The Balanced Cross-Layer Design Routing Algorithm in Wireless Sensor Networks Using Fuzzy Logic

Transcription

1 Sesors 205, 5, ; do:0.3390/s Artcle OPEN ACCESS sesors ISSN The Balaced Cross-Layer Desg Routg Algorthm Wreless Sesor Networks Usg Fuzzy Logc Ng L *, José-Ferá Martíez ad Vcete Herádez Díaz Cetro de Ivestgacó e Tecologías Software y Sstemal Multmeda para la Sostebldad (CITSEM), Campus Sur Uversdad Plotécca de Madrd (UPM), Madrd 2803, Spa; E-Mals: jfmart@datel.upm.es (J.-F.M.); vheradez@datel.upm.es (V.H.D.); * Author to whom correspodece should be addressed; E-Mal: l.g@upm.es; Tel.: ; Fax: Academc Edtor: Leohard M. Redl Receved: 0 Jue 205 / Accepted: 5 August 205 / Publshed: 0 August 205 Abstract: Recetly, the cross-layer desg for the wreless sesor etwork commucato protocol has become more ad more mportat ad popular. Cosderg the dsadvatages of the tradtoal cross-layer routg algorthms, ths paper we propose a ew fuzzy logc-based routg algorthm, amed the Balaced Cross-layer Fuzzy Logc (BCFL) routg algorthm. I BCFL, we use the cross-layer parameters dsperso as the fuzzy logc ferece system puts. Moreover, we gve each cross-layer parameter a dyamc weght accordg the value of the dsperso. For gettg a balaced soluto, the parameter whose dsperso s large wll have small weght, ad vce versa. I order to compare t wth the tradtoal cross-layer routg algorthms, BCFL s evaluated through extesve smulatos. The smulato results show that the ew routg algorthm ca hadle the multple costrats wthout creasg the complexty of the algorthm ad ca acheve the most balaced performace o selectg the ext hop relay ode. Moreover, the Balaced Cross-layer Fuzzy Logc routg algorthm ca adapt to the dyamc chagg of the etwork codtos ad topology effectvely. Keywords: cross-layer desg; routg algorthm; fuzzy logc; balaced performace; dyamc weght

2 Sesors 205, Itroducto I recet years, the wreless sesor etwork routg protocol has bee studed wdely. May excellet routg protocols have bee proposed, such as AODV [], DSR [2], DSDV [3], etc. However, as the research moves alog, more ad more researchers realze that the tradtoal Ope System Itercoect Referece Model (OSI) caot meet the curret qualty of servce (QoS) requremets of a wreless sesor etwork; eve the OSI model smplfes the etwork desg ad mproves the robustess. The reasos for ths ssue are, frstly, the wreless sesor etwork s a serous resource-costraed etwork [4], e.g., the lmted badwdth, the lmted eergy, the lmted data processg capablty, etc. Secodly, the OSI model oly allows the commucato betwee the adjacet layers, whch caot adapt to the dyamc chagg of the wreless evromet flexbly. Recetly, the research proposes a cross-layer method for wreless sesor etwork commucato protocol desg, ad may cross-layer methods have bee proposed [5,6]. The cross-layer desg allows the dfferet layers to commucate wth each other to coordate the resource allocato betwee dfferet layers, ad allows the routg protocols to adapt to the wreless evromet ad the varous applcatos. The core dea of the cross-layer desg s to acheve the optmal resource allocato automatcally dfferet layers. The cross-layer desg s flexble due to ts adaptve ablty to adjust to meet the QoS requremets ad the etwork costrats at the same tme. Amog varous dfferet developed polces, two mportat methods are the optmzato-based routg algorthm ad the fuzzy logc-based routg algorthm. For the optmzato-based routg algorthm, e.g., [7], the authors propose the Delay-Aware cross-layer desg for etwork utlty maxmzato mult-hop etworks; [8], the authors troduce a ew cross-layer desg framework whch jo the schedulg ad power cotrol together; [9], the authors show the optmzato method a cross-layer desg of the wreless etwork; [0], the authors preset a survey of cross-layer solutos based o the ature of the adaptato usg a systematc evaluato of exstg approaches ad detfy crtcal crtera applcable to geerc cross-layer framework desg. I [ 4], the authors research the layerg as optmzato decomposto, detal, cludg the problems, the curret status, the ope ssues, the mathematcs, the etwork archtectures, ad the framework; more recet works ca be see [5 8]. For the fuzzy logc-based routg algorthm, e.g., [9], the authors take the remag battery reserve capacty, the lk qualty, ad trasmsso power to cosderato, by usg the fuzzy logc ferece system to determe the ext hop relay ode. I [20], the authors use the umber of lk breaks, the terface queue legth, ad the type of applcato as the puts of the fuzzy logc system to eable each moble ode to separately swtch betwee a reactve routg mode ad a proactve routg mode. I [2], the authors use a fuzzy logc system to coordate the physcal layer, data-lk layer, ad applcato layer for cross-layer desg; the groud speed, average delay, ad packets successful trasmsso rato are selected as atecedets for the fuzzy logc system. More related works ca be foud [22 26]. However, the recet works also have some dsadvatages. Frst, both of the two types of routg algorthms metoed above wll become extremely complex whe the umber of costrats creases, whch s uacceptable a wreless sesor etwork as the computato capablty of a ode s lmted. Secod, due to the complexty, they have lmted ablty to deal wth the ssue of multple costrats. Thrd, they caot adapt to the dyamc chagg of the etwork codtos,.e., whe the

3 Sesors 205, costrat or the topology chages, the routg algorthm eeds to be redesged [27], whch s ot flexble the moble wreless etwork. Fourth, all these two types of routg algorthms are cocetrated o the specfc aspect of the etwork performace (such as the cogesto, the eergy cosumpto, or the throughput), so they caot acheve the balaced performace of the etwork. Motvated by ths, ths paper, we propose a ew fuzzy logc-based routg algorthm, amed the Balaced Cross-layer Fuzzy Logc (BCFL) routg algorthm To the best of our kowledge, BCFL s the frst that troduces the dsperso to the fuzzy logc-based routg algorthm stead of the absolute cross-layer parameter values as the fuzzy logc ferece system puts (whch s dfferet wth the tradtoal fuzzy logc-based routg algorthm, such as the routg algorthms dscussed [9 2], etc.), the frst settg every cross-layer parameter a dyamc weght, ad also the frst that proposes the dsperso formula. Based o these ovatos, the BCFL wll acheve better performace tha the tradtoal routg algorthms metoed above. We lear the propertes of BCFL ad compare the performace of BCFL wth the tradtoal fuzzy logc-based routg algorthm (the algorthm used [9,20]) ad the optmzato-based routg algorthm (the algorthm used [9]). The smulato results also show that the BCFL has better performace o selectg the ext hop relay ode tha the other two algorthms. Moreover, the complexty of BCFL s much less tha the other two algorthms. Fally, we apply the BCFL a multple costrats scearo; the result shows that the BCFL ca deal wth the multple costrats perfectly. The advatages of BCFL are: the umber of f-the rules wll keep costat whe the umber of cross layer parameters crease; the BCFL has the capablty to hadle multple costrats wthout creasg the complexty of the algorthm; we gve each parameter a dyamc weght, whch ca dyamcally chage accordg to the etwork codtos; as we use the dsperso of each cross-layer parameter as the put, whe the etwork codto chages, the f-the rules wll rema stable; therefore, we do ot eed redesg the f-the rules; BCFL, the large dsperso parameter has a small weght ad the small dsperso parameter has a large weght, whch ca decrease the fluece of the parameters whose dsperso are large ad obta a more balaced soluto. The rest of ths paper assgmet s as follows. I Secto 2, we troduce the related works about the fuzzy logc-based cross layer routg algorthms. I Secto 3, we wll state the problem ad troduce the otatos ad the deftos that we wll use ths paper. I Secto 4, we troduce the prcple of the Balaced Cross-layer Fuzzy Logc routg algorthm. I Secto 5, we compare the performace of the BCFL wth the optmzato-based algorthm ad fuzzy logc-based routg algorthm, ad talk about the performace a multple costrats scearo. I Secto 6, we wll dscuss the cocluso ad talk about the future developmet of BCFL.

4 Sesors 205, Related Works Due to the excellet propertes of the fuzzy logc-based method, may fuzzy logc-based routg protocols have bee proposed recet years. I ths secto, we wll troduce these routg algorthms brefly. The fuzzy logc-based method s effectve routg selecto ad cluster header selecto, whch s show as follows. 2.. The Fuzzy Logc-Based Algorthm Used Routg Selecto I [9], the authors propose a eergy-effectve cross-layer routg protocol for wreless sesor etworks based o fuzzy logc. I ths protocol, for mmzg the cosumed eergy ad maxmzg the etwork lfetme, the algorthm takes the remag battery reserve capacty, the lk qualty, ad the trasmsso power of the eghbor odes to cosderato to select the ext hop relay odes, dyamcally. I [20], for reducg the average ed-to-ed delay of the moble ad hoc etwork, the authors propose a fuzzy logc-based adaptve cross-layer routg protocol for the delay-sestve applcatos. I ths algorthm, each ode ca swtch betwee reactve routg mode ad proactve routg mode based o the curret ode status separately. The algorthm uses the fuzzy logc cotroller to decde the routg model of each ode. The puts of the fuzzy logc cotroller are the umber of lk breaks, the terface queue legth, ad the type of applcato for each ode. I [26], the authors troduce a ew routg algorthm for the wreless sesor etwork to exted the etwork lfetme ad balace the eergy cosumpto by combg the fuzzy approach ad the A-star algorthm together. I ths algorthm, the remag battery power, the umber of hops to the destato ode, ad the traffc loads are take to cosderato to determe a optmal routg path from the source ode to the destato ode. I [28], to prolog the lfetme of the wreless sesor etwork, a fuzzy logc-based eergy-optmzato routg protocol s proposed. I ths algorthm, the socal welfare fucto s used to predct equalty of resdual eergy of eghbor odes after selectg dfferet ext hop odes. The algorthm computes the degree of eergy balace based o the eergy equalty. The fuzzy logc system uses the degree of ode closeess to the shortest path, the degree of ode closeess to sk, ad the degree of eergy balace to acheve the routg decso. Addtoally, [29], the ode desty, the delay, ad the umber of dead odes are the puts of the fuzzy logc system to select the ext hop relay ode to acheve the balaced eergy cosumpto across all of the sesor odes wth mmum delay. More related works ca also be foud [30 33] The Fuzzy Logc-Based Algorthm Used Cluster Head Selecto I [34], the author proposes a eergy-aware dstrbuted dyamc clusterg protocol (ECPF). I ECPF, the o-probablstc cluster head selecto s mplemeted by troducg a delay versely proportoal to the resdual eergy of each ode. Based o ths, the cluster heads are selected accordg ther remag eergy. The fuzzy logc s used to evaluate the ftess of a ode to choose a fal cluster head from the eghbor cluster heads. The puts of the fuzzy logc system are the ode degree ad the ode cetralty. I [35], the authors propose a fuzzy logc-based eergy-effcet multple cluster head selecto routg protocol for the wreless sesor etworks. I ths algorthm, the dstace from the base stato ad the resdual eergy are the puts of the fuzzy logc system to decde

5 Sesors 205, the possblty of the ode to be the cluster head. I [25], cosderg the expected resdual eergy, the authors propose the fuzzy logc-based clusterg approach wth a exteso to the eergy predcato to prolog the lfetme of the wreless sesor etwork. I ths algorthm, the resdual eergy ad the expected resdual eergy are the puts of the fuzzy logc system, ad the output s the chace of the ode to be the cluster head. The ew algorthm selects the cluster head cosderg the expected resdual eergy of the sesor odes. More papers o the fuzzy logc-based cluster head selecto algorthm ca be foud [36 39]. 3. Problem Statemet I ths secto, we wll state the problem we eed to solve ths paper ad troduce the otatos ad the basc deftos that wll be used throughout the paper. Cosderg the dsadvatages (whch have bee dscussed Secto ) tradtoal cross-layer routg algorthms, for the ew routg algorthm, the more cross-layer parameters we ca get from other layers, the better the performace of the algorthm [6,40]. I addto, we should ote the fact that hghlghtg oe aspect of performace of the etwork may have mpact o other aspects. Sce the etwork costrats are ot solated, they ca teract ad fluece each other. I the routg algorthm desg, for gettg a more balaced ad effectve soluto, we should take as may cross-layer parameters to cosderato as possble. To ths ssue, the ew routg algorthm should have the ablty to hadle multple costrats ad, furthermore, ot crease the complexty of the algorthm. The ma goal of ths paper s to desg a ew routg algorthm whch has the propertes as follows: () the calculato wll ot serously crease wth the creased umber of costrats; (2) the algorthm ca hadle as may cross-layer costrats as possble; (3) the algorthm should have the ablty to adapt to the dyamc chagg of the etwork codtos ad topology, especally the uderwater wreless sesor etwork whch the etwork codtos ad topology chage frequetly; ad (4) the algorthm should acheve the balaced performace o selectg ext hop relay ode. The otatos ad basc deftos that wll be used throughout the paper are ow troduced. v v v v v x : The sequece umber of dfferet cross-layer parameter; : The sequece umber of dfferet odes; α : The weght of dfferet cross-layer parameter; α : The weght matrx; : The cross-layer parameter matrx of parameter ; : The cross-layer parameter of ode ; D : The dsperso of parameter ; D : The dsperso matrx; ad U : The utlty of ode ; Defto : The weght matrx α s the set of dfferet cross-layer parameter weghts ad ca be expressed as: [ ] α= α, α2, α3,, α ()

6 Sesors 205, Defto 2: The cross-layer parameter matrx s the set of cross-layer parameters that are obtaed from ode, ad ca be expressed as: T 2 3 =,,,, (2) Defto 3: The dsperso s used to decde the scatter of dfferet cross-layer parameters; the dsperso matrx D ; s the mea of the cross-layer parameters from dfferet odes. D ad D ca be expressed as: D = ( )/ [,,,, ] T D= D D D D (4) (3) Defto 4: The utlty of ode s used to decde the order of the eghbor odes to be the ext hop relay ode, ad ca be expressed as: U =α (5) The object of BCFL s to calculate the value of U ad chose the most sutable ext hop relay ode accordg to U. 4. The Prcple of the Balaced Cross-Layer Fuzzy Logc Routg Algorthm I ths secto, we wll troduce the prcple of the Balaced Cross-layer Fuzzy Logc routg algorthm detal. The prcple of BCFL s show Fgure. Frst, the source ode collects the cross-layer parameters from ts eghbor odes ad calculates the dsperso D of each parameter. Whe the source ode gets the dsperso D, D wll be putted to the fuzzy logc ferece system to decde the weghts α. Fally, as show Equato (5), α ad wll be used to calculate the utlty of each ode, whch s the referece to decde whch eghbor ode wll be the best ext hop relay ode. D α D() U () U 4.. The Calculato of the Dsperso Fgure. The prcple of the BCFL. Whe the source ode wats to sed packets, t wll collect the cross-layer parameters from ts eghbor odes. After that, the source ode wll beg the pre-processg for the cross-layer parameters. The reaso why the source ode eeds to do pre-processg to the cross-layer parameters s show as follows.

7 Sesors 205, As we kow, the cross-layer parameters of dfferet layers are varable,.e., the order-of-magtudes are dfferet. For stace, as dscussed Secto 2, the dstace to the base stato s 000 m, the umber of lk breaks s 5, the terface queue legth s 20, the remag battery power s 50%, the umber of hops to the destato ode s 0, etc. The orders of magtude of these parameters are dfferet; f we utlze these parameters drectly, there wll be some problems. Cosder the parameters show Table. Table. The raw data. Node Node 2 Node I Table, we ca fd that the parameter s much larger tha others. By meas of the Balaced Cross-layer Fuzzy Logc routg algorthm, we ca get the weghts of each parameter that s show Table ; the weghts are show Table 2. Table 2. The weght of the parameters. 2 3 α Cosderg Equato (5), for the data Table, the utltes of ode, ode 2, ad ode 3 are , , ad 507, respectvely. As a result, ode 3 wll be chose as the ext hop relay ode. However, accordg the value of the parameters Table, we ca coclude that ode 3 s ot the best caddate as the ext hop relay ode. For provg ths, we utlze the tradtoal fuzzy logc-based routg algorthm (used [8,9]) to choose the best ext hop relay ode, wth the result show Fgure 2a. Fgure 2a demostrates that ode 2 rather tha ode 3 s the best ext hop relay ode. The reaso of ths ssue s that the parameters Table are ot the same orders of magtude, so the parameters whose orders of magtude are much hgher wll have greater effects o the fal result of BCFL. For addressg ths problem, the ew algorthm, we trasfer all the cross-layer parameters to the same orders of magtude, whch are show Table 3. The dspersos of the parameters Table 2 are the same as that Table (ths s also the reaso why we use Equato (3) stead of the varace formula to calculate the parameters dsperso, because the varaces Table are dfferet wth that Table 2; the result of Equato (3) has othg to do wth the order of magtude), thus the parameters weghts are the same, too. Table 3. The data after pre-processg. Node Node 2 Node

8 Sesors 205, Fgure 2b shows the result of the BCFL that uses the parameters show Table 2. Fgure 2b llustrates that ode 2 wll be the best ext hop relay ode, whch s the same wth the tradtoal fuzzy logc based routg algorthm show Fgure 2a. The values of utlty Utlty The value of parameter ad utlty Parameter Parameter 2 Parameter 3 Utlty ode ode2 ode3 The odes (a) 0 ode ode2 ode3 The parameter dstrbuto of dfferet odes (b) Fgure 2. (a) The result of the tradtoal fuzzy logc-based algorthm (used [9,20]) wth the raw data; (b) The result of the ew routg algorthm wth the data Table 2. Therefore, we ca coclude that the dea that settg all the cross-layer parameters to the same order of magtude s a approprate ad effectve method. I terms of ths cocluso, more geerally, we ca use the umbers betwee 0 ad to represet the cross-layer parameters. Oce the pre-processg of the cross-layer parameters s fshed, we ca apply Equato (3) to calculate the parameter dsperso. Furthermore, the dspersos wll be used as the fuzzy ferece system puts The Desg of the Fuzzy Logc Iferece System Fuzzy logc has the advatages of easy mplemetato, robustess, ad ablty to approxmate to ay olear mappg [4,42]. It s relatvely smple to covert kowledge of doma experts to cotrol algorthms. The desg of a fuzzy-logc cotroller starts wth costructg the membershp fuctos for lgustc put/output ad f-the rules. I BCFL, the put of the fuzzy logc ferece system s the parameter dsperso ad the output s the cross-layer parameter weght. The ew fuzzy logc ferece system s a sgle put-sgle output system, whch s show Fgure 3. I the rest of ths secto, we wll troduce the membershp fuctos ad the f-the rules of BCFL detal. The put ad output membershp fuctos are show Fgure 4, ad the f-the rules are show Table 4. The lgustc varables of put ad output are: very small (vsmall), medum small (msmall), small, medum, large, medum large (mlarge), very large (vlarge), whch are show Table 4. As show Table 4, the large dsperso has small weght ad the small dsperso has large weght. The reaso s that the parameter whose dsperso s large wll have a greater effect o the algorthm performace; however, the BCFL, we ted to get the most balaced soluto, so ths stuato should be avoded as much as possble. Therefore, the ew routg algorthm, the larger the dsperso s, the smaller value of α.

9 Sesors 205, D α Fgure 3. The prcple of the fuzzy ferece system. vsmall msmall small m large mlarge vlarge vsmall msmall small m large mlarge vlarge Degree of membershp Degree of membershp put (a) output (b) Fgure 4. (a) The membershp fucto of put; (b) The membershp fucto of output. Table 4. The fuzzy f-the rules of BCFL. Iput ( D ) Very small Medum small Small Medum Large Medum large Very large Output ( α ) Very large Medum large Large Medum Small Medum small Very small From Fgure 4 ad Table 4, we ca coclude that the f-the rules ad membershp fuctos wll keep costat eve whe the etwork codto ad topology chage; moreover, the f-the rules are very smple ths algorthm. The BCFL s easy to desg ad s robust. O the cotrary, the tradtoal fuzzy logc-based routg algorthm (the algorthm used [8,9]), the f-the rules wll become uacceptable wth the creasg fluece of the parameters. I addto, whe the etwork codto or the topology chages, the f-the rules eed to be redesged, whch s ot flexble. Oce puttg the parameters dsperso to the fuzzy logc system, the fuzzy logc ferece wll set the weghts for each parameter based o the dsperso, whch wll be used to calculate the utlty of each ode The Calculato of the Utlty of Each Node The utlty s used to decde the order of the eghbor odes to be the ext hop relay ode. Whe we get the weghts from the fuzzy logc ferece system, we ca use Equato (5) to calculate the utlty of each ode.

10 Sesors 205, As defed Secto 2, the utlty of ode ca be expressed as: U =α +α2 2+α3 3+ +α (6) where represets the cross-layer parameters (such as the dstace to the base stato, the umber of lk breaks, the terface queue legth, the remag battery power, the umber of hops to the destato ode, etc.) of ode ; α s the dfferet parameter weght, whch ca be obtaed from Secto 4.2. The process of BCFL s show as follows: Algorthm The proposed fuzzy logc based routg algorthm (BCFL) Iput: : The cross-layer parameters from ode ; : The threshold of the cross-layer parameters; th Output: NR : The rak of the eghbor ode to be the ext hop relay ode; Fucto: Dsperso( ): The fucto to calculate the dsperso of the cross-layer parameters; Fuzzylogc( D ): The fuzzy logc ferece fucto to calculate the weght of each cross-layer parameters; Utlty(, α ): The fucto to calculate the utlty of each ode; Probablty( U ): The fucto to decde the rak of the eghbor ode to be the ext hop relay ode; Italzato: Routedscovery=0; Nodestatus==false; Ma: Whle Routedscovery= do Broad hello message to eghbor odes; For cross-layer parameters receved from other odes, store these parameters; f ( th) Nodestatus true; else f ( < th) Nodestatus false; ed f whle Nodestatus==true do D Dsperso( ); α Fuzzylogc( D ); U Utlty(, α ); NR Probablty( U ); ed whle ed whle

11 Sesors 205, Performace Evaluato I ths secto, we wll dscuss the propertes ad the performace of the BCFL detal. Durg the smulato Sectos 5. ad 5.2, geerally, we do ot specfy the cross-layer parameters (, 2, 3,, ) to the specfc factors (such as the dstace to the base stato, the umber of lk breaks, the terface queue legth, the remag battery power, the umber of hops to the destato ode, etc.); we use the radom umber sequece (from 0 to ) to represet the value of the cross-layer factors (whch has bee prove Secto 4. that ths method s approprate ad effectve). I Secto 5., we wll compare the performace of the BCFL wth the tradtoal fuzzy logc-based routg algorthm ad the optmzato-based routg algorthm; Secto 5.2, we wll show the performace of the BCFL uder multple costrats. 5.. The Performace of BCFL Compared wth the Tradtoal Routg Algorthm I ths part, we compare the performace of the BCFL wth the tradtoal fuzzy logc routg algorthm (used [9,20]) ad the optmzato-based routg algorthm (used [9]), respectvely. I vew of that the tradtoal fuzzy logc routg algorthm, the optmzato-based routg algorthm has lmted capablty to hadle multple costrats, so the smulato of ths part, we oly cosder three costrats the algorthm. As dscussed Secto 4, we use the fucto rad() MATLAB to geerate the cross-layer parameters. The parameters are show Table 5. Table 5. The cross-layer parameters. Node Node 2 Node 3 Node 4 Node Fgure 5a,b demostrate that the ew routg algorthm ca come to the smlar cocluso wth the tradtoal fuzzy logc-based routg algorthm: the best ext hop relay ode s ode ; the performace of ode 3, ode 4, ad ode 5 are alke; ad ode 2 has the worst performace of these fve odes. The result also proves that the BCFL s effectve ad balaced. As show Fgure 5a, the le graph of dsperso llustrates that the parameters ode have the smallest dsperso; the dsperso of ode 3 ad ode 5 are smlar ad all larger tha ode ; ode 2 ad ode 4 have the largest parameter dsperso. Ths le graph s cosstet wth the le graph of utlty Fgure 5a (the ode whose parameter dsperso s small wll have large utlty). For the utlty Fgure 5a, ode s the largest, ode 3 ad ode 5 are alke ad they are the medum. Note that eve ode 2 ad ode 4 have the smlar parameter dsperso, but sce the parameters ode 2 are too small, the the utlty of ode 4 s greater tha ode 2. Therefore, the ew routg algorthm ca ot oly cosder the balace but also the effectveess of the etwork performace. Note that the dsperso show Fgure 5a s dfferet wth the dsperso that s expressed Defto 3. The dsperso Defto 3 meas the dfferece betwee the same cross-layer parameters from dfferet odes, e.g., the parameters, 2, 3,, (the parameter from ode,

12 Sesors 205, ode 2,, ode ). The dsperso show Fgure 5a meas the dfferece of dfferet cross-layer parameters of the same ode, e.g., the parameters, 2, 3,, (the parameter, parameter 2,, parameter from ode ). Thus, the parameter dsperso show Fgure 5a ca represet the balace of odes. The value of parameter, utlty ad dsperso Parameter Parameter 2 Parameter 3 Utlty Dsperso The value of parameters ad utlty Parameter Parameter 2 Parameter 3 Utlty 0 ode ode2 ode3 ode4 ode5 The parameter dstrbuto of dfferet odes (a) The value of parameters ad utlty ode ode2 ode3 ode4 ode5 The parameter dstrbuto of dfferet odes (b) Parameter Parameter 2 Parameter 3 Utlty ode ode2 ode3 ode4 ode5 The parameter dstrbuto of dfferet odes (c) Fgure 5. (a) The result of the BCFL; (b) The result of the tradtoal fuzzy logc-based routg algorthm (the algorthm used [9,20]); (c) The result of the optmzato-based routg algorthm (the algorthm used [9]). I Fgure 5b, the utlty of ode 4 s larger tha ode 5; however, as show Fgure 5a, the parameter dsperso of ode 5 s smaller tha ode 4. Cosderg the parameter s value ad the parameter dsperso of these two odes, we ca coclude that ode 5 s more approprate as the ext hop relay ode tha ode 4. O ths pot, the Fgure 5a,b prove that the BCFL ca get a more balaced performace tha the tradtoal fuzzy logc routg algorthm.

13 Sesors 205, The Fgure 5c shows the result of optmzato-based routg algorthm. I Fgure 5c, the ode 3 has hgher possblty to be the ext hop relay ode tha ode. However, as show Fgure 5a,b, ode has a more balaced performace tha ode 3, thus ode s more sutable to be the ext hop relay ode tha ode 3. Furthermore, both Fgure 5b,c, the utlty of ode 4 s larger tha ode 5; but as dscussed Fgure 5a, the ode 5 has a more balaced performace tha ode 4. The reaso for ths ssue s that the optmzato-based routg algorthm ad tradtoal fuzzy logc-based routg algorthm, the large parameters wll have a greater effect o the algorthm performace; ad the odes that these parameters belog to are easy to be chose as the ext hop relay ode, whch s cosstet wth the performace of ode 4 ad ode 5 Fgure 5b,c, respectvely. The Fgure 5 dcates that the BCFL ad the tradtoal fuzzy logc-based routg algorthm (used [9,20]) have the smlar performace, ad they are all better tha the optmzato-based routg algorthm (used [9]). O the other had, eve the tradtoal fuzzy logc-based routg algorthm has smlar performace o selectg the ext hop relay ode wth the BCFL, but cosderg the umber of the fuzzy f-the rules, the BCFL wll have greater advatage tha the tradtoal fuzzy-based routg algorthm. As show Fgure 6, the tradtoal fuzzy-based routg algorthm, the umber of f-the rules creases sharply wth the creasg of the lgustc varables ad the umber of cross-layer parameters; moreover, ths crease s expoetal. O the cotrary, the BCFL, the umber of fuzzy rules wll stay costat whe the cross-layer parameters crease (Fgure 6a), ad eve whe the lgustc varables crease, the growg of the fuzzy f-the rules s lear (Fgure 6b), whch s much less compared to the tradtoal fuzzy logc-based routg algorthm The tradtoal fuzzy logc based routg algorthm The ew fuzzy logc based routg algorthm The tradtoal fuzzy logc based routg algorthm The ew fuzzy logc based routg algorthm The umber of f-the rules The umber of f-the rules The umber of cross-layer parameters (a) The umber of lgustc varables (b) Fgure 6. (a) The relatoshp of the umber of f-the rules ad the umber of cross-layer parameters; (b) The relatoshp of the umber of f-the rules ad the umber of the lgustc varables. The Fgure 6a,b demostrate that the tradtoal fuzzy logc routg algorthm caot hadle multple costrats. If the umber of cross-layer parameters s large, the umber of f-the rules wll become too large to be acceptable. Moreover, the fuzzy rules have great effect o the fuzzy ferece system performace, so a approprate fuzzy rule s very mportat to the fuzzy logc system. For ths

14 Sesors 205, pot of vew, the BCFL ca reduce the complexty of the algorthm greatly; more mportatly, the rules of the ew algorthm are clear ad fxed, whch makes t easy to desg ad more accurate A Example Scearo for Multple Costras The performace of the BCFL uder multple costrats wll be show ths secto. From ths scearo, we ca fd the greater advatage of the BCFL more drectly. I ths smulato, we cosder fve odes as the caddates of the ext hop relay odes ad seve cross-layer parameters for each ode. So the cross-layer parameter matrx s a 5 7 matrx. Ths matrx s geerated by the fucto rad() MATLAB. The parameters are show Table 6. Table 6. The cross-layer parameters of multple costrats Node Node Node Node Node The result of ths scearo s show Fgure 7. The value of parameters, utlty ad dsperso Parameter Parameter 2 Parameter 3 Parameter 4 Parameter 5 Parameter 6 Parameter 7 Utlty Dsperso ode ode2 ode3 ode4 ode5 The parameter dstrbuto of dfferet odes Fgure 7. The result of the BCFL uder multple costrats. From Fgure 7, we ca fd that ode 5 has the best performace amog all the caddate odes; as show Table 6 ad the le graph of dsperso Fgure 7, the cross-layer parameters of ode 5 are more balaced tha the other odes. From the le graph of utlty Fgure 7, we ca coclude that the performace of ode 3 s better tha ode, ode has the better performace tha ode 4, ad the performace of ode 2 s the worst these odes. The smulato result s cosstet wth the

15 Sesors 205, character of the cross-layer parameters dfferet odes, whch s show the hstogram ad the le graph of dsperso Fgure 7. The Table 6 dcates that the parameters of ode 5 are ot always the hghest amog all of the odes, but they are the most balaced, whch ca be foud the le graph of dsperso Fgure 7. The le graph of dsperso demostrates that the ode whose parameters dsperso s small wll have hgh probablty to be the ext hop relay ode, ad vce versa, because the small dsperso leads to the balaced performace. I ths scearo, as the umber of cross-layer parameter s seve, so for the optmzato based routg algorthm, the ukow varables ad the fuctos are at least seve, the the calculato wll be extremely complex; for the tradtoal fuzzy logc-based routg algorthm, whe there are seve parameters the system, the umber of f-the rules s 287 (assumg that the umber of lgustc varables s three), whch s uacceptable. However, for the BCFL, the umber of f-the rules s costat ad the same wth the umber of the lgustc varables ( BCFL, the umber of f-the rules s seve), whch s much smpler tha the other two algorthms. Ths example also llustrates the huge advatage of the ew fuzzy logc-based routg algorthm. 6. Coclusos I ths paper, we propose a ew fuzzy logc-based routg algorthm (the BCFL routg algorthm). The ovatos of ths algorthm are: () we use the parameter dsperso rather tha the absolute parameter value as the put of the fuzzy logc ferece system, whch ca reduce the complexty of the algorthm observably; (2) the dsperso formula ca guaratee that whe the order of magtude chages. the dsperso wll rema uchaged; (3) the parameter whose dsperso s large wll have small weght ad whose dsperso s small wll have large weght. Accordg ths, the BCFL ca acheve some oble propertes that the tradtoal routg algorthms caot obta: Smply, the f-the rules of the BCFL are very smple ad they wll stay costat wth the crease the costrats; Effcetly, the BCFL has excellet capablty to deal wth the multple costrats wthout creasg the complexty; Adaptvely, the BCFL ca adapt to the chagg of the etwork codtos ad topology, especally the uderwater wreless sesor etwork whch the etwork codtos ad topology chage frequetly; Balaced, the BCFL ca get a more balaced soluto tha the tradtoal algorthms. The BCFL s compared wth the optmzato-based routg algorthm (the algorthm used [9]) ad the tradtoal fuzzy logc-based routg algorthm (the algorthm used [9,20]) ( Secto 5.). I addto, we also dscuss the performace of the BCFL uder multple costrats ( Secto 5.2). The smulato results Secto 5. show that the BCFL ad the tradtoal fuzzy logc-based routg algorthm have smlar performace, ad they all better tha the optmzato-based routg algorthm. Moreover, eve the performace of BCFL s smlar wth the tradtoal fuzzy logc-based routg algorthm, however, whe cosderg the fuzzy rules, the BCFL has greater advatage tha the tradtoal fuzzy logc-based routg algorthm used [9,20]. I Secto 5.2, the smulato results

16 Sesors 205, demostrate the excellet capablty of the BCFL o dealg wth the multple costras, whch s balaced, smple, ad effcet. However, ths paper, we propose the routg algorthm ad evaluate the algorthm performace by smulato wthout a real scearo. Therefore, the future, we wll propose the routg protocol based o ths algorthm ad vestgate the performace a real scearo. I addto, the performace-related parameters of the routg protocol, such as the eergy cosumpto, the tme delay, ad the memory use, etc. wll be evaluated future work. Moreover, how the routg protocol ca work wth the IEEE stadards (such as the , ) also deserves to be vestgated. As the BCFL has remarkable performace o adaptg to the dyamc chagg of the etwork codtos ad topology, the future the BCFL ca be used the dyamc topology etwork, such as the moble wreless sesor etwork, the ad hoc etwork, or the uderwater wreless sesor etwork. Furthermore, ths algorthm also ca be used to select the cluster head the cluster-based routg protocol. Ackowledgmets Ths work s supported by the Europea project Desg, Motorg ad Operato of Adaptve Networked Embedded Systems (DEMANES) (project code ARTEMIS-JU: ). Author Cotrbutos Ng L, José-Ferá Martíez, ad Vcete Herádez Díaz are resposble for the theoretcal aalyss of the routg algorthm. Ng L ad Vcete Herádez Díaz desg the smulato procedure ad aalyze the smulato results. Coflcts of Iterest The authors declare o coflct of terest. Refereces. Perks, C.; Beldg-Royer, E. Das, S. Ad-hoc O-Demad Dstace Vector Routg. I Proceedgs of the Secod IEEE Workshop o Moble Computg System ad Applcatos, New Orleas, LA, USA, February 999; pp Davd, B.J.; Davd, A.M.; Josh, B. Ad Hoc Networkg; Addso-Wesley Logma Publshg: Bosto, MA, USA, 200; pp Perks, C.E.; Bhagwat, P. Hghly dyamc Destato-Sequeced Dstace-Vector routg (DSDV) for moble computers. ACM SIGCOMM Comput. Commu. Rev. 994, 24, Prathap, U.; Deepa, S.P.; Veugopal, K.P.; Patak, L.M. Wreless Sesor Networks Applcatos ad Routg Protocols: Survey ad Research Challeges. I Proceedgs of the 202 Iteratoal Symposum o Cloud ad Servces Computg, Magalore, Ida, 7 8 December 202; pp Srvastava, V.; Mota, M. Cross-layer desg: A survey ad the road ahead. IEEE Commu. Mag. 2005, 43, 2 9.

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19 Sesors 205, Mao, S.; Zhao, C.; Zhou, Z.; Ye, Y. A mproved fuzzy uequal clusterg algorthm for wreless sesor etwork. Mob. Netw. Appl. 203, 8, Jahashah, M.; Rahma, S.; Ghader, S. A effcet cluster head selecto algorthm for wreless sesor etwork usg fuzzy ferece systems. It. J. Smart Electr. Eg. 203, 2, Sgh, A.K.; Puroht, N.; Varma, S. Fuzzy logc based clusterg wreless sesor etworks: A survey. It. J. Electro. 203, 00, Jarupa, B.; Ekc, E. A survey of cross-layer desg for VANETs. Ad Hoc Netw. 20, 9, Kullkar, R.V.; Forster, A.; Veayagamoorthy, G.K. Computatoal Itellgece Wreless Sesor Networks: A Survey. IEEE Commu. Surv. Tutor. 20, 3, Feg, G. A Survey o Aalyss ad Desg of Model-Based Fuzzy Cotrol Systems. IEEE Tras. Fuzzy Syst. 2006, 4, by the authors; lcesee MDPI, Basel, Swtzerlad. Ths artcle s a ope access artcle dstrbuted uder the terms ad codtos of the Creatve Commos Attrbuto lcese (