A Group-Based Architecture for Wireless Sesor Networs Jaime Lloret, Miguel Garcia ad Jesus Tomas Departmet of Commuicatios Polytechic Uiversity of Valecia Valecia, Spai jlloret@dcom.upv.es, migarpi@teleco.upv.es, jtomas@dcom.upv.es Abstract May routig protocols for ad-hoc etwors ad sesor etwors have bee desiged, but oe of them are based o groups. We propose to divide the etwor ito several groups of sesors. Whe a sesor sed data to other groups, the data has to arrive just to oe sesor from each group, the they propagate it to the rest of sesors i their groups. We have simulated our proposal for differet types of sesor topologies to ow which type of topology is the best depedig o the umber of sesors i the whole etwor or depedig o the umber of iterior sesors. We have also simulated how much time is eeded to propagate iformatio betwee groups. The applicatio areas for our proposal could be rural ad agricultural eviromets to detect plagues ad to propagate it to eighbourig areas, or for military purposes to propagate iformatio betwee eighbourig squads. Keywords-Sesor Networ; Group-Based Architecture; Groupbased routig algorithm. I. INTRODUCTION There are may routig protocols that ca be applied to sesor etwors. They ca be classified ito two groups [] [2]. Oe group is formed by protocols based o the etwor topology ad the other group the oes that do ot tae it ito accout. First group ca be broe dow ito three subgroups: - Plae routig. All odes i the etwor have the same role ad perform the same tass. Because of the umber of odes i these etwors, the use of a global idetifier, for every ode, is ot feasible. It uses a data-cetric routig where the base statio seds requests to some regios ad the odes from that regios reply. Some of the algorithms i this group are SPIN, Direct diffusio, Rumour routig, MCFA, GBR, IDSQ, CADR, COUGAR, ADQUIRE, ad so o. 2- Hierarchical routig. It is very scalable ad has a efficiet commuicatio. It has bee desiged for eergy savig purposes, because cetral odes have ulimited eergy, while leaf sesors have limited eergy. Whe the sesor etwor topology is formed, data ca be routed. Some algorithms such as LEACH, PEGASIS, TEEN, APTEEN, MECN, Virtual grid architecture routig ad TTDD are hierarchical routig algorithms. 3- Positio-based routig. All data is routed through the sesors depedig o their positio. Distaces betwee sesors are ow because of eighbourig sesors sigals. There are other protocols that base ode s situatio o GPS ad, usig that iformatio, route the data to the most adequate sesor. These algorithms cosume more eergy tha others because of the eed of GPS sigal. Some of those algorithms sleep sesors whe the etwor has ot ay activity. Some examples are GAF, GEAR, GOAFR ad SPAN. Secod group does ot have ito accout the structure of the etwor. It ca be broe ito five subgroups: - Multipath Routig Protocols. The iformatio could reach the destiatio through differet paths. Because sesors have to calculate several paths, they use a mai route whe they have eough eergy; otherwise, they use a alterative path. 2- Query-Based Routig protocols. They are based o a cetral ode that seds a query about a evet to the specific area. Whe the query arrives to that area, it is routed to the destiatio sesor, ad the it will reply. A sesor from a area could be sleepig, savig eergy, while there is ot ay query to that area. 3- Negotiatio-Based Routig Protocols. Before data trasmissio, the sesor has to egotiate the data it has to sed, so redudat data could be deleted, ad resources will be available while data exchage. SPIN protocols use this type of routig, but they tae ito accout the etwor structure. 4- QoS protocols. The iformatio is routed to the sesors taig ito accout quality parameters such as delay, eergy, badwidth ad so o. SAR ad SPEED protocols are based o quality of service algorithms. 5- Data coheret/icoheret processig based protocols. These algorithms use several routig techiques taig ito accout the data processig of a coheret or icoheret result. Noe of the routig protocols aforemetioed are groupbased. We propose to divide the etwor of sesors ito several groups ad if a sesor has to sed data to other groups, whe this data arrives to oe sesor from a group, it propagates it to the rest of sesors i its group. The paper is structured as follows. Sectio 2 examies some wors related with our proposal such as eighbour selectio ad architectures based o groups, ad explais our motivatio. There is a descriptio of our architecture proposal i sectio 3. Aalytical model for some types of topologies of sesors are show i sectio 4. The propagatio time to reach a sesor from other group is aalyzed i sectio 5. Fially, sectio 6 gives our coclusios ad future wors.
II. PREVIOUS WORKS AND MOTIVATION Throughout the years, differet types of strategies for eighbors selectio have bee developed. O oe had, there are the oes used for trasfer coordiatio to icrease cotet availability. They ca be applied for P2P etwors [3], [4] ad [5], for cotet delivery systems [6] or for distributig systems [7]. May other systems locate odes i the topology based o mathematical structures such as CAN, Chord, Pastry ad Tapestry, but these systems do ot tae care of the uderlyig etwor, so a eighbor of a ode could be very far (i terms of roud-trip time RTT-) or it could ot have eough capacity available to perform its ecessities. There are proposals where odes coectios are based o the uderlyig etwor, such as Plethora [8] or o their geographic locatio such as the oe described i [9]. Other systems locate ew odes i the topology taig ito accout that they are possibly close to a give ode, ad the, perform RTT measuremets to idetify the actual closest ode such as the oe preseted i [0], ad others use a proximity eighbor selectio (PNS) usig heuristics approximatios such as the oe preseted i []. There are also some researches for wireless etwors, where coectios are established oly if they are closed, because of their coverage area ([2] ad [3]). But oe of the eighbor selectio strategies show cosider to group odes ad structure coectios betwee odes from differet groups. O the other had, oe of them tae ito accout the capacity of the odes to select the eighbor to have a coectio with. There are several wors i the literature where odes are grouped ito groups ad coectios are established betwee odes from differet groups, but all of them have bee developed to solve specific issues. Rhubarb [4] orgaizes odes i a virtual etwor, allowig coectios across firewalls/nat, ad efficiet broadcastig. The odes ca be active, if they establish coectios, or passive, if they do t. Rhubarb system has oly oe coordiator per group ad coordiators could be grouped i groups i a hierarchy. The system uses a proxy coordiator, a active ode outside the etwor, ad all odes iside the etwor mae a permaet TCP coectio with the proxy coordiator, which is reewed if it is broe by the firewall or NAT. If a ode from outside the etwor wishes to commuicate with a ode that is iside, it seds a coectio request to the proxy coordiator, who forwards the request to the ode iside the etwor. Rhubarb has a three-level group s hierarchy. It may be sufficiet to support a millio odes but whe there are several millios of odes i the etwor it could ot be eough, so it suffers from scalability problems. O the other had, all odes eed to ow the IPs of the proxy coordiator odes to establish coectios with odes from other virtual etwors. A Peer-to-Peer Based Multimedia Distributio Service has bee preseted i [5]. That paper proposes a topology-aware overlay i which earby hosts or peers self-orgaize ito applicatio groups. Ed hosts withi the same group have similar etwor coditios ad ca easily collaborate with each other to achieve QoS awareess. Whe a ode i this architecture wats to commuicate with a ode from other group, the iformatio is routed through several groups util it arrives to the destiatio but this solutio oly ca be applied to logical etwors because of eighborig odes could be so far. There are other architectures based o super-peer models such as Gutella 2 ad FastTrac etwors. Each super-peer i these etwors creates a group of leaf odes. Superpeers perform query processig o behalf of their leaf odes. A leaf ode seds the query to its superpeer that floods it to its superpeer eighbors up to a limited umber of hops. The mai drawbac of this architecture is that all iformatio has to be routed through the superpeer logical etwor. Fially, there are some hierarchical architectures were odes are structured hierarchically ad some parts of the tree are grouped ito groups such as the oes preseted i [6] ad i [7]. I some cases, some odes have coectios with odes from other groups although they are i differet layers of the tree, but i all cases, the iformatio has to be routed through the hierarchy to achieve odes from other groups, so all layers of the hierarchy could be overloaded i case of havig may data to be trasferred. Let s suppose we eed to divide the etwor ito groups or areas because of the physical implemetatio of the sesor etwor or for scalability purposes. All architectures previously show do t solve that problem efficietly, because i the case of cetralized architectures, the server will have may wireless coectios at the same time, so it will eed may resources. O the other had, there is a cetral poit of failure ad a bottleec. I the case of fully distributed architectures, it is very difficult to cotrol the system ad it eeds much time to process tass, because of the time eeded to reach far odes, decreasig the performace of the whole system. III. ARCHITECTURE DESCRIPTION Our proposal is based o the creatio of groups of sesors with the same fuctioality i the etwor. There is a cetral sesor that limits the zoe where the sesors from the same group will be placed, but its fuctioality will be the same that the rest of the sesors. A sesor ows i which group is because it is give maually or by GPS. Whe there is a evet i oe sesor, this evet is set to all sesors i its group. All odes i a group ow all iformatio of their group. Border sesors are those sesors of the of the group, ad they have coectios with sesors from other groups as it is show i figure. Border sesors are used to sed iformatio to other groups or to receive iformatio from other groups ad distribute it iside. Whe a sesor has to sed some iformatio to its group ad to eighborig groups, the iformatio is forwarded usig Reverse Path Forwardig (RPF) Algorithm [8] (each group has oe RPF database), but whe the iformatio has to be set to other groups oly, the iformatio is routed directly to the sesor closest to that group. Whe the sesor from the eighbor group receives that iformatio, it routes it to all odes i its group. Because the system is based o groups, the iformatio is forwarded very fast to other groups (the iformatio is routed through the shortest path to the area sesor). Coectios betwee sesors from differet groups are established as a fuctio of their available processig capacity, their available umber of coectios, their available power or because a eighbor sesor failure. Figure 2 shows a logical view of the proposed architecture.
Group B Group D Cetral sesor It sesor Border Sesor Cetral coectio It Border coectio Group limit S S 3 Group A Group C Figure. Topology example IV. ANALITICAL MODEL This sectio describes the architecture aalytically taig ito accout that it is a system based o groups. Now, we are goig to aalyze the architecture for several types of etwor architectures iside the groups. Let a etwor of sesors G (V, λ, E) be, where V is the set of sesors, λ is the set of their capacities (λ(i) is the capacity of the i-th sesor ad λ(i) 0 i-th sesor) ad E is the set of coectios betwee sesors. Let be a fiite umber of disjoit subsets of V, so V V ad there is ot ay sesor i two or more subsets ( V 0). Let s suppose V (the umber of sesors i V) ad the umber of subsets of V. We obtai equatio. V i () Every V has a cetral sesor, several it sesors ad several sesors as it is show i expressio 2. it (2) Now we ca describe the whole etwor as the sum of all these sesors from all groups as it is show i equatio 3. Sesor Coectio betwee sesors from the same group Coectios betwee odes from differet groups ( cetral it ) ( it) ( ) i i i (3) Now we are goig to model our proposal as a fuctio of the umber of it ad sesors i a etwor for several types of etwors. A. Tree topology Tree topologies have a sesor actig as a tru ad from this sesor leaves several braches. There are two types of tree topologies: N-ary trees (every sesor has the same umber of leaf odes, biary, terary ad so o) ad bacboe trees, where there is a tru ad there are sesors that brach from it. I both cases the iformatio flows hierarchically. We are goig to study the first case oly, because it could be easily implemeted by limitig the umber of icomig coectios i a sesor. The bacboe tree is a special case of the partially cetralised P2P Networs with superpeers ad it will be discussed later. Figure 2. Logical view of the proposed architecture I a tree topology, the umber of sesors is equal to M, where M2 i case of a biary tree, M3 i a terary tree ad so o, ad is the umber of levels of the tree). The umber of lis is - ad the diameter of the etwor is 2-2. We suppose balaced trees where all braches have the same umber of levels, so the umber of it sesors is give by expressio 4. it (4) grade Where grade is the umber of leaf sesors for each sesor. Usig expressios 2 ad 4, we obtai expressio 5. It gives the umber of sesors related with the umber of it sesors. (grade-) it grade (5) Tree topologies have bee implemeted i several sesor etwors such as the oe show i [9]. B. Grid topology We are goig to cosider 2-dimesioal Grid ad 3- dimesioal Grid with all its sides equals. To mae easy the mathematical developmet, i a 2D Grid we will use a square matrix where m for 3 ad i a 3D Grid we will use a cube matrix where ml for 3. I both cases, the case of 3 has oe cetral sesor, but there is ot ay it sesor. The umber of sesors i a 2D Grid, with all sides equals, sesor etwor is 2 ( 3, 4...). The umber of eighbours of a it sesor is 4, the sesor has 3 eighbours ad the vertex sesor has 2 eighbours. The umber of coectios i the topology is give by expressio 6. ( ) l 2 (6) Expressio 7 gives the diameter of a 2D Grid topology. ( ) d 2 (7) We have observed that the umber of sesors i a 2D Grid topology follows the expressio 8. 4 ( ) (8) Usig expressio 2, we obtai expressio 9. It gives the umber of it sesors. ( ) 4 (9) it S 2
Usig expressios 8 ad 9, we obtai expressio 0 that relates the umber of sesors related with the umber of it sesors. ( ) 4 it (0) 2D Grid topologies have bee implemeted i several sesor wors such as the oe show i [20]. The umber of sesors i a 3D Grid, with all sides equals, sesor etwor is 3 ( 3, 4...). The umber of eighbours of a it or cetral sesor is 6, sesors have 5 eighbours ad the vertex sesors have 4 eighbours. Expressio gives the umber of coectios i the topology. ( ) l 3 () Expressio 2 gives the diameter of a 3D Grid topology. ( ) d 3 3 (2) The umber of sesors i a 3D Grid topology ca be measured by expressio 3. 3 6 2 8 (3) Usig equatio 2, we ca obtai the umber of it sesors i a 3D Grid topology. 3 6 2 9 (4) it Usig the cube geometry, we ca obtai the umber of sesors as a fuctio of the umber of it sesors. This relatio is give by equatio 5. 6 ( ) 2 3 ( ) 8 (5) it it 3D Grid topology is used i etwors that eed may paths to reach the same destiatio. C. Power Law I [2], M. Faloutsos et al. show that the odes of a distributio etwor ca be modelled usig mathematical laws. This paper states that power law fits real measuremets with correlatio coefficiets of 96%. Power law states that the grade of a ode (d v ) is proportioal to its rage (r v ) to the power of a costat called R as it is show i expressio 6. R d v r v (6) Where R varies depedig o it is applied. Applyig Lemma, from paper [2], the grade of a ode is give by expressio 7. R d v r (7) R v Where is the umber of sesors i the etwor, d v ad r v are the grade ad the rage of the v sesor respectively. From the power law appears the Zipf s law. It states that some odes have may lis while may odes have oe or two lis. Zipf s law has bee proposed by B. A. Huberma et al. to model Iteret i [22], ad by Z. Ge et al. to model Gutella ad Napster Networs i [23]. Zipf s fuctio states that the rage of r odes follows the proportioality show i expressio 8. f α ( r) C r (8) Where α varies depedig o the type of distributio of the odes. It is also ow as the Zipf coefficiet. C is a costat that varies depedig o the type of etwor. Taig ito accout expressios 7 ad 8, we ca assume that R-α. Applyig Zipf s law to our sesor architecture, we obtai expressio 9. α (9) ( ) α it Taig expressio 2 ito accout, we ca obtai expressio 20. It relates the umber of sesors with the total umber of sesors i the topology. α ( ) α / α ( ) (20) O the other had, replacig expressio 2 i expressio 9 we obtai the umber of sesors as a fuctio of the umber of it sesors as it is show i expressio 2. ( it ) ( ) α (2) it As Iteret topology has varied alog the years, because of the growth of the umber of computers coected to it, α value has varied from 0.74 to 3 i last measures, as it ca be see i [2] ad [24]. D. Logarithmic law Logarithmic law was itroduced by György Herma i [25]. This law proposes that the odes, or the odes with higher roles i the etwor, are the resposible of the stability of the etwor. It also proposes that the odes are the resposible of the security of the etwor because they are the oes that commuicate with exterior odes. This proposal follows the model developed by D. J. Watts et al. i [26], where coectios are established based o efficiecy, stability ad security features. This law states that the distace betwee two sesors is give by expressio 22. l l ) (22) max l( it Where l max is the diameter of the etwor. It is equal to the logarithm of the odes that do t are i the of the etwor (the cetral sesor plus the it sesors). The relatioship betwee the umber of sesors ad the it sesors is give by expressio 23. ( ) c ( ) l( ) c (23) it it ermedate it ermedate C is a costat that depeds o the model of the etwor. So, the umber of sesors i the etwor is set betwee limits show i equatio 24. α
2 ( ) ( l( ) ) it it Whe mi Whe max (24) E. Partially cetralized P2P etwors I [27], J. Lloret et al. proposed a architecture for partially cetralized P2P etwors. They measured the umber of broers or superpeers (depedig o the type of etwor), that was iside the architecture o behalf of all broers or superpeers i the whole etwor. Those values could be applied to the proposal preseted i this paper if we suppose that the it sesors plus the cetral oe are the distributio odes ad the sesors are the odes cosidered i the access layer. The relatioship betwee it sesors ad sesors are differet accordig o the type of P2P etwor as it is show i expressio 25. it i a broer model 96 ( it ) i a superpeer model Usig expressio 2 we obtai expressio 26. 2 ( 2) 96 97 i a broer model i a superpeer model (25) (26) F. Architectures comparatio. This sectio compares the umber of sesors versus the umber of it sesors ad the umber of sesors versus the umber of sesors i the group for all architectures show. I both cases, partially cetralized P2P etwors with broers model is the same case tha the miimum values of the logarithmic model. Figure 3 graphs the umber of sesors i the group as a fuctio of the umber of it sesors for all models previously aalyzed. For Zipf s law we have used umerical methods to obtai its graph. I figure 6, we ca observe that if a group with few sesors is eeded, if there are less tha 24 it sesors, the best electio is the miimum value of the logarithmic law, but if we have more tha 24 it sesors the best oe is 2D Grid. What is desirable is to have may sesors i order to have may coectios with sesors from other groups, so there will be higher probability to cotact with more eighbourig groups. We have checed that for less tha 770 it sesors the best topology is the partially cetralized P2P etwors with superpeer model, but if the umber of it sesors is equal or higher that 770, the best topology is Zipf s law with R-2.45. Figure 4 shows the umber of sesors i the group as a fuctio of the umber of sesors i the group. We have used umerical methods to ow the umber of sesors as a fuctio of the umber of sesors i the group for the logarithmic model ad for Zipf s law. I figure 4, we ca observe that, whe may sesors are eeded versus the umber of sesors i the group, for less tha 40 sesors the best electio is 3D Grid, but for 40 sesors or more, the best electio is the partially cetralized etwor with superpeers model. Whe we eed few sesors versus the umber of sesors i the group, for less tha 0 sesors the best topology is the terary tree, but for more tha 0 sesors the best topology is 2D Grid. V. PROPAGATION TIME Every time a sesor has to sed iformatio to a specific group, first it has to sed the iformatio to the sesor closest to that group, ad the, the iformatio has to be set through the groups till the iformatio arrives to the destiatio group. Expressio 27 formulates it mathematically. i T t t t (27) to _ max_ it ragroup _ i i _ i _ i Where t to_ is the time eeded to reach the sesor closest to that group, is the umber of it groups through that path, t max_itragroup_i is the time eeded to cross the i- th group ad t _i-_i is the time eeded to trasmit the iformatio from oe sesor to aother sesor from other group. Let s suppose that t p is the mea value of the propagatio time for all trasmissios betwee 2 sesors i the architecture. So, we ca assume that t _i-_i t p ad, give d hops to reach from a source sesor to the sesor closest to the destiatio group, we ca assume t to_ d t p. We ca defie the time eeded to cross the i th -group as t max_itragroup_i d i t p, where d i is the umber of hops to cross the i th -group. Expressio 28 gives the time eeded to reach a group as a fuctio of the mea value of the propagatio time. T d d i t (28) p i Let s cosider four groups alog a path to a group destiatio. Figure 5 shows two simulatios. The first oe (source group) shows the time eeded whe the mea value of the umber of hops to cross the groups ivolved i the path is 0 ad the umber of hops from the source sesor to the sesor closest to the destiatio group vary from to 32. The secod oe (mea value of groups) shows the time eeded whe the umber of hops from the source sesor to the sesor closest to the destiatio group is 0 ad the mea value of the umber of hops to cross the groups ivolved i the path vary from to 32. I figure 5, we ca observe that the delay is higher whe the mea value of the umber of hops i the groups icreases, but it is less sigificat whe the umber of hops from the source sesor to the sesor closest to the destiatio group icreases. VI. CONCLUSIONS To the extet of our owledge, there is ot ay previous itercoectio system to structure coectios betwee groups of odes lie the oe preseted i this paper. This paper demostrates that it is a feasible optio ad it is idepedet of the structure of the sesors of the group, but some group architectures perform better tha others. It could be applied to specific eviromets such as rural eviromets or for military purposes. We are ow desigig its fault-tolerace.
00000 000 0000 Border sesors Number of hops 000 00 35 30 25 20 5 0 0 Biary Tree Quaterary Tree Grid 3D mi l P2P Superpeers Teary Tree Grid 2D Zipf (R2-5) max l Zipf (R-2.45) 0 240 560 900 It sesors Figure 3. Border sesors as a fuctio of the it sesors 5 0 Source group mea value of groups 0 50 00 50 200 Time to reach a group Figure 5. Time to reach a group as a fuctio of the umber of hops ACKNOWLEDGMENT Authors tha Mr. Atoio Caos, from the Polytechic Uiversity of Valecia, because of his support obtaiig, usig umerical methods, the iverse of some fuctios used here. REFERENCES [] L.M. Feeey, A taxoomy for routig protocols i mobile ad hoc etwors, October 999, SICS Techical Report T99:07. [2] J. N. Al-Karai, A. E. Kamal, Routig techiques i wireless sesor etwors: a survey. IEEE Wireless Commuicatios Volume, Issue 6, pp. 6-28, Dec. 2004. [3] L. Zou, E. Zegura, M.H. 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