A Predictive QoS Control Strategy for Wireless Sensor Networks

Transcription

1 The 1st Worshop on Resource Provsonng and Management n Sensor Networs (RPMSN '5) n conjuncton wth the 2nd IEEE MASS, Washngton, DC, Nov. 25 A Predctve QoS Control Strategy for Wreless Sensor Networs Byu Lang 1, Jeff Frol 2, and X. Sean Wang 1 Department of Computer Scence, Unversty of Vermont, USA 1 Department of Electrcal and Computer Engneerng, Unversty of Vermont, USA 2 {blang, xywang}@cs.uvm.edu, jfrol@uvm.edu Abstract The number of actve sensors n a wreless sensor networ has been proposed as a measure, albet lmted, for qualty of servce (QoS) for t dctates the spatal resoluton of the sensed parameters. In very large sensor networ applcatons, the number of sensor nodes deployed may exceed the number requred to provde the desred resoluton. Heren we propose a method, dubbed predctve QoS control (PQC), to manage the number of actve sensors n such an overdeployed networ. The strategy s shown to obtan near lfetme and varance performance n comparson to a Bernoull benchmar, wth the added beneft of not requrng the networ to now the total number of sensors avalable. Ths beneft s especally relevant n networs where sensors are prone to falure due to not only energy exhauston but also envronmental factors and/or those networs where nodes are replenshed over tme. The method also has advantages n that only transmttng sensors need to lsten for QoS control nformaton and thus enablng nactve sensors to operate at extremely low power levels. eywords Wreless sensor networs, networ spatal resoluton, qualty of servce, dstrbuted control 1. Introducton Broadly dstrbuted wreless sensor networs (WSN) promse to provde envronmental data wth very hgh spatal and temporal resolutons. Deployments are envsoned whch may utlze 1 s or 1 s of thousands of sensor nodes for purposes such as montorng hgh-rs forests [1], homeland securty, and ndustral systems. Much wor to date has been focused on adaptng exstng computer or wreless networng approaches to the energy constraned realm n whch WSN must operate [2]. However, many of these archtectures requre all nodes to be able to perform routng, processng, etc. all of whch ncrease node cost. Costs can be consdered n terms of energy usage, weght, sze, relablty; functons all of whch drve dollars per unt. In short, the overall system cost assocated wth mang the nodes more capable and robust may become prohbtve for large scale applcatons. Another consderaton s that the envronment tself s harsh therefore causng sensors to fal at unpredctable rates. In ether scenaro, the networs may be ntally over-deployed n that the total number of sensors at the begnnng of lfe exceeds the number requste to provde the desred system performance. At the system level, networ lfe s maxmzed when only a mnmum number of sensors needed to acheve the applcaton s data requrements are actve. Thus controllng the number of partcpatng sensors can be equated to controllng the networ s qualty of servce (QoS) (Iyer [4] and Frol [5]). Heren, we consder a networ archtecture n whch each node operates usng local rules and wth mnmal control nformaton to acheve the overall system QoS requrement. In ths wor, a Predctve QoS Control (PQC) strategy s proposed to manage the number of sensor actve n large deployments. PQC s shown to approach a Bernoull benchmar method proposed earler [3] wth respect to the equalty n partcpaton, networ lfe and responsveness to networ dynamcs. In the Bernoull benchmar method, each sensor partcpates n the networ wth probablty of p = Q/N; where N s the total number of sensors avalable, and Q s the QoS requred. Explct nowledge of N s requste to mplementaton of the Bernoull benchmar method. However, unless the networ s contnuously quered, N may be unnown due to ndvdual nodes becomng depleted of energy or falng due to envronmental or hardware causes. To query a node requres that t be awae, whch s energy neffcent, smply to learn whether the sensor can provde nformaton f requred.

2 The ntroduced PQC methodology has advantages over the Bernoull benchmar method n that t has nether constrant. The rest of ths paper s organzed as follows. Related wor on the QoS control s dscussed n 2. We present the PQC QoS control protocol, algorthms and analyss n 3. Results from a performance study and dscussons of the results are gven 4. We conclude the wor n Related Wor Use of an automaton structure as a bass for a spatal resoluton control strategy was frst proposed n [4]. Employng a smple Goore game strategy, QoS was shown to be controllable up to Q N/2 wthout nowledge of N but requrng all sensors to lsten for control nformaton. Ths constrant was removed by usng a revsed automaton n [5], such that only transmttng sensor were requred to lsten for control nformaton. In addton, the new automaton was shown to enable QoS up to N. Ths latter automaton has been further analyzed wth the followng results: The mean and varance of the acheved QoS can be controlled by selecton of automaton parameters. There s a tradeoff between varance and networ dversty [6]. The mean and varance of QoS s scalable as networ sze ncreases. The technque s also expedent n comparson to an equal partcpatng (Bernoull benchmar) method [3]. The shortcomng of these exstng automaton structures s that the partcpaton among nodes n the networ s less even than n the equal partcpatng Bernoull method. As such, the wor to date has not been able to acheve lfetmes comparable to the Bernoull benchmar. The ey contrbuton of the wor presented heren s to address ths shortcomng whle at the same tme not requrng nowledge of N and not requrng all sensors to lsten for control nformaton. 3. Predctve QoS Control Strategy For the dscusson heren, we wll assume that the objectve s to control the number of sensors reportng durng each epoch n a sngle-hop cluster. The ndvdual sensors wll locally mae the decson on when (whch epoch) to transmt ts next data pacet based on a control value, p, provded by the clusterhead as part of an acnowledgement (AC) for data receved. The proposed strategy provdes the same control value, p, only to the nodes actve n the present epoch. As to be detaled n followng sectons, the clusterhead determnes the approprate p based on the past, current and desred QoS. Indvdual sensors then utlze the control parameter to locally determne a schedule for transmttng ther next data pacet. Throughout we wll assume that the amount of data to be sent n the networ s very low n comparson to the avalable bandwdth;.e., the networ s not bandwdth constraned. As such, sensors may employ smple contenton based protocols (e.g., ALOHA, slotted- ALOHA or CSMA) wth hgh lelhood that ther data pacet wll get through n the same epoch durng whch they are sent. 3.1 Mechansm to Control Data Transmsson Rate of Indvdual Sensors In the PQC approach each sensor controls ts own sendng probablty based on a transmsson probablty value, whch s the control value t receves n the AC from the clusterhead. We denote the transmsson probablty of sensor s as p s, where p s 1. In dong a Bernoull tral, ndvdual sensors generate a unformly dstrbuted random number on the nterval [, 1] and transmt a data pacet f t falls n the nterval [, p s ]. Ths repeats for every epoch. As noted, the dsadvantage of ths technque s that t requres explct nowledge of N and all the nodes need to be updated. To resolve these problems, we propose a tmer-based mechansm for controllng data sendng rate of ndvdual sensors. To mplement a tmer-based method, the ey parameter to control s the nterval (epochs) between successve transmssons by a node;.e., how long a node sleeps. If the nter-transmsson nterval s small a sensor wll transmt more often. Explctly, gven the transmsson probablty p s, n the Bernoull tral, we have the followng dstrbuton for the random varable κ,.e., the length of nter-transmsson nterval, κ = ) = (1 p s ) p s (1) where =, 1, 2,. To ntroduce our tmer-based mechansm for controllng data sendng rate, we frst dvde the range [, 1] nto smaller sub-ranges as [κ < ), κ ) ], where =, 1, 2,. A random number, ξ, s then generated followng unform dstrbuton wthn the range [, 1]. If the random number s wthn the th sub-range:.e., ξ ( κ < ), κ ) ], the sensor wll set ts own tmer value, TV, to. The sensor wll then wae up to send a data pacet after sleepng for epochs (.e. there are epochs between

3 the epoch where t sent ts last data pacet and the epoch for t to wae up agan). Settng the tmer value as s dscussed above wll lead to the same probablty dstrbuton for the length of nter-transmsson nterval as performng a Bernoull tral at each epoch. Indeed, the probablty of ξ fallng n the th sub-range, thus sensor s gettng a tmer value, s the length of ths sub-range κ ) κ < ), whch exactly equals κ = ) of the Bernoull tral. In mplementaton of the tmer-based control, we mposed an upper bound T UB (each sensor has ts own T UB, whch depends on ts p s ) on the tmer value to avod the case of any sensor havng too low of a response rate. An approprate T UB can be derved from the control value p as follows. T T UB UB TUB+ 1 P ( κ TUB) = κ = ) = (1 p) p = 1 (1 p) 1 α = = (2) Here the confdence that a sensor wth transmsson probablty p wll transmt another data pacet n no more than T UB epochs s 1 α. Thus, n settng ths upper bound, we use T UB ln(α)/ln(1 p) 1. (3) Pseudo-code for the node control strategy s gven n Algorthm 1. In ths algorthm, t s also proposed that the sensor send ts last tmer value to the clusterhead along wth the current readng data. Ths s needed to mae the predcton and develop an updated control value p, as wll be dscussed n 3.2. Loop { 1. Waeup and send current readng wth last tmer value TV to clusterhead; 2. Wat for AC wth control value p; 3. Update local control value to p s := p and determne the probablty dstrbuton κ = ) from (1). 4. Calculate T UB from (3). 5. Generate a unform random number ξ wthn the range [, 1]; 6. Fnd that satsfes ξ ( κ < ), κ ) ]; 7. TV := mn{, T UB }; // tmer value 8. Reset tmer to TV and restart tmer; 9. Sleep for the comng TV epochs; } Algorthm 1. Sensor Transmsson Rate Control 3.2 Predcton Strategy for the Clusterhead to Determne the Control Value p The most straght-forward approach to determne the control value s to set p = Q/N. Ths s the Bernoull benchmar method. However, there are several dsadvantages assocated ths method, as s noted before. In the PQC strategy, the clusterhead eeps a record of networ traffc nformaton,.e. control values used and the number of sensors that have transmtted, etc. n the recent epochs. Snce T UB s the upper bound of the tmer value, ths s also the maxmum memory sze for ths networ traffc nformaton. Fgure 1 llustrates the predcton model employed by the clusterhead. Control nformaton s sent out wth each AC and thus the next epoch e' s no longer controllable at the end of current epoch. As such we must determne the probablty dstrbuton of the number of data pacets receved durng the epoch e'', the second epoch followng the current one. M 3 '' 2 current adjusted to p desred QoS Fgure 1. Illustraton of the predcton model As the dstrbuton of the number of data pacets that wll be receved durng e'' depends largely on what control value p e' s used for epoch e', we must frst determne an approprate control value p e'. We denote the number of pacets receved durng epoch and the control value used as n and p respectvely. Let m be the number of sensors, amongst the n ones, that have not transmtted snce epoch. The value of m s ntalzed wth n ; and upon recevng a data pacet, the clusterhead wll chec the TV n the data pacet to see when ths partcular sensor sent ts last data pacet. If the last transmsson s durng epoch, then the correspondng m wll be deducted by 1. These values of n, p and m are the networ traffc nformaton recorded at the clusterhead for predcton purpose. Tae any of these m sensors. Snce t has not sent any pacet untl now (otherwse t shouldn t have been counted n m ), by our dscusson n 3.1, the probablty that t sends a data pacet durng the epoch e' s: ' 1 e' e' e'' t p = p (4)

4 And, the probablty that the sensor wll send ts next data pacet durng the epoch e'' s: p = ( 1 p ) p (5) Let the random varable be the number of sensors that wll send a pacet durng the epoch e' amongst these m sensors, then follows a bnomal dstrbuton,.e., ~ B m, p ). Thus, z (), the pdf for s: z ( m m ( ) : = = ) = p (1 p ) (6) Lewse the pdf for the random varable, the number of sensors that wll send ther next data pacet durng the epoch e'' amongst these m sensors, s: z m m ( ) : = = ) = p (1 p ) (7) Let random varables ' and '' be defned for e' and e'' (see Fgure 1) respectvely as: and = M (8) 1 2 = M (9) 1 2 where M s the maxmum memory sze under the consderaton. Random varable ' means the number of sensors that wll send a data pacet durng epoch e'; whle '' means the number of sensors that wll send ther next data pacet durng epoch e'', but not n e'. As our mechansm for decrementng the m ensures the ndependency between the random varables at rghthand sde of (8), the pdf of ' can be determned as the convoluton of the ndvdual pdfs of ; that s, ' ~ z' = z z L z, where s the convoluton operator. So ' = ) = z'(). Lewse '' = ) = z''(), 1 2 M where the pdf z'' = z z L z. 1 2 M If the random varable e' s the number of sensors that wll send a data pacet durng the epoch e'' amongst the ' sensors that send a data pacet at e' and thus get a control value update p e', then we have e u p = = u) = e (1 p ) u e, u, > u (1) Recall that varable p e' s the control value to be used durng epoch e'. By averagng over all possble ' values, we can obtan the followng approxmate dstrbuton of e' ˆ = = = = e ) u) e = u= ˆ u u = z u) p e (1 pe ) u= u) ( (11) where ˆ s the maxmum possble '. Fnally, let the random varable be the number of pacets that wll be receved durng epoch e'', then t can be seen from Fgure 1 that = '' + e'. Thus = ) = = v= v= e = v) = e = v) z ( v) v) ˆ u v u v = z ( u) pe (1 pe ) z ( v) v= u= v v (12) Ths gves the probablty dstrbuton of the number of pacets that wll be receved durng epoch e''. Based on ths dstrbuton, we can calculate the approprate p e' to be used n the epoch e'. Ideally, we should maxmze the probablty of beng the same as the desred QoS. Gven the desred QoS requrement as the number of data pacets n every epoch, we propose the optmzaton problem as maxmzaton of the probablty that, the number of data pacets receved n an epoch, s wthn a range [Q HB, Q + HB], whch s centered at Q (the desred QoS). One may consder HB as half the band (nterval) about whch the optmzaton occurs (HB = 1 or 2 has wored well n smulatons). To determne the approprate control value, p, to be sent to the transmttng nodes, the followng expresson must be teratvely solved to maxmze the probablty Q HB Q + HB): Q+ HB = Q HB v= u= v ˆ z u v v u v ( u) p e (1 pe ) z ( v) (13) Note that ths teraton s a sngle-varable optmzaton wth respect to p e'. In our smulatons, the clusterhead solves ths optmzaton problem by evaluatng (13) wth each of 1 Monte Carol random ponts n the range [, 1] as p e' and fnd out whch p e' value gves the maxmum value of (13).

5 3.3 Dealng wth Sensor Falures We call those sensors that sent ther last pacets n epoch as epoch sensors. The number of epoch sensors that haven t shown up but are stll alve (we call these potental sensors from epoch ) can be less than m, snce some of them may have already faled and wll no longer send any data. We now determne a means to detect falure of sensors from the number of epoch sensors that have shown up n the last two epochs respectvely,.e. r,1 (for the current epoch) and r,2 (for last epoch,.e., the epoch mmedately before the current epoch). Suppose there s no sensor falure,.e., there are stll m potental sensors from epoch by the end of the current epoch as ndcated by recorded networ traffc nformaton, then we now that the random varable R,1, the number of epoch sensors that should have shown up n the current epoch, follows the dstrbuton B(m +r,1, p ); and that the random varable R,2, the number of epoch sensors that should have shown up n last epoch, follows the dstrbuton B(m +r,1 +r,2, p ). Based on these dstrbutons, we can derve the confdence nterval of certan percentage, e.g. 95%. When r,1 and r,2 fall out of ther respectve confdence nterval, we nterpret t as there are sgnfcant sensor falures among the m sensors. Thus we cannot trust m as the number of potental sensors anymore. In PQC, a two-step estmaton s used to estmate the number of potental sensors from epoch based on r,1 and r,2 as follows: m = (r,2 /p + r,1 /p + r,2 )/2 (r,1 + r,2 ) (14) Algorthm 2 summarzes the role of the clusterhead n our predctve QoS control scheme. Algorthm 2a s trggered on the arrval of a data pacet at the clusterhead; whle Algorthm 2b s trggered on the end of every epoch to compute new control value for next epoch and mantan networ traffc nformaton record. event data_pacet_receved( ) { 1. Send bac an AC wth the control value p; 2. Extract the tmer-value TV sent along n the data pacet, and decrease by 1 the m of the entry correspondng to the epoch TV epochs before (wth TV epochs n between); Also, ncrease the correspondng r,1 by 1; } Algorthm 2a. Clusterhead Acton on Data Pacet Arrval event epoch_ends( ) { 1. Record networ traffc: add a new entry to record the control value and the number of pacets receved n the epoch that just ended; 2. Clean useless networ traffc nformaton: remove expred entres, whose lfetme (T UB ) have ended; 3. If sensor falure s detected for a specfc recorded entry, use two-step estmaton to estmate m based on r,1 and r,2 nstead of usng what s recorded; 4. Approxmate the probablty dstrbuton of the number of pacets to be receved the epoch e'', whch follows the next epoch, based on recorded networ traffc nformaton; 5. Iteratvely solve (13) to fnd ts maxmum thus determnng the approprate control value p e'. Set p, the control value to be sent to nodes, to p e'. 6. for each : r,2 := r,1 ; r,1 := ; } Algorthm 2b. Clusterhead Acton on Epoch Ends Table 1 llustrates an example of networ traffc nformaton recorded at the clusterhead for the predcton purpose (see 3.2), the falure detecton and two-step estmaton of the number of potental sensors. In ths example, Q = 4 and N = 7. Ths s the real-tme networ traffc nformaton durng the current epoch #1. Loong bac at the epoch #3, a total of n 3 = 41 data pacet were receved. All 41 epoch #3 sensors receved the same control value (.58), whch comes from the soluton of (13) n 3.2; and m 3 = 12 of these sensors have not sent snce. That s, there are no more than 12 potental sensors from the epoch #3 at current tme. The current epoch #1 s ongong, and r 3,1 = 8 data pacets have snce been receved from epoch #3. In last epoch (#2), r 3,2 = 21 data pacets were receved from epoch #3 sensors. The entry for epoch #3 has a lfetme of T UB = 5. Thus the number of potental sensors m 3 = = 12. Also, note that the sum of the column r,1 equals n 1 = 34; and the sum of the column r,2 equals n 2 = 42. The value of T UB s derved from (3) n 3.1. epoch # () n p m r,2 r,1 T UB ? 5 Table 1. Example Networ Traffc Informaton

6 4. Performance Experments Smulatons were carred out to study the performance of the proposed PQC protocol, and compare t wth the equal partcpatng Bernoull technque as the control benchmar [3]. In the frst study, 7 sensors were deployed each of whch has a lfetme of 1 (battery energy allows sendng 1 data pacets). In these smulatons, we assume that a sensor wll de f and only f t runs out of battery (no other falure mechansms). We set the desred QoS to be 4 data pacets every epoch. Smulatons were repeated 1 tmes, and the mean of number of data pacets receved at each epoch s shown n Fgure 2. It shows that PQC obtans the same mean QoS as the Bernoull benchmar, and the networ lfe of PQC approaches to that of the Bernoull benchmar. However, n these smulatons, the Bernoull benchmar dd not count the energy consumed n acqurng N and n contnuous lstenng of all sensors to control messages; otherwse the lfetme of the Bernoull benchmar wll be much shorter than what we see. mean # of pts receved predctve control bernoull control epoch tme Fgure 2. Networ lfe-tme comparng wth the Bernoull benchmar Next, we have vared the desred QoS and repeated the study wth the assumpton that every sensor has nfnte power. The results are gven n Fgures 3 and 4, whch show that the mean and varance of QoS of PQC approach the Bernoull benchmar under varous QoS requests. As llustrated n Fgure 5, f we ntalze the transmsson probablty of all the sensors wth 1, they wll converge to the Bernoull benchmar transmsson probablty, whch s 4/7.57 n approxmately 1 epochs. Thus, the PQC qucly acheves near Bernoull benchmar equalty n sensor partcpaton. mean # of pts receved predctve control bernoull control desred QoS Fgure 3. Desred QoS vs. mean QoS obtaned comparng wth the Bernoull benchmar standard devaton n QoS predctve control bernoull control theoretcal desred QoS Fgure 4. Desred QoS vs. Varance n QoS ntalng wth Bernoull benchmar transmsson probablty of sensors epoch tme Fgure 5. transmsson probablty (control value p) of sensors under PQC wth 99% confdence nterval

7 To measure the networ lfe quanttatvely, we defne the metrc -β lfetme: we chec the total number of data pacets receved durng every epoch to see f t falls out of the 1 β confdence nterval centered at Q; when we observe consecutve fall-outs we presume the networ lfe has ended snce the frst of these fallouts. Fgure 6 shows that PQC acheves smlar -β networ lfetme ( = 1, β =.455,.e., the 95.45% confdence nterval) as the Bernoull benchmar under varous QoS requests n energy smulatons (each sensors has a lfetme of 1). panc drop spe n PQC when N rses suddenly from 5 bac to 14 as there was n [3]. mean # of pts receved predctve control bernoull control networ lfetme predctve control bernoull control epoch tme Fgure 7. Responsveness to change n desred QoS 15 Number of sensors N desred QoS Fgure 6. Networ lfetme vs. desred QoS (-β settngs of = 1 and β =.455) 1 5 E(Q) N Var(Q) Bernoull Var The followng scenaros consder the cases where there s a change n QoS request or when there are large swngs n the number of avalable sensors. In these smulatons, we assume sensors have nfnte power. The goal of these smulatons s to study the response of PQC control protocol to the system and networ dynamcs. We frst vared the desred QoS, but fxed the total number of sensors. Fgure 7 shows that PQC adapts to the changes n QoS request very qucly. Comparng to the results from [3], PQC has a much better response. What s more, there s no panc drop spe n PQC when QoS request s suddenly lowered. The Bernoull benchmar protocol adapts to these changes mmedately snce t s assumed that all sensors are updated at each epoch. Fgure 8 shows the response of PQC when N, the total number of sensors, vares and QoS request s fxed. Agan, PQC has better response to changes n N than what s proposed n [3]. For example, when N drops from 14 to 7, the scheme proposed n [3] taes around 4 epochs to recover; whle PQC only taes around 1 epochs to recover. What s more, there s no mean # of pts receved Epoch predctve control bernoull control total sensors deployed epoch tme Fgure 8. Responsveness n reactng to change n total number of sensors deployed. Top: Automaton from [3]. Bottom: PQC and Bernoull benchmar

8 5. Concluson Heren, we presented a predctve strategy for adjustng the transmsson ntervals n a wreless sensor networ. Whle the control parameter s determned centrally based on the actual versus desred QoS, ndvdual nodes have control over ther partcular actvty. The methodology was shown to acheve performance smlar to a Bernoull benchmar n terms of networ lfe, mean and varance n QoS and responsveness to networ dynamcs. The ey advantages of the technque are that t does not requre explct nowledge of the total number of networ sensors, and that t does not requre all sensors to lsten to control nformaton at each epoch; both of whch are shortcomngs of the Bernoull benchmar method. Reference [1] Meguerdchan, S., et al, Coverage problems n wreless ad-hoc sensor networs, Proceedngs of IEEE IN- FOCOM 21, Vol. 3, pp [2] Proceedngs of the IEEE s SNPA 23, ACM s SenSyS 23/4, IEEE/ACM s IPSN 24/5, etc. [3] ay, J. and Frol, J., An expedent wreless sensor automaton wth system scalablty and effcency benefts, submtted to IEEE Trans. Systems, Man and Cybernetcs, Part A, February 25. [4] Iyer, R. and lenroc, L., QoS Control for Sensor Netows, IEEE Internatonal Communcatons Conference (ICC 23), Anchorage, A, May 23 [5] Frol, J., QoS Control for Wreless Sensor Networs, Wreless Communcaton and Networng Conference (WCNC 24), Atlanta, GA, March 24 [6] ay, J. and Frol J., Qualty of Servce analyss and control for wreless sensor networs, 1st IEEE Internatonal Conference on Moble Ad-hoc and Sensor Systems (MASS 24), Ft. Lauderdale, FL., Oct. 24