Optimization of WSNs Flooding Rates by Khalimsky Topology

Transcription

1 Optimizatin f WSNs Flding Rates by Khalimsky Tplgy 1 Mahmud Mezghani, 2 Riyadh Garguri and 3 Mahmud Abdellaui 1 Natinal Engineering Schl f Sfax (ENIS), Sfax University, Tunisia; 2 Department f Sciences Taibah University, Saudi Arabia; 3 Engineering Schl f Electrnics and Cmmunicatin f Sfax (ENET'COM), Sfax University, Tunisia; 1 mahmud.mezghani@gmail.cm; 2 tn_riadh_30@yah.fr; 3 mahmudabdellaui4@gmail.cm ABSTRACT In this paper, we prpsed a new methd f deplying and building an rganized architecture f gateway ndes in a Wireless Sensrs Netwrk (WSN) frmed als by randmly deplyed sensrs arranged in clusters. This methd, based n the Khalimsky thery, reduces the energy cnsumptin and the flding rates f the cnventinal flding algrithm. Our slutin allwed t build a hierarchical tplgy reduces the number f cmmunicatin links between ndes while maintaining the adjacency list t minimize the data redundancy. It allws calculating an ptimal set f frwarding gateway ndes t rute data packets between a surce and a destinatin. This set includes all ptimal paths using the less number f ndes. Our simulatin study shws that the Khalimsky thery reduces cnsiderably the flding rates and the energy cnsumptin. Our slutin can be applied in the fields needing prefixed gateway ndes and randmly deplyed sensrs which use urgent data with real-time aspect such as the security and the mnitring f industrial znes and hme building. Keywrds: Wireless Sensr Netwrk; WSN; Flding; Khalimsky Tplgy; Flding Khalimsky Algrithm; Flding Rates; Energy Cnsumptin; WSN Deplyment. 1 Intrductin Technlgical advances in recent years have enabled the develpment f new types f sensrs equipped with wireless cmmunicatin system that can be cnfigured t frm autnmus netwrks called WSNs. These WSNs are used in varius dmains such as hme autmatin, health care, military dmain and envirnment mnitring. In the netwrk, the sensrs ndes cperate between them t treat and t cnvey the cllected data twards the base statin which acts accrding t prgrammed scenaris. These sensrs are characterized by a small memry size, a lw capacity fr treatment and limited energy resurce [1, 2]. Generally, dissipated energy by a sensr is the ttal f energies used t gather, treat and send/receive data. Mst f this energy is used by the radi mdule in sending/receiving infrmatin. The main fcus f WSN research has been n energy efficiency. The bjective is the develpment f tplgies and ruting prtcls allwing the reductin f the dissipated energy by the radi cmpnent. We shuld nte that the effectiveness f a ruting prtcl depends n the architecture f sensrs ndes deplyment and their perating prcesses. Fr that, flding is very used fr the WSN architecture cnstructin. It identifies relatinships between ndes and their DOI: /tnc Publicatin Date: 16 th Nvember 2014 URL:

2 Mahmud Mezghani, Riyadh Garguri and Mahmud Abdellaui; Optimizatin f WSNs Flding Rates by Khalimsky Tplgy, Transactins n Netwrks and Cmmunicatins, Vlume 2 N 6, Dec (2014); pp: psitins t calculate and maintain the ruting tables. It cnsumes a lt f energy and needs t be refined and ptimized t eliminate unnecessary data redundancy [3, 4]. Accrdingly, we devte ur research tasks t adapt scientific advances research in the fields f mathematics such as Khalimsky thery and the multi-agents systems t carry ut a sensrs deplyment methd fr WSNs reducing the flding rates and minimizing the energy cnsumptin. Our idea cnsists t create a WSN frmed by a set f fixed sensrs used as gateway ndes based n the Khalimsky tplgy and a set f clusters cntaining member ndes t gather infrmatin. The Khalimsky tplgy permits t cnvey the flding prcess using ptimal paths between gateway ndes and the sink when a nde transmits a data packet. The multi agents system permits t assign the jbs fr each nde in the clusters and in the set f the gateway ndes t cmplete a task f cllecting and transmitting infrmatin between a surce and a destinatin. Our bjective is t minimize the flding rates by the limiting f the flding in the set f the gateways, based n the Khalimsky architecture, using nly thse which frm ptimal paths. In this paper, we present Khalimsky tplgy used t build the architecture f deplyed gateways in a WSN. This tplgy prvides a hierarchical architecture in which each sensr nde is capable t cnvey data t their destinatin in an ptimal set f ndes minimizing the flding rates. In the secnd time, we present the evaluatin results f this methd cmpared with cnventinal flding algrithm. This evaluatin is carried ut by the TOSSIM simulatr and the PwerTOSSIM-Z mdule which allws t mdel pwer cnsumptin by sensrs ndes using the TinyOS2.1 perating system [5-7]. The remainder f this paper is rganized as fllws: sectin 2 presents an utline n WSN deplyment architectures, types f ruting prtcls and flding prblems such energy cnsumptin and infrmatin redundancies. Sectin 3 shws the Khalimsky tplgy characteristics and the aut-rganizatin algrithm f sensr ndes. Sectin 4 shws the nvel flding algrithm accrding t Khalimsky thery. Sectin 5 presents the simulatin and evaluatin results f the develped algrithms. Sectin 6 presents sme future wrks. Finally, sectin 7 gives sme cnclusins. 2 Related Wrk Several research studies have appeared t ptimize the energy cnsumptin f ndes thrugh the use f innvative cnservatin methds t imprve netwrk perfrmance, including the maximizatin f its life. Since the radi mdule is the greediest cmpnent, the trend was t reduce the cmmunicatins rates by ptimizing the data ruting t reduce the energy cnsumptin. Cnsequently, several ruting prtcls have been develped. Hwever, they cannt be applied apprpriately t any applicatin cntext. Depending n the architecture, the deplyed sensrs take place by a randm r rganized way. In the rganized way, sensrs must be deplyed in predetermined psitins where it is pssible t prgram their activities and data packets rutes. In the randm way, the ndes are scattered n the cllecting field in mass by several means such as thrwing them by plane. In this mde, an aut-rganizatin algrithm is necessary t imprve the perfrmance f the WSN [8]. In the literature, WSNs ruting prtcls can be classified in three main classes: flat, hierarchical and gegraphic netwrk ruting prtcls. In flat architecture, each nde plays the same rle and has the same functinality as ther sensr ndes in the netwrk. Sensrs can send data t the base statin directly using a high pwer, r hp URL: 26

3 Transactins n Netwrks and Cmmunicatins; Vlume 2, Issue 6, December 2014 by hp with a very lw pwer. The mst ppular flat-based ruting prtcl is data-centric prtcls like flding. In this type f prtcls, it is nt necessary t have an addressing mechanism fr sensr ndes. Data is prpagated gradually t the interested neighbrs requiring the data annunced r in fld twards selected r all the neighbrs with an imprtant redundancy until reaching the base statin [8-10]. The unnecessary flded data packets, the nt ptimum paths, the data transmissin time and the different ratis f energy cnsumptin between sensr ndes are the mst disadvantages in the dense flat netwrks. In hierarchical architecture, the nde representing the cluster-head transmits directly cllected data frm member-ndes t the base statin, r via a multi-hp mde between the cluster-heads. The cluster-heads are generally a sensrs mre pwerful than the member ndes r sensrs whse battery level is the highest in the cluster. This type f prtcl is the mst adpted tday. It minimizes mre the energy cnsumptin cmpared t flat architecture and it has tw great advantages: scalability and the simple implementatin f the aggregatin mechanisms. Leach, TEEN and PEGASIS are the mst ppular hierarchical ruting prtcls fr WSNs [8-10]. The data prpagatin between the cluster-heads and the sink uses multiple paths which are nt necessary ptimized. It requires an aut-rganizatin algrithm t select cluster heads and t affect member ndes t the calculated cluster. In a gegraphic ruting prtcl, a nde is suppsed t knw its gegraphical psitin, its neighbrs and the destinatin nde. T transmit data t the sink, the nearest nde destinatin, amng the neighbring ndes, is selected as the next hp. Multiple gegraphic ruting prtcls like GPSR, SPEED, GEAR, GAF... are prpsed. In such prtcl, the ruting data is ptimized and the cst t cntrl the algrithm is reduced. Hwever, the disadvantage f gegraphic-based ruting prtcls is the means used fr ndes lcalizatin. The lcalizatin is ensured by the exchange f a big number f messages by flding algrithm t discver ndes between them [8-10]. The flding mechanism is used by several ruting prtcls fr sensr ndes rganizatin. It permits the rutes setup, the neighbring discvery fr each nde and the links state updates. Such mechanism suffers frm a huge amunt f infrmatin redundancy due t the big number f exchanged aut-rganizatin data packets. Hwever, the reductin f the flding rates is imperative in rder t reduce data redundancy and t minimize energy cnsumptin. Fr all these reasns, we devted this paper t the cmmunicatins energy efficiency in WSNs. The main bjective f ur wrk cnsists t develp a WSN aut-rganizatin methd ptimizing the cmmunicatin links between sensrs and reducing the flding rates. Fr that, we used the mathematical Khalimsky thery t cnstruct a gegraphic-hierarchical tplgy [11-15]. This thery permits t calculate the ptimized paths when a sensr need t frward data. Theses paths are frmed by a successin f ndes belnging t an emplyed ptimal set f gateways between a surce and destinatin. 3 WSN Deplyment accrding t Khalimsky Tplgy In this sectin we present the Khalimsky thery and the develped algrithms fr the WSN deplyment and the flding f data packets between the sensrs and the sink. 3.1 Khalimsky thery definitins In what fllws, we present sme terminlgy and definitins necessary fr understanding the results f the Khalimsky tplgy. Cpyright Sciety fr Science and Educatin United Kingdm 27

4 Mahmud Mezghani, Riyadh Garguri and Mahmud Abdellaui; Optimizatin f WSNs Flding Rates by Khalimsky Tplgy, Transactins n Netwrks and Cmmunicatins, Vlume 2 N 6, Dec (2014); pp: Let B = {2nn + 1}; nn Z {2nn 1,2nn, 2nn + 1}; nn Z be a family f subsets f the set f integersz. Then B is a base f a tplgy n Z called the Khalimsky tplgy and dented by Κ. The Khalimsky plane is the Cartesian prduct f tw Khalimsky tplgies (Z, KK) (Z, KK). This tplgy n Z² is characterized as fllws. A pint at its tw crdinates f the frm (2kk; 2kk ) is clsed pint (they are shwn in figure 1 by the black squares), if bth crdinates are f the frm (2kk + 1; 2kk + 1) pint is an pen pint (shwn in the figure 1 by the white squares). These types f pints are called pure pints. Other pints are called mixed pints (presented by tw lines). It is clearly that (Z², kk) is cnnected space [11-15]. Figure 1 shw a cnnectivity graph f the Khalimsky tplgy. Figure 1: Cnnexity graph part f Khalimsky tplgy n Z² Accrding t the Khalimsky tplgy, we define: SS (XXSS,YY SS ): Surce pint. QQ XXQQ,YY QQ : Destinatin pint. AA QQ SS : A digital arc jining the pints SS and QQ. MM QQ SS : A minimal digital arc jining the pints SS and QQ. BBBB(SS, QQ) = MM QQ SS : The whle f minimal digital arcs jining the pints SS and QQ. dd (SS, QQ) = mmmmmm XX QQ XX SS, YY QQ YY SS : The nrm in Z² Accrding t these definitins, we define: SS (XXSS,YY SS ): Surce sensr nde. QQ XXQQ,YY QQ : Destinatin sensr nde. AA SS QQ : A link regruping a set f intermediate sensrs jining tw sensr ndes SS and QQ. MM SS QQ : A minimal link jining the sensr ndes SS and QQ. BBBB(SS, QQ) = MM QQ SS : The whle f minimal link jining the sensr ndes SS and QQ. dd (SS, QQ) : The number f sensrs in the link jining ndes SS and QQ. 3.2 Khalimsky deplyment algrithm Accrding t the previus definitins, ur algrithm permits the deplyment f the gateway sensrs in the cllecting field as the Khalimsky tplgy as shwn in figure 2. The gateway ndes in this tplgy are either pure r mix. Pure ndes have 8 neighbrs and mix ndes have nly 4 neighbrs. Mix ndes cmmunicate with pure ndes nly. The ndes are rganized in levels. The sink SS (0,0) belngs t the level 0 its neighbrs belng t the level 1 and respectively until level n. URL: 28

5 Transactins n Netwrks and Cmmunicatins; Vlume 2, Issue 6, December 2014 Figure 2: Sensrs crdinates assignment in the Khalimsky tplgy T create the tplgy, the sink S (0,0) diffuses a message twards all the ndes in its range t allw the crdinates between them. This message is a structure cmpsed by five variables: IDSender : the identifier f the sender nde, (XSender, YSender): the crdinates f the sender nde, NISender : the level f the sender in the Khalimsky hierarchy, NB: the ndes number in the current level f the sender nde. The NB variable is calculated by the fllwing (UU nn ) : UU UU nn = 0 = 1 UU nn+1 = UU nn + 2 Each nde receiving the message, run the aut-rganizatin algrithm as shwn in the fllwing algrithm t calculate its crdinates f the aut-rganizatin structure, and then diffuses them twards the ndes in its range. (1) 4 Khalimsky Flding Algrithm In rder t avid data redundancy and the prblems due t the implsin and the verlapping caused by the cnventinal flding apprach, we develped a nvel algrithm based n the Khalimsky tplgy which reduces the field f used ndes when a surce sensr Q XQ,Y Q bradcasts data t the sink S (0,0). This field is defined by BL(S, Q) = M Q S the set f ndes frming all minimal links which cnnect the surce nde Q XQ,Y Q t the sink S (0,0). Figure 3 shws BL(S, Q) f a ndes set used when a sensr Q XQ,Y Q bradcasts data t the sink S (0,0). Cpyright Sciety fr Science and Educatin United Kingdm 29

6 Mahmud Mezghani, Riyadh Garguri and Mahmud Abdellaui; Optimizatin f WSNs Flding Rates by Khalimsky Tplgy, Transactins n Netwrks and Cmmunicatins, Vlume 2 N 6, Dec (2014); pp: Figure 3: BBBB(SS, QQ) f ndes belnging minimal paths between QQ XXQQ,YY QQ and SS (00,00) 4.1 BBBB(SS, QQ) Cnstructin Khalimsky tplgy distinguishes five cases t determine the lists f ndes t traverse t frm the minimal paths separating tw ndes Q XQ,Y Q and S (0,0) [11-15]. These ndes are in the zne I; II; III r IV; as well as, n the lines D (Y=X) r D (Y= X) as shwn in figure 4. Figure 4: Minimal path znes in Khalimsky tplgy n Z² In the fllwing, P represents an intermediate sensr nde in the ptimal whle f sensrs jining tw ndes SS (XXSS,YY SS ) and Q XQ,Y Q. Case 1 : If SS is a pure nde and XX QQ XX SS = YY QQ YY SS then Q is a pure nde and P BL(S, Q) X P X S + X Q X p = X Q X S Y P Y S + Y Q Y p = Y Q Y S The set f sensrs jining ndes S (0,0) and Q XQ,Y Q are n the lines D (Y=X)r D (Y= X). (2) Case 2 : If SS is a mixed nde and XX QQ XX SS = YY QQ YY SS then Q is a mixed nde and P BL(S, Q) BL(S, Q) = BL(S 1, Q 1 ) BL(S 2, Q 2 ) {S, Q} (3) With S 1 X S, Y S Y S Y Q Y S Y Q, S 2 X S X S X Q X S X Q, Y S, Q 1 X Q X Q X S X Q X S, Y Q, Q 2 X Q, Y Q Y Q Y S Y S Y Q URL: 30

7 Transactins n Netwrks and Cmmunicatins; Vlume 2, Issue 6, December 2014 When SS (XXSS,YY SS ) and QQ XXQQ,YY QQ area mixed nde, it s necessary t jin tw pure nde frm (SS 1, QQ 1 ) and (SS 2, QQ 2 ) t calculatebbbb(ss, QQ). Then the set f ndes jining SS and QQ is the unin f determined ndes between (SS 1, QQ 1 ) and(ss 2, QQ 2 ), and the ndes SS and QQ as shwn in figure 5. Figure 5: BL (S, Q) when S and Q are mixed ndes Case 3 : If SS and Q are pure ndes and XX SS XX QQ YY SS YY QQ, then there is tw cases : a. If XX SS XX QQ > YY SS YY QQ then X P X S + X Q X p = X Q X S P BL(S, Q) Y P Y S X P X S Y Q Y p X P X Q In this case, the ndes jining SS and Q are in zne I r III as shwn in figure 4. b. If XX SS XX QQ < YY SS YY QQ then Y P Y S + Y Q Y p = Y Q Y S P BL(S, Q) X P X S Y P Y S X Q X p Y P Y Q In this case, the ndes jining SS and Q are in zne II r IV as shwn in figure 4. Case 4 : If SS and Q are nt bth pure ndes r mixed ndes and XX SS XX QQ YY SS YY QQ, then there is tw cases : a. SS is a pure nde and Q is a mixed nde and XX SS XX QQ > YY SS YY QQ, then with P BL(S, Q) P BL(S, Q ) {Q} (6) Q X Q X Q X S X Q X S, Y Q a pure nde as shwn in figure 6. (4) (5) Figure 6: BBBB(SS, QQ) when SS is a pure nde and QQ is a mixed nde and XX SS XX QQ > YY SS YY QQ b. SS is a pure nde and Q is a mixed nde and XX SS XX QQ < YY SS YY QQ, then P BL(S, Q) P BL(S, Q ) {Q} (7) Cpyright Sciety fr Science and Educatin United Kingdm 31

8 Mahmud Mezghani, Riyadh Garguri and Mahmud Abdellaui; Optimizatin f WSNs Flding Rates by Khalimsky Tplgy, Transactins n Netwrks and Cmmunicatins, Vlume 2 N 6, Dec (2014); pp: With Q X Q, Y Q Y Q Y S a pure nde as shwn in figure 7. Y S Y Q Figure 7: BBBB(SS, QQ) when SS is a pure nde and QQ is a mixed nde and XX SS XX QQ < YY SS YY QQ Case 5 : If SS and Q are bth mixed ndes and XX SS XX QQ YY SS YY QQ, then there is tw cases: a. If XX SS XX QQ > YY SS YY QQ, then P BL(S, Q) P BL(S, Q ) {S, Q} (8) With S X S X S X Q X S X Q, Y S and Q X Q X Q X S X S X Q, Y Q are pure ndes as shwn in figure 8. Figure 8: BBBB(SS, QQ) when SS and QQ are bth mixed ndes and XX SS XX QQ > YY SS YY QQ b. If XX SS XX QQ < YY SS YY QQ, then P BL(S, Q) P BL(S, Q ) {S, Q} (9) With S X S, Y S Y Q Y S and Q X Y S Y Q Q, Y Q Y Q Y S are pure ndes as shwn in figure 9. Y S Y Q Figure 8: BBBB(SS, QQ) when SS and QQ are bth mixed ndes and XX SS XX QQ < YY SS YY QQ 4.2 Khalimsky flding algrithm The Khalimsky flding algrithm determines the relay ndes prgressively fr transmitting data packets frm a surce gateway nde Q XQ,Y Q t the sink nde S (0,0) inbl(s, Q). Each nde receiving a package, diffuses it nce twards the ndes which it has calculated their crdinates. Fr URL: 32

9 Transactins n Netwrks and Cmmunicatins; Vlume 2, Issue 6, December 2014 each nde in BL(S, Q), there is ne, tw r three gateway ndes t frward data in each step accrding t the Khalimsky thery as shwn in the figure 9. Figure 9: Khalimsky flding cases f frwarding packets in BBBB(SS, QQ) ; (a): three gateway ndes; (b): tw gateway ndes; (c): ne gateway nde Accrding t the five cases f the Khalimsky thery, in the previus subsectin, we have develped the fllwing flding algrithm which permits t calculate the BL(S, Q) and the gateway ndes, hpe by hpe, in the prcess f data transmissin. Algrithm 2: Khalimsky flding algrithm Cpyright Sciety fr Science and Educatin United Kingdm 33

10 Mahmud Mezghani, Riyadh Garguri and Mahmud Abdellaui; Optimizatin f WSNs Flding Rates by Khalimsky Tplgy, Transactins n Netwrks and Cmmunicatins, Vlume 2 N 6, Dec (2014); pp: Simulatin results T evaluate the perfrmance f the Khalimsky thery applied n the WSNs area, we used the TOSSIM simulatr. We simulated a WSN cmpsed f 50 MicaZ sensrs where the energy cnsumptin is mdeled by the PwerTOSSIM-Z plugin, cmpatible with TinyOS2.1, fr each nde [5-7]. The sensrs are deplyed hierarchically and unifrmly accrding t the Khalimsky architecture in a sectr f the plane, with a sink placed at the center f the sectr as shwn in figure 2. This tplgy is defined in a specific file that we called ''tplgy.txt'' in TOSSIM t cnfigure the links and adjacency lists between the simulated sensrs as shwn in figure 10. This file defines the gain in the 4 th clumn between the surce nde in the 2 ed clumn and the destinatin nde in the 3 rd clumn. Figure 10: extract f tplgy file cnfiguratin in TOSSIM simulatr T launch the simulatin we have develped a prgram file written in the Pythn language. This prgram is used t lad entities, representing the sensrs in the cmputer memry as the Khalimsky tplgy file previusly created, t apply nise mdel and t bt sensrs starting with the Sink. Figure 11 shws an extract f the Pythn prgram that we used t run the simulatin. This extract cntains three parts. The first part allws the lading f the tplgy file previusly created. The secnd part cncerns the applicatin f the nise mdel and the start sensr ndes. The third sectin determines the time f simulatin and run each prgram f sensrs. Figure 11: Extract f Pythn prgram running the simulatin When TOSSIM run simulatin, each bted sensr nde run the aut-rganizatin algrithm that we develped in algrithm 1 t calculate its crdinates. Figure 12 shws a part f the result f the URL: 34

11 Transactins n Netwrks and Cmmunicatins; Vlume 2, Issue 6, December 2014 executin f this algrithm fr several sensrs. It shws the sensr ID in TOSSIM, the calculated crdinates and the mment f reaching. Figure 12: Aut-rganizatin algrithm results The last part f the Pythn prgram cnsists t run the prgram f each simulated sensr accrding t the Khalimsky thery. Each sensr has a timer that rganizes these tasks. These tasks are called evenements. The main activities f a sensr are the data cllecting frm its envirnment and the ruting f created and received packets. Figure 13 shws a part f the executin result f the ruted packet by Khalimsky flding algrithm frm the nde 31 via the nde 20 t the Sink. The nde 20, after calculating the destinatin nde selects the nde 12 t pass the received packet. It is the case 1 in Khalimsky flding algrithm since the nde 20 is a pure nde and its crdinates are x= y = 4. Figure 13: Result part f Khalimsky flding algrithm simulatin Well TOSSIM simulatr that can simulate a WSN, it is nt pssible t mdel the energy cnsumptin. PwerTOSSIM-Z is a plugin cmpatible with TinyOS2.1 used t mdel the energy cnsumptin f each sensr. It uses the results prvided by TOSSIM t determine the energy cnsumed by the sensr ndes. Figure 14 shws the ttal cnsumed energy by the nde 36 and the simulated time. It shws als the energy cnsumed by the different cmpnents in the nde when it's pssible t ignre amng them. All ndes have the same pwer mJ when starting the simulatin. Figure 14: PwerTOSSIM-Z energy mdeling results part In the fllwing, ur evaluatin is based n cmparing the flding rates and the energy cnsumptin f cnventinal flding algrithm versus Khalimsky flding algrithm by the analysis f result files generated by TOSSIM simulatr and PwerTOSSIM-Z as shwn in Figure 14. Cpyright Sciety fr Science and Educatin United Kingdm 35

12 Mahmud Mezghani, Riyadh Garguri and Mahmud Abdellaui; Optimizatin f WSNs Flding Rates by Khalimsky Tplgy, Transactins n Netwrks and Cmmunicatins, Vlume 2 N 6, Dec (2014); pp: Figure 15 shws the flding rates values f cnventinal flding algrithm versus Khalimsky flding algrithm. At the beginning the tw algrithms have the same values f the flding rates. After 11 hurs, the cnventinal flding algrithm attains transmissins while the Khalimsky flding algrithm makes transmissins. After 23 hurs, the cnventinal flding algrithm attains transmissins while the Khalimsky flding algrithm makes transmissins. Figure 15: Flding rates Accrding t the btained results, we dente that the Khalimsky tplgy allwed reducing the flding rates t abut 31%. Figure 16 shws the energy cnsumptin difference between cnventinal flding algrithm and Khalimsky flding algrithm. The amunt f dissipated energy applying the Khalimsky thery is very lwer than the secnd algrithm. At the beginning all ndes have mJ. After 11 hurs, in the cnventinal flding algrithm the cnsumed energy attain mJ while in the Khalimsky flding algrithm the value is mJ. After 23 hurs, the cnventinal flding algrithm makes mJ when the Khalimsky flding algrithm des nt exceed mJ. Figure 16: Flding pwer cnsumptin results Accrding t the pwer cnsumptin btained results, we dente that the energy cnsumptin average gain btained after 11 hurs is abut 50% but after 23 hurs is abut 75%. We deduct frm the tw figures figure 15 and figure 16 an imprtant gap between the red and the blue curves (representing the energy cnsumptin and the flding rates f Khalimsky flding algrithm and the cnventinal flding apprach). The Khalimsky tplgy reduces the links URL: 36

13 Transactins n Netwrks and Cmmunicatins; Vlume 2, Issue 6, December 2014 between sensrs. When a nde sends a data packet by flding, the number f used sensrs determined by Khalimsky thery is limited by ndes frming ptimal paths as shwn in figure 3. 6 Advantages & Future Wrks Our slutin fr deplying a WSN based n the tplgy f Khalimsky can be applied effectively in many areas such as dmtic field and industrial field, fr mnitring and building security f infrastructures and industrial areas against fires, gas leakage and pllutin. In these areas, it is necessary t deply fixed ndes acting as gateways t cnvey the data ruting tward base statin. These gateways prvide the transfer f data cllected by sensrs members gruped int clusters t the base statin. The cllected data can be imprtant and have a real-time aspect. In this case, the data must be transmitted t the base statin in a safe and immediately manner. S with ur flding slutin, based n the Khalimsky thery, it s pssible t perfrm the tasks in an ptimal way with minimal data redundancy and the minimum cnsumed energy. Fr future wrks, we have used the Khalimsky thery t develp a ruting prtcl fr WSNs, based n the clustering methd and the multi-agent systems. These WSNs may cntain sensrs randmly deplyed and prefixed sensrs acting as gateway. The randmly deplyed sensrs are gruped int clusters. Each cluster must be able t reach ne r mre gateways. Gateway sensrs are deplyed accrding t the Khalimsky tplgy. The simulatin tests, in the prcess, shwed encuraging results. 7 Cnclusin In this paper, we have been develped a nvel hierarchical tplgy fr WSNs based n mathematical Khalimsky thery. This methd calculates a subset f ndes t use as gateways fr rting data between a surce nde and a destinatin nde. This subset f these ndes includes all ptimal paths. Hwever, a diffused data packet by a nde will never g thrugh utside this subset. This implies the reductin f the flding rates in a WSN. Thereafter, a cnsiderable minimizatin f the energy cnsumptin is dented. This methd was validated by a simulatin f a WSN using TOSSIM and PwerTssim-Z in TinyOS2.1 that allws the energy cnsumptin mdeling. The Khalimsky prtcl has a great capacity f energy cnservatin and f flding rates reductin. Fllwing these simulatins, we clearly nte the ptimality and the effectiveness f the Khalimsky flding algrithm cmpared t the cnventinal flding algrithm in term f energy cnsumptin and flding rates. REFERENCES [1]. M. Mezghani, G. Elluze, A. Grati, I. Buabidi, M. Abdellaui, Multitasks-Generic platfrm via WSN. Internatinal Jurnal f Distributed and Parallel Systems (IJDPS), Vl.2, N.4, July 2011, p [2]. A. Nayak, I. Stjmenvic,Wireless Sensr and Actuatr Netwrks: algrithms and prtcls fr scalable crdinatin and data cmmunicatin. WILEY series, 2010, chapter 4 and 5, p [3]. G. Anastasi, M. Cnti, M. Di Francesc, A. Passarella,Energy cnservatin in wireless sensr netwrks: A survey, Ad Hc Netwrks,7 (2009), p [4]. Y. Yussef, Rutage pur la gestin de l'energie dans les réseaux de capteurs sans fil. These de dctrat, Haute Alsace-France, Juillet Cpyright Sciety fr Science and Educatin United Kingdm 37

14 Mahmud Mezghani, Riyadh Garguri and Mahmud Abdellaui; Optimizatin f WSNs Flding Rates by Khalimsky Tplgy, Transactins n Netwrks and Cmmunicatins, Vlume 2 N 6, Dec (2014); pp: [5]. M. Mezghani, O. Mezghani, H. Rekik, M. Abdellaui, TinyOS2.1 with nesc, TOSSIM and PwerTOSSIM-Z Emulatin and Simulatin Envirnments t Netwrked Dmtic Embedded Systems.12th Internatinal cnference n Sciences and Techniques f Autmatic cntrl and cmputer engineering (STA2011), December 18-20, 2011, Susse, Tunisia. [6]. E. Perla, A. O. Cathain, R. S. Carbaj, PwerTOSSIM-z: Realistic Energy Mdelling fr Wireless Sensr Netwrk Envirnments. Prceedings f the 3nd ACM wrkshp n Perfrmance mnitring and measurement f hetergeneus wireless and wired netwrks, Octber 31, 2008, Vancuver, BC, Canada, p [7]. P. Levis, D. Gay, TinyOS prgramming. Cambridge University Press, 2009, p [8]. M. Hadjila, M. Fehman, A cmparative study f the wireless sensr netwrks ruting prtcls scalability. Internatinal Jurnal f Distributed and Parallel Systems (IJDPS), Vl.2, N.4, July 2011, p [9]. K. Beydun, Cnceptin d'un prtcle de rutage hiérarchique pur les réseaux de capteurs. Thèse de dctrat, Franche-Cmte-France, Décembre [10]. M. Lehsaini, Diffusin et cuverture basées sur le clustering dans les réseaux de capteurs : aplicatin à la dmtique. Thèse de dctrat, Franche-Cmte-France, Juillet [11]. E. Buacida, The jrdan curve therem in the Khalimsky plane, Applied General Tplgy 9, 252 (2008). [12]. U. Eckhardt, L.J. Latecki, Tplgies fr the digital spaces Z2 and Z3. Cmput. Visin Image Understanding, 90 (2003), p [13]. E.D. Khalimsky, On tplgies f generalized segments. Sviet Math. Dkl., 10 (1999), p [14]. E.D. Khalimsky, R. Kpperman, P.R. Meyer, Bundaries in digital planes. J. Appl. Math. Stch. Anal. 3 (1990), p [15]. E. Khalimsky, R. Kpperman, P. R. Meyer, Cmputer graphics and cnnected tplgies n finite rdered sets.tpl. Appl. 36, 1 (1990). URL: 38