivity. For the other vlues of β, the Q-UDG propgtion effect domintes nd the power ssignment hs little effect on the results (i.e., the confidence intervls on the results overlp). From Figure 4 one cn clerly see tht the connectivity in heterogeneous network is considerbly lower thn the homogenous cse no mtter wht the cuse of the heterogeneity. III. CONNECTIVITY IMPROVEMENT SCHEMES We propose schemes tht for n unconnected heterogeneous network identify the links whose ddition will connect the network. The pproch is bsed on identifying the isolted groups (i.e. clusters) of nodes nd determining the links required to connect between clusters. Consider network prtitioned into N CL wekly connected clusters (i.e., ech cluster hs t lest directed link to some other cluster). The Lplcin mtrix L with re-lbeled node IDs cn be written s where ech L k represents the Lplcin mtrix of connected cluster C k of nodes. There re N CL zeros in the eigenvlue set λ = [λ 1, λ 2,... λ Ν ] of L(. From the N CL eigenvectors x i ssocited with the zero eigenvlues one cn determine the nodes in ech cluster. Specificlly the nodes in cluster will hve non-zero vlues in the eigenvector ssocited with zero eigenvlue [15]. Once the sets of member nodes in ech isolted cluster re identified, cluster djcency mtrix, CL_A, cn be determined which represents how the clusters re symmetriclly connected. The cluster djcency mtrix cn be determined by: _ 1,, 1 (4), otherwise where CL i is nodes set of ech cluster i, nd A is the network djcency mtrix. The cluster djcency mtrix provides informtion bout which cluster needs to be connected to nother cluster to provide network connectivity. We propose two schemes to identify the links needed to reconnect the network bsed on given cost constrints: (1) Simple Merging Scheme (SMS) nd (2) Cost Optimized Merging Scheme (COMS). The link cost is the cost to improve the link so tht bi-communiction cn occur. Note tht vriety of techniques such s node movement, trnsmission power, directionl ntenn, nd etceter cn be used to dd link to the network. In this pper, we mnipulte the trnsmission power to improve the links in question nd the link cost constrint LC limit in terms of distnce is determined from the mximum trnsmission power together with the propgtion model. A. Simple Merging Scheme (SMS) The Simple Merging Scheme (SMS) tries to dd links until ech isolted cluster hs bi-directionl connection with it s neighbor clusters. The lgorithm finds the set of locl minimum cost links between n isolted cluster nd neighbor cluster using distnce informtion. Specificlly between ech pir of neighbor clusters SMS finds the minimum distnce links tht re within the mximum possible trnsmission rnge s determined by LC limit. The distnce between nodes in isolted clusters cn be obtined by Globl Positioning System (GPS) or locliztion techniques [14, 15]. SMS cn be implemented loclly by the cluster heds (nodes with directed link to nother cluster) in ech cluster. SMS cn be put in lgorithm form s below. Simple Merging Scheme (SMS) Step 1 : Perform h-cta to determine if the network is prtitioned, if Yes go to step 2, otherwise STOP. Step 2 : From the h-cta results determine the number of clusters N CL nd the node sets of ech cluster, C i, nd the cluster djcency mtrix CL_A. Step 3 : Find the set of minimum cost links between ech pir of isolted clusters,, ;,, where MLC ij is minimum cost link from cluster i to j nd LC(k,l) is the link cost between node k in cluster i nd l from cluster j. Exclude the existing links. Step 4 : Select the dequte links bsed on constrints such tht the link direction stisfying CL_ ij = nd MLC ij < LC limit. B. Cost Optimized Merging Scheme (COMS) In order to provide benchmrk comprison to SMS we developed the Cost Optimized Merging Scheme (COMS) which finds the set of globlly minimum cost links between isolted clusters, MLC = {for ll i nd j; MLC ij } while stisfying the cost constrint LC limit. This process is very time consuming since it hs to check every combintion of 2 1 links nd its computtion time is exponentil. Therefore, before solving the optimiztion problem we dd step to merge smll clusters with one node to the nerest lrger cluster. COMS cn be implemented in centrlized fshion t super node nd put in lgorithm form s follows. Cost Optimized Merging Scheme (COMS) Step 1 : Perform h-cta to determine if the network is prtitioned, if Yes go to step 2, otherwise STOP. Step 2 : From the h-cta results determine the number of clusters N CL nd the node sets of ech cluster, C i, nd the cluster djcency mtrix CL_A. Step 3 Merge the clusters with single member to the nerest bigger cluster. Add these links to n improvement required set of links. If this process resolves the prtition problem, STOP. Otherwise, go on step 4. Step 4 Find the minimum Totl Cost (TC) : 1, set of links to provide bi-communicble connectivity between to ll nodes. Step 5 : Add the set of links from step 4 into the set of links from step 2. () Originl clusters (b) COMS (c) SMS Fig. 5. Added links by SMS (RED) nd COMS (BLUE)

5 C. Comprison of Cluster Merging Schemes Figure 5 shows simple exmple illustrting the differences between SMS nd COMS. Figure 5 () shows the originl connections between the three clusters of network. The nodes in cluster C 3 cn obtin topology informtion from C 1 nd C 2 nd one cn initite COMS. Figure 5(b) shows the topologicl results of running the COMS lgorithm. Observe tht only single directed link is dded to provide bi-communicble connectivity to ll clusters. In contrst the topology fter running SMS is shown in Figure 5(c). Obviously SMS dds more links then COMS nd thus costs more but it hs the dvntges of being distributed nd mking the network more robust to filures. Note tht one node in C 2 nd one in C 3 will independently initite the SMS lgorithm. As more extensive, evlution nd comprison of SMS nd COMS, we conducted set of simultion bsed experiments similr to those reported in Section II B. Specificlly, using the ns2 simultor we generted rndom topologies with different node densities (i.e., 5, 75, nd 1) in network re of m 2. The nodes were independently distributed ccording to uniform [-15] rndom vrible in the re. We dopted bseline prmeters from 82.11b equipment (e.g., P RSST = -9 dbm). Heterogeneous conditions were creted by hving ech node i selects its trnsmission power P Ti ccording to uniform [13.5dBm dBm] rndom vrible nd creted non-uniform signl propgtion between nodes using the Qusi-Unit Disk Grph (Q-UDG) model with α = , β =.75 or β =.85. We rndomly generted topologies in this fshion until 5 wekly connected topologies were found for ech node density. For ech wekly connected topology both SMS nd COMS were implemented to improve the connectivity. We exmined three mximum node trnsmission powers constrints nmely: 2dBm, 25dBm, nd unlimited. In the unlimited power cse for COMS the power ws incresed to the minimum power required to provide the minimum cost links necessry for bi-communicble 1-connectivity. In the unlimited power cse for SMS, the power ws incresed until Averge number of directed links dded SMS (β =.75, Tx = 2dBm) COMS (β =.75, Tx = 2dBm) SMS (β =.75, Tx = 25dBm) COMS (β =.75, Tx = 25dBm) SMS (β =.75, Tx = Unlimited) COMS (β =.75, Tx = Unlimited) Averge number of directed links dded SMS (β =.85, Tx = 2dBm) COMS (β =.85, Tx = 2dBm) SMS (β =.85, Tx = 25dBm) COMS (β =.85, Tx = 25dBm) SMS (β =.85, Tx = Unlimited) COMS (β =.85, Tx = Unlimited) () Averge number of directed links dded for β =.75 (b) Averge number of directed links dded for β =.85 Averge number of hops in pths SMS (β =.75, Tx = 2dBm) COMS (β =.75, Tx = 2dBm) SMS (β =.75, Tx = 25dBm) 5.5 COMS (β =.75, Tx = 25dBm) SMS (β =.75, Tx = Unlimited) COMS (β =.75, Tx = Unlimited) Averge number of hops in pths SMS (β =.85, Tx = 2dBm) COMS (β =.85, Tx = 2dBm) SMS (β =.85, Tx = 25dBm) COMS (β =.85, Tx = 25dBm) SMS (β =.85, Tx = Unlimited) COMS (β =.85, Tx = Unlimited) (c) Averge number of hops in pths for β =.75 (d) Averge number of hops in pths for β =.85 Fig. 6. Comprison of SMS nd COMS in verge number of directed dding links nd hops in pths with 95% of confidence intervl

6 the minimum power necessry to dd links tht result in full mesh of links between ll clusters. While the unlimited trnsmit power cse is imprcticl it provides benchmrk scenrio for the results. Figure 6 shows typicl simultion results. For the three mximum trnsmit power limit investigtes fter pplying SMS or COMS ll topologies were t lest bi-communicble 1-connected. Figure 6 () nd (b) show the verge number of directed links dded to the network versus network density for both SMS nd COMS. As expected, when the network density increses fewer links re required to be dded in order to provide connectivity regrdless of whether SMS or COMS is used. For exmple, COMS dds n verge of 5.52 links in 5 node networks nd 1.96 links in 1 node networks with β =.75 nd mximum trnsmit power limit of 2dBm. Compring SMS nd COMS one cn see tht COMS needs fewer links to provide connectivity. In exmining the effects of the mximum trnsmit power limit one cn see tht the two schemes behve differently. For SMS s the power increses more links re dded beyond the minimum needed for 1-connectivity. In the extreme cse of unlimited vilble trnsmit power, links re dded until the clusters re interconnected with full mesh of links. In contrst, COMS lwys chooses the cost optimized minimum number of dditionl links. Hence, the men number of dditionl links decreses slightly with incresing mximum power limit. Further compring the effect of β on the results one cn see tht s β decreses nd the signl propgtion becomes more irregulr the verge number of directed links need to provide connectivity increses. Figure 6(c) nd (d) show how the verge hop count in source-destintion pths chnges versus the network density for both schemes. The verge hop count of ll pths between every pir of nodes is considered. From the figures SMS outperforms COMS for ll network densities, β vlues, nd restortion restrictions. For exmple, with 2dBm mximum power level restriction, the verge hop count for SMS is 6.72 nd COMS is 7.35 for 5 node network with β =.75. Since COMS finds the minimum number of dditionl links to provide connectivity, while SMS generte s mny s it could, the verge hop count by SMS should be lwys smller thn COMS. On the other hnd, in terms of the verge link cost COMS lwys results in lower verge cost nd the difference is more significnt s the mximum power level limit increses. Note tht, the worse cse mximum number of directed links to connect N CL clusters is 2(N CL 1). The time complexity of SMS cn be shown to be nd tht of COMS is where k is number of possible link combintions. The rnge of the number of link combintions is 1 to 2(N CL 1) nd k cn be computed by, where, 2 (5) 2 Therefore, the computtion time of SMS is smller thn tht of COMS. If the number of isolted clusters N CL increses, the computtion time of COMS increses more quickly thn SMS. IV. CONCLUSIONS Mny 1-connected homogeneous wireless networks become disconnected when the network becomes heterogeneous. In this pper we hve proposed new lgorithm to determine the connectivity of heterogeneous wireless networks. The results of simultion bsed numericl study utilizing our proposed lgorithm to exmine the effects of severl fctors (vritions in power levels, irregulr signl propgtion, nd network nodl density) on connectivity re presented. Further we propose two connectivity mngement schemes SMS nd COMS to dd dditionl links to prtitioned heterogeneous network in order to provide t lest 1-connectivity. A simultion bsed study of the two schemes shows tht both schemes cn correctly dd links to provide connectivity, but SMS is esier to implement with the drwbck of higher cost. REFERENCES [1] I. F. Akyildiz nd X. Wng, A survey on wireless mesh networks, IEEE Communictions Mgzine, Vol. 43, No. 9, pp. S23 S3, Sept., 25. [2] H. Moustf nd Y. 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