Low Complexty Duty Cycle Control wth Jont Delay and Energy Effcency for Beacon-enabled IEEE 8254 Wreless Sensor Networks Yun L Kok Keong Cha Yue Chen Jonathan Loo School of Electronc Engneerng and Computer Scence Queen Mary Unversty of London Emal: yunl mchaelcha yuechen@qmulacuk Department of Computer and Communcatons Engneerng Mddlesex Unversty Emal: JLoo@mdxacuk Abstract IEEE 8254 defnes a duty cycle based medum access control (MAC protocol to reduce the energy consumpton for devces n wreless sensor networks (WSNs A low duty cycle sgnfcantly mproves the energy effcency but reduces the avalable transmsson tme thereby ncreases end-to-end delay In ths paper we solve an adaptve duty cycle control problem for beacon-enabled IEEE 8254 networks whch ams at mnmsng a jont-cost of energy consumpton and end-to-end delay The problem s formulated as a classcal nventory control problem and the optmal adaptve duty cycle of the devce s derved by applyng dynamc programmng (DP We further propose a low complexty suboptmal adaptve duty cycle control by takng nto account the computatonal lmtaton of the sensor devces Smulaton results show that the proposed duty cycle control effectvely reduces energy consumpton end-to-end delay and packet drop rato under varous network traffc Keywords wreless sensor networks duty cycle control dynamc programmng convex optmsaton medum access control I INTRODUCTION In newly emergng applcatons of wreless sensor networks (WSNs devces wthn one network may have varous requrements on energy effcency and end-to-end delay [] IEEE 8254 standard [2] utlses low duty cycle to conserve energy by puttng devces nto nactve mode However a low duty cycle ntroduces hgh end-to-end delay In addton the unformed duty cycle control n current standard may not provde the best overall performance Some effort has been made to acheve a trade-off between energy effcency and end-to-end delay by adaptvely changng the duty cycle of MAC protocols In Dynamc Sensor MAC protocol (DSMAC [3] the sleepng nterval s adjusted based on the thresholds of energy utlsaton effcency and average latency experenced by the sensor However the proposed sleepng nterval adaptaton can only be double or half of the ntal settng In [4] an adaptve duty cycle control called Traffc-adaptve Dstance-based Duty Cycle Assgnment (TDDCA s proposed to ncrease the duty cycle when there s severe contenton among devces n the network or otherwse decrease the duty cycle n every tme perod down to a mnmum value However to enable the TDDCA control contenton reports pggyback flags and modfcatons of the packet header are needed In [5] DutyCon s proposed to guarantee end-to-end delay by assgnng a local delay requrement to each sngle hop along the communcaton flow In ths method a feedback controller s desgned to adapt the sleep nterval to meet the sngle-hop delay requrement However ths approach requres sgnfcant amount of sgnallng from the neghbour devces to compute the delay To reduce the sgnallng among neghbour devces a dstrbuted duty cycle controller s proposed n [6] by controllng the local queue length of the devce to be the same as the predetermned threshold The dstrbuted duty cycle control s acheved by adjustng sleep duratons of each devce based on the local queue length ndependently However ths approach needs a specfc synchronsaton scheme among all devces and the duty cycle evoluton depends on the ntal duty cycle settng and control parameters Whle the aforementoned lteratures lad a sold foundaton n desgnng adaptve duty cycle MAC protocols lmted work has been done n the duty cycle optmsaton wth jont consderaton of energy consumpton and end-to-end delay In ths paper we solve an adaptve duty cycle control problem ams at mnmsng the jont-cost of energy consumpton and end-to-end delay n a mult-hop cluster-tree WSN We desgn a jont-cost functon whch follows a smlar logc of the jont consderaton of purchase cost and store cost n nventory control problem [7] The jont-cost s desgned as the weghted sum of energy consumpton and end-to-end delay where the weghtng factors are adjustable accordng to dfferent requrements n energy consumpton and end-to-end delay of the specfc applcaton The contrbutons of ths paper are summarsed as follow: frst we formulate an optmsaton problem to mnmse the jont-cost of energy consumpton and end-to-end delay wth the consderaton of both network traffc and the devce poston Then the optmal duty cycle control s derved by applyng dynamc programmng (DP Furthermore a low complexty suboptmal control s proposed to reduce the computaton complexty of runnng DP on sensor devces II SYSTEM MODEL As the mult-hop case can be vewed as the combnaton of several two-hop scenaros ths paper dedcated to the analyss of two-hop cluster-tree network as shown n Fg The level of the devce s denoted as l n The coordnator n s n level- thus l n = ; there are N full-functon devces (FFDs n ( N n level-2 Reduced-functon devces (RFDs are 978--4799-5863-4/4/$3 c 24 IEEE 26
n level-3 We denote the chld RFDs set of FFD n as ch n and the number of RFDs n ch n s M n RFD FFD Coordnator n n level- Fg : Network Model n j level-2 level-3 The duraton between two consecutve beacons s called Beacon Interval (BI whle the duraton of an actve perod s called Superframe Duraton (SD Specfcally BI = abasesuperf rameduraton 2 BO ( SD = abasesuperf rameduraton 2 SO (2 where Beacon Order (BO and Superframe Order (SO are two ntegers rangng from to 4 ( SO BO 4 and abasesuperf rameduraton = 536ms at 24 GHz wth 25 kbps bandwdth The duty cycle s defned as Duty Cycle = SD/BI = 2 SO BO In mult-hop transmsson each FFD dvdes ts BI nto two superframes named ncomng superframe and outgong superframe as shown n 2 As there are two SDs n each BI we have the condton that SO BO for FFDs Fg 2: Superframe structure For each FFD as the ncomng superframe duty cycle s enclosed n the receved beacon sent by ts parent FFD t can only decde ts own outgong superframe duty cycle (refer as duty cycle n ths paper We set all devces to be actvated at the begnnng of each BI The same BO s set to all devces n the network wth the am of smplfyng the synchronsaton Thus the duty cycle control s acheved by settng SO A Queue and Traffc Models We assume all generated packets are avalable at the begnnng of each tme perod All the packets are forwarded to the coordnator n for uplnk transmsson and s the maxmum queue length of the devce n The new arrved packets wll be dropped f the queue length n the buffer reaches ts maxmum Smlar to [5] the queue length of tme perod k + of devce n s gven as ( = mn [qn k + rn k fn k + gn k ] + (3 q k+ n where k K [ ] + = max( gn k s the number of packets beng generated by devce n n tme perod k; fn k s the number of packet transmtted by devce n n tme perod k; and r k n s the number of packets receved by devce n n tme perod k Note r k n equals to zero f devce n has no chld devce We assume the number of packets each devce sends to ts parent devce follows Posson dstrbuton and each devce generates a Posson dstrbuted nteger number of packets n each tme perod (BI Thus f k n and g k n are ndependent random varables III PROBLEM FORMULATION To ensure the costs of energy consumpton and end-toend delay are addtve we defne the transmttng energy consumpton cost E t (f k n recevng energy consumpton cost E r (r k n dle lstenng energy consumpton cost E l (r k n and end-to-end delay cost D(r k n of the devce n all based on the number of packets The specfc defnton of each cost s gven as E r(rn k = cr rk n l n (4 E t(fn k = c f fn k l n (5 E l (rn k = c l [fn k gn k qn k rn k ] + (6 l n D(rn k = c d [qn k + rn k + gn k fn k ] + (7 l n where c f c r c l and c d are the coeffcents of transmttng recevng dle lstenng and delay of the devce respectvely To dfferentate FFDs and RFDs devce buffer sze and level of the devce l n have also been ntegrated nto the problem formulaton The devces closer to coordnator have more accumulated packets to forward thus these devces wll have hgher energy consumpton costs and delay cost Note that c r < c l as f c r were greater than c l t would never be optmal to receve new packets n the last perod and possbly n earler perods We further ntroduce α and β to assgn the weghtngs of energy effcency and end-to-end delay requrements of dfferent applcatons Wth the condton 3α + β = the expected weghted-sum jont-cost functon for devce n at tme perod k s ( J(rn k = E α E t(fn k + E r(rn k + E l (rn k + βd(rn k We adopt IEEE 8254 (2 standard whch apples slotted carrer-sense multple access wth slotted collson avodance (CSMA/CA for packet transmsson Before the packet transmsson we assume devces need to perform two clear channel accesses (CCAs Wthn each superframe duraton the beacon transmsson duraton s D bcn Thus the total packet transmsson duraton P D = SD D bcn If acknowledgement (ACK s requred for each packet the successful packet transmsson perod P s = P CCA + P L + δ + P ACK where P CCA s the transmsson tme for two CCAs P L s the transmsson tme for each packet δ and P ACK are watng and transmsson tme of the ACK packet respectvely Hence the number of packets that can be receved by devce n at k th tme perod r k n = P D/P s (8 262
A well accepted dscrete tme Markov chan analytc model of the IEEE 8254 slotted CSMA/CA s proposed n [8] The coeffcent b shows mpact of the backoff and contenton on throughput Then the relatonshp between SO n (k and the amount of packets the devce could receve n tme perod k s gven as follow SO n (k = P n : log 2 ( rk n P s b mn π n D E + D bcn (9 Our objectve s to fnd the control of the optmal duty cycles πn for each devce n whch mnmse the overall expected jont-cost over K tme perods Hence the jont optmsaton problem s: K k= st q K n = J(r k n r k n r max n ( where D s vald duty cycle sets of devce n whch s restrcted by the maxmum vald SO IV ADAPTIVE DUTY CYCLE CONTROL By applyng the prncple of DP the problem P n s decomposed nto a sequence of subproblems S(rn k where k K The objectve of each subproblem S(rn k s to mnmse the sum of jont-cost functons from tme perod k to K Thus the total cost of P n s equal to that of S(rn whch means the optmal soluton of S(rn s the optmal soluton of P n Based on (9 the cost-to-go functon U(rn k of S(rn k s U(rn k = mn α(e r(rn k π n S + E t(fn k + H(rn k ( + EU(rn k+ where H(rn k = E αe l (rn k + βd(rn k shows the tradeoff between dle lstenng energy consumpton cost and the end-toend delay cost For smplcty we ntroduce m k n = qn k + rn k and n k n = fn k gn k then H(rn k can be rewrtten as H(m k n = E αc l max(qmax n [n k n m k n ] + (2 q max l n + βc d max(qmax n [m k n n k n ] + q max l n As the convexty preserved by takng expectaton over n k n wth each fxed n k n H(m k n s convex To take the convexty of H(m k n we rewrte (2 as U(m k n = mn E W (m k n π n S α c r where n q max n q k n l n (3 W (m k n =αe t(fn k + αc r m k n + H(m k n (4 + E U([m k+ n qn k+ ] + Then the objectve of S(r k n s to fnd the mnmum value of (5 Based on ( and (2-(6 the optmal duty cycle control at each tme perod can be acheved by runnng DP Throrem : If W (m k n s convex and m k n = Tn = arg mn W (m k n (5 m k n R where R as the set of all vald values of m k n Thus the optmal soluton of P n s SOn k log = 2 ( rk n Ps + D b bcn f q n (k < T n (6 log 2 (D bcn f q n (k T n Proof: For k = K functon U(m K n s the zero functon so t s convex Snce c r < c d and the dervatve of H(m K n tends to c d /l n as qn K + rn K thus W (m K n has a dervatve that becomes negatve as m K n and becomes postve as m K n Therefore W (m K n s convex As W (m K n s mnmsed by T n gven the convexty of U(m K n the convexty of U(m K n s proved For k = K 2 the above arguments can be repeated: f U(m k+ n s convex we can have U(m k n and W (m k n are convex Substtutng (8 n n (k = f n (k g n (k and r n (k = m n (k q n (k back nto (7 the mnmum cost-to-go s attaned at rn k = T n qn k f qn k < T n and at rn k = otherwse Accordng to above analyss the optmal duty cycle control can be acheved by runnng DP However ths needs to conduct exhaustve search over all possble solutons at each tme perod whch s very energy neffcent and tme consumng Thus t dffcult or mpractcal to make the computatonallylmted sensor devces run DP algorthm To overcome the computaton complexty of the optmal control we further propose a low complexty suboptmal control As proved above the soluton to the problem has a threshold structure Instead of searchng the optmal soluton by runnng DP we propose a suboptmal duty cycle control based on (8 In order to ensure the stable of the queue length the devce should receve same number of packets as t transmts at each tme perod Thus we propose a suboptmal duty cycle control where T n s equals to fn k of the devce n Based on equaton (8 the suboptmal soluton of P n s gven as SOn k log = 2 ( rk n Ps + D b bcn f q n (k < fn k (7 log 2 (D bcn f q n (k fn k We also gve two remarks for the proposed suboptmal duty cycle control Frst the proposed suboptmal control has lower computaton complexty as compared to DP optmal control We denote Q as the average maxmum queue length of the devces the computaton complexty of DP optmal control s O(KQ N+Q whle that of the proposed suboptmal control s only O( Second the proposed suboptmal controls has lower synchronsaton overhead as compared to controls n [5] and [6] The proposed control does not need addtonal SYNC packet to ensure the devces are actve at the same tme as t employs the same BO as defned n the IEEE 8254 (2 and all devces are actvated at the begnnng of each BI 263
TABLE I: Smulaton Parameters Parameter Value Parameter Value frequency 24 GHz α 2 transmt power 365 mw β receve power 44 mw CCA sze 8 symbols dle lsten power 44 mw ACK packet sze symbols sleep power 42 mw unt backoff perod 2 symbols V SIMULATION RESULTS We consder a two-hop cluster-tree network as explan n secton II We compare the performance of DP optmal control the proposed suboptmal control and a fxed duty cycle control Energy consumpton parameters n the smulaton are based on CC242 data sheet [9] and MAC layer parameters are based on IEEE 8254 (2 standard [2] The duraton of each tme perod (BI s 9s wth BO = 5 fn k follows posson dstrbuton wth the mean value equals to 3 packets per actve perod and the number of observaton tme perods K s We assume there s no packet loss durng the transmsson The maxmum buffer sze of FFDs s 5 packets and that of the RFDs s 2 packets Packets are dropped when the queue length of the devce reaches ts maxmum The results are the averaged values of runs of the devce n Specfc smulaton parameters are gven n TABLE I We evaluate two scenaros n the smulaton: Scenaro : In ths scenaro we assume the maxmum queue length of FFDs s 5 packets and that of the RFDs s 2 packets whch are large enough to buffer all generated packets durng the smulaton Hence there s no packet drop n ths scenaro The performance metrcs are: average energy consumpton per transmtted packet; and average two-hop end-to-end delay between the coordnator n and FFD n Scenaro 2 : In ths scenaro we set the maxmum queue length of FFDs s 5 packets and that of the RFDs s 2 packets Packets are dropped when the queue length of the devce reaches ts maxmum The performance metrcs are: average energy consumpton per transmtted packet; average two-hop end-to-end delay of packets receved by the the coordnator and; the rato of packet drop due to the queue exceeds the maxmum allowable queue length A Smulaton Results and Anlyss of Scenaro : In ths scenaro as the maxmum queue length s large enough to buffer all the generated packets there s no packet drop Fg energyinfnte and Fg delayinfnte show the results n terms of energy consumpton per packet and end-to-end delay respectvely Smulaton results are dvded nto two phrases for analysng as follow: Fg 3 and Fg 4 show that DP optmal control and the proposed suboptmal control acheve lower energy consumpton and less end-to-end delay by adjustng the actve perods based on the amount of packets generated by RFDs Compared to the fxed duty cycle control the energy consumptons of DP optmal control and suboptmal control are not constant between to 5 generated packets because the actual number of receved packets rn k can be dfferent wth same SO The end-to-end delay begns to ncrease when the number of generated packets by RFDs becomes hgher than the maxmum number of packets the devce n can receve wthn each actve perod The detaled analyss of the smulaton results are dvded nto two phrases as follow: In when m j ch n f k n (before 3 packets/actve perod the energy consumpton per packet and endto-end delay of the suboptmal control begn to be hgher than that of the optmal control snce 2 packets/actve perod as shown n Fg 3 and Fg 4 respectvely Ths s because the threshold of the suboptmal control lmts the maxmum number of packets the devce can receve at each tme perod Hence the dle lstenng energy consumpton and end-to-end delay of the suboptmal control start to ncrease earler than of the optmal control In I when m j ch n > f k n (after 3 packets/actve perod the number of receved packets reach ts maxmum wth the lmtaton of the threshold n the suboptmal control The energy consumpton of the suboptmal control becomes flat as shown n Fg 3 The energy consumpton per packet of the optmal control s lower than that of the suboptmal control wthout the lmtaton of the threshold In Fg 4 the end-to-end delay curves keep ncreasng wth the ncrement of the number of generated packets by the RFDs Ths s due to the ncreased number of the buffered packets for all three evaluated controls n ths phase To summarse the performance n ths scenaro the proposed adaptve duty cycle control: performs smlar wth the optmal duty cycle control under lght network traffc ( m j ch n 2 packets/actve perod; 2 reduces both energy consumpton and end to end delay compared to the fxed duty cycle control 25 energy consumpton per packet (mj optmal suboptmal fxed I average end to end delay (s 2 5 5 DP optmal suboptmal fxed I 2 number of generated packets by RFDs (packets/actve perod Fg 3: Energy consumpton per packet number of generated packets by RFDs (packets/actve perod Fg 4: Two-hop end-to-end delay 264
energy consumpton per packet (mj DP optmal suboptmal fxed I 2 number of generated packets by RFDs (packets/actve perod Fg 5: Energy consumpton per packet average end to end delay (s 6 5 4 3 2 I DP optmal suboptmal fxed number of generated packets by RFDs (packets/actve perod Fg 6: Two-hop end-to-end delay packet drop rato 2 I DP optmal suboptmal fxed number of generated packets by RFDs (packets/actve perod Fg 7: Two-hop packet drop rato B Smulaton Results and Anlyss of Secnoro 2: In ths scenaro packets are dropped when qn k fn k +rn k > Fg 5 Fg 6 and Fg 7 show the results n terms of energy consumpton per packet end-to-end delay and packet drop rato respectvely Smulaton results are dvded nto two phrases for analysng as follow: In when m j ch n gm k j fn k DP optmal and suboptmal controls acheve both lower energy consumpton and end-to-end delay as expected as shown n Fg 5 and Fg 6 It can be seen from Fg 6 and Fg 7 that the end-to-end delay and packet drop rato of the optmal and suboptmal controls only begn to ncrease when RFDs generate more than 2 packets/actve perod whle that of the fxed duty cycle control begn to ncrease dramatcally around 7 packets/actve perod The mprovement of both optmal control and suboptmal control are acheved by adaptvely adjust the actve perods based on the amount of generated packets The end-to-end delay curves n Fg 6 have the same trend wth the results n [6] The end-to-end delay of the fxed duty cycle control begns to decrease snce 8 packets/actve perod as more packets generated n earler tme perods are dropped due to the lmted buffer sze In I when m j ch n gm k j > fn k more packets n the queue are buffered to next actve perod In Fg 5 the energy consumptons of the optmal and suboptmal controls are slghtly hgher than that of the fxed control n ths phase Ths s because the round-up operaton of SO ensure longer actve perods However the maxmum number of packets whch can be receved s lmted by fn k Ths leads to the ncrease of dle lstenng energy consumpton We also notce that the energy consumpton per packet n ths scenaro s slghtly hgher than that n scenaro n ths Phase The reason s that the number of packets the devce can receved n each tme perod s decreased due to the smaller maxmum queue length compared to scenaro In Fg 6 the end-to-end delay of DP optmal and suboptmal controls are ncreased due to the ncreased buffer tme of the packets as the maxmum number of packets devce n can receve at each actve perod s lmted by the threshold fn k To summarse the performance n ths scenaro the proposed suboptmal control has a tght approxmaton to the optmal control; reduces energy consumpton end-to-end delay and packet drop rato under lght traffc condton ( m j ch n f k n ; sgnfcantly reduces packet drop rato of the network wth slghtly ncreased energy consumpton and end-to-end delay under hgh traffc condton ( m j ch n > f k n VI CONCLUSION In ths paper we formulated an optmsaton problem to mnmse the expected jont-cost of energy consumpton and end-to-end delay for IEEE 8254 based WSNs Then the optmal duty cycle control s derved by applyng DP algorthm Takng the computatonal lmtaton of sensor devces nto consderaton a low complexty suboptmal adaptve duty cycle control was proposed Smulaton results show that the proposed adaptve duty cycle control can effectvely reduces energy consumpton end-to-end delay and packet drop rato under varous network traffc Furthermore the proposed suboptmal control requres no ntal control settng and s well compatble wth the current IEEE 8254 (2 standard REFERENCES [] M R Palattella N Accettura M Dohler L A Greco and G Bogga Traffc Aware Schedulng Algorthm for Relable Low-Power Mult-Hop IEEE 8254e Networks n Proc IEEE Internatonal Symposum on Personal Indoor and Moble Rado Communcatons PIMRC Sydney NSW September 22 pp327-332 [2] IEEE std 8254 Part 54: Wreless Medum Access Control (MAC and Physcal Layer (PHY Specfcatons for Low-Rate Wreless Personal Area Networks (LR-WPANs IEEE Std 2 [3] P Ln C Qao and X Wang Medum Access Control Wth A Dynamc Duty Cycle For Sensor Networks n Proc IEEE Wreless Communcatons and Networkng Conference WCNC Atlanta GA USA March 24 vol 3 pp534-539 [4] Z Yuqun F Chen-Hsang I Demrkol and WB Henzelman Energy- Effcent Duty Cycle Assgnment for Recever-Based Convergecast n Wreless Sensor Networks n Proc IEEE Global Telecommuncatons Conference GLOBECOM Mam Florda USA December 2 [5] X Wang X Wang G Xng and Y Yao Dynamc Duty Cycle Control for End-to-End Delay Guarantees n Wreless Sensor Networks n Proc IEEE Internatonal Workshop on Qualty of Servce IWQoS Bejng Chna June 2 pp-9 [6] H Byun and J Yu Adaptve Duty Cycle Control wth Queue Management n Wreless Sensor Networks IEEE Transactons on Moble Computng June 23 vol 2 no 6 pp 24-224 [7] D P Bertsekas Dynamc Programmng and Optmal Control 3rd Edton Athena Scentfc 25 [8] TR Park TH Km JY Cho S Cho and WH Kwon Throughput and energy consumpton analyss of IEEE 8254 slotted CSMA/CA Electroncs Letters 25 vol 4 no 8 [9] CC242 24 GHz IEEE 8254 Complant and ZgBee Ready RF Transcever onlne: http://wwwtcom/product/cc242 265