Real Time Communication Capacity for Data Delivery in Wireless Sensor Networks

Transcription

1 Real Tme Communcaton Capacty for ata elvery n Wreless Sensor etworks eepal Vrman an Satbr Jan epartment of CSE, BPIT, GGSIPU, elh, Ina, 85. eepalvrman@gmal.com epartment of CSE, SIT, U, elh, Ina, 3. Jan_satbr@yahoo.com Abstract Real-tme applcatons are performance crtcal applcatons that requre boune servce latency. In mult-hop wreless a-hoc an sensor networks, communcaton elays are omnant over processng elays. Therefore, to enable real-tme applcatons n such networks, the communcaton latency must be boune. In ths paper, we erve epressons of realtme capacty that characterze the ablty of a network to elver ata on tme as well as evelop network protocols that acheve ths capacty. Real-tme capacty epressons are obtane an analyze for the earlest ealne frst, ealne monotonc. Ths paper presents a treatment of the real-tme capacty lmts. The lmts are erve for two etreme traffc topologes namely, the loa balance topology an the convergecast (.e., many-to-one) topology. It consers M an EF scheulng algorthms, an scusses the mplcatons of the capacty lmt epressons. eywors: Real tme, Communcaton, Capacty, ealne lmts, Wreless Sensor etworks ) Introucton The performance-crtcal applcatons that requre boune elay latency are referre to as real-tme applcatons. Those wreless sensor networks that are capable of provng boune elay guarantees on packet elvery are referre to as real tme wreless sensor networks. A multtue of problems nees to be solve to acheve the goal of supportng real-tme applcatons n WS. As mentone earler, the network uses share (wreless) meum for communcaton. Therefore, one nees a strbute meum access control (MAC) protocol that s capable of provng guarantee banwth over multple hops. Boune latency guarantee of en-to-en packet elvery s a necessary frst step. The real-tme support must be acheve at low power an low message overhea to lmt nterference an conserve energy. We efne real-tme capacty of a network to be ts nformaton carryng ablty for gven ealnes, where only those nformaton bts that arrve at ther estnaton wthn the specfe ealne count. For WS the unt of ata s a packet rather than bts. If a packet oes not reach ts estnaton by the gven ealne, then ts contrbuton to the real-tme capacty s. Ths s n contrast to the capacty efne n [] an other research cte above where every transfer of bt counts. Analytc epressons for real-tme capacty facltate the process of esgnng a network that s guarantee to meet specfe throughput an elay requrements. The epressons escrbe values of a set of varables that wll enable the network to meet antcpate real-tme requrements. In other wors, they efne the feasblty regon n the space of such varables. In the event of ynamcally changng network, whch s epecte of WS, beses plannng an esgnng, the feasblty regon allows optmzaton of the operaton of the network. Abelzaher et al. presente the frst results on the real-tme capacty lmts of wreless sensor networks []. Epressons for the real-tme capacty lmts are obtane usng suffcent contons on scheulablty. A class of tme nepenent fe prorty scheulng algorthms s consere. Loa-balance an converge cast the two etreme traffc topologes are consere. In ths paper, we present the results an eten them for the EF scheulng algorthm. Yan et al. propose an energy-effcent servce for provng fferentate survellance by varyng the egree of sensng coverage [3].

2 Cao et al. present an stochastc performance analyss of WS for survellance applcatons base on network parameters [4]. Tng Yan presente scheulablty analyss of peroc flows n WS [5]. Schmtt an Roeg use an eten the etwork Calculus [6] to formulate the trae off between the buffer sze requrements an power consumpton wth the worst case elay [7]. A sutable arrval curve for WS s presente. oubaa et al. eten the Sensor etwork Calculus formulaton of Schmtt an Roeg for a cluster base tree topology an IEEE 8.5.4/ZgBee MAC protocol [8]. The authors conclue that the banwth requrement grows eponentally wth the epth of the tree. Ther concluson s base on the ncorrect assumpton that number of clusters grow eponentally wth tree epth. The growth s nfact quaratc n tree epth. To see ths, the number of clusters at epth n s appromate by the rato of the area contane wthn the rng of ra nr an ( n ) R R an the area contane wthn one cluster. Thus, the number of clusters at epth n s appromately n. Therefore, the total number of clusters n the tree n n up-to epth n s n n. Furthermore, the elay boun obtane s base on the Concatenaton Theorem of etwork Calculus. Whle the theorem has been prove for wre networks, t oes not hol n ts current form for wreless networks. Ths paper presents a treatment of the real-tme capacty lmts. The lmts are erve for two etreme traffc topologes namely, the loa balance topology an the convergecast (.e., many-to-one) topology. It consers M an EF scheulng algorthms, an scusses the mplcatons of the capacty lmt epressons ) Problem Formulaton We conser a mult-hop wreless sensor network where the number of noes s enote by n. The set of noes that can receve packets from noe s enote by P packets are enote by. The arrval tme of a At neghbourhoo(). The packet, s efne as the tme when the packet arrves at the transmt queue of the orgnatng noe. Each packet has a relatve ealne assocate wth t. The packet must be elvere to ts estnaton by the tme At. We assocate a per-hop T transmsson tme, wth each packet. Ths transmsson tme s a functon of raw banwth an characterstcs of the physcal meum. In terms of the effectve banwth, B, T s the rato of the packet sze an B. The per-hop T utlzaton s efne as. A packet contrbutes ths much to the overall utlzaton of At every noe n ts path from tme At to (t). Therefore, f s the set of packets that are present n the network at some gven tme t, whose ealne has not epre yet an whose path nclues noe, then the utlzaton of noe, enote by efne as Ut ( t) P ( t) T Ut () BT Snce s the packet sze, BUt (t) gves the real-tme capacty eman at noe. Therefore, the real-tme capacty eman for the B Ut ( t) entre network s gven by. If we Ut obtan an upper boun on such that f the s Ut then all noe s utlzaton oes not ecee packets are guarantee to meet ther ealne, then no ealne mss woul occur f the realtme capacty eman oes not ecee B Ut ( t). In other wors, B Ut (t) () Where enotes real tme communcaton capacty. 3) Assumptons For channel access, we assume an eal MAC protocol, as the MAC protocol transmts packets n prorty orer. The propagaton spee n

3 wreless meum s spee of lght, an the stance scale s of the orer of a few klometers. Therefore, the propagaton elay of the packets s neglgble as compare to queung an transmsson elays. Accorngly, we gnore the propagaton elay of packets n the followng analyss. We o not assume crcular rao range n the theoretcal ervatons. We, however, assume that the number of noes that may be blocke ue to a transmsson s upper boune, an that the boun s known. We assume that the per-hop transmsson tme of a packet remans constant throughout the route of the packet. We use the assumpton of large number of noes to perform appromatons of fe prorty realtme capacty lmt epressons. 4) Feasblty Contons We conser transmsson of a packet through a sequence of noes, whch we call the packet s path. We now erve a path-specfc conton on meetng en-to en ealnes as a boun on a functon of utlzaton values. If the value of ths functon oes not ecee the boun, then the packets transmtte along ths path are guarantee to meet ther ealne. In the followng analyss, we use theorems for scheulablty of tasks contenng for a gven set of resource(s). In the contet of WS, the resource s the channel at the recever noe. Let neghbourhoo() enote the set of noes who conten for the transmsson of noe. The broacast nature of wreless meum allows only one noe of ths to transmt at a tme. Therefore, all packets scheule for transmsson n neghbourhoo() form one sngle vrtual queue whose total utlzaton s equal to Ut neghbourhoo() (3) Where s the neghborhoo utlzaton. Let u be upper boun on the sze of neghbourhoo() for all. Then u ut, wrtten as. Therefore, () can be RTTC B u (4) 4.) Correctons for prorty nverson In wreless networks, snce no concurrent transmsson can occur n the neghborhoo of a recever, the transmsson of a packet can block another transmsson up to two hops away. From the pont of vew of prortze transmssons, ths can lea to prorty nversons of a unque kn []. For eample, conser the case of a recever recevng a hgh prorty packet. o noe n the neghborhoo n the recever can transmt smultaneously. If there s some lower prorty packet sener at the perphery of the neghborhoo that has packets for a recever n the nearby neghborhoo, then t gets blocke. If ths latter transmsson were the hghest prorty for the latter recever, from the perspectve of the recever, ths s a prorty nverson. Snce ths phenomenon arses not ue to watng for a lower prorty transmsson, t s referre to as pseuo prorty nverson. The effect of elays ue to pseuo prorty nverson ecreases the real-tme capacty. We quantfy the effect of pseuo prorty nverson as an ncrease n neghborhoo utlzaton by a factor. Applyng ths correcton to the epresson for the real-tme capacty (5) gves, B u 4.) Fe Prorty Scheulng P Let us conser some packet a. Let (5) TA enote Pa the tme between the arrval of the last bt of at noe an eparture of ts last bt from the TA same noe. In other wors, s the packet s elay at noe. The followng theorem prove by Abelzaher [] gves the boun on the elay of a task as a functon of utlzaton for tmenepenent fe prorty scheulng algorthms: Theorem 4. (The Stage elay Theorem []) If TA at resource Ut, an task T spens tme s a lower boun on the mamum utlzaton at that hop, then:

4 TA Ut (6) Where ma s the mamum en-to-en ealne of all tasks of hgher prorty than T. Ths theorem apples to a very general class of resources, where the access to the resource s grante to only one task. Corresponngly for wreless sensor networks, from the stage elay theorem, TA ma (7) In other wors, f the neghborhoo utlzaton of noe oes not ecee, then the packet TA elay at that noe oes not ecee. The ento-en boun on the elay s obtane by smply summng over all noes: TA ( ) ma (8) Where s the number of hops on the packet s path. For the packet to meet t s ealne, the en-to-en elay must not ecee ts relatve ealne, r. Therefore, ma Rearrangng the terms, we get: r r ma (9) () To obtan a suffcent boun, the rato of the P ealne of packet a to that of a hgher prorty packet that elays ts transmsson, r ma ut Ut must be mnmze over all possble cases. Let us enote the mnmum of ths rato ma for a gven fe prorty scheulng polcy. ealne monotonc algorthm assgns prorty n the orer of ecreasng relatve ealnes. Thus we efne, for ealne monotonc scheulng algorthm. Clearly, ths rato can not be larger than. Therefore, ealne monotonc scheulng algorthm gves the mamal boun: 4.3) EF Scheulng () We use Theorem 4. to erve scheulablty boun on neghborhoo utlzaton for EF. Smlar to the ervaton for fe prorty scheulng algorthms presente n the prevous secton, we conser transmsson of a packet along some path whose noes are labele. Snce s the neghborhoo utlzaton of each noe on ths path, the total utlzaton on the path s. From Theorem 4. all packets on ths path are scheulable prove U Boun 4 Theorem 4. ( s U Boun4 ), U n u () that, s a suffcent conton for J,, Jn scheulablty of jobs n a ppelne usng EF f the ecomposton of the eecuton tmes of the jobs s unknown. 5) Capacty Lmts In ths secton, we present the analyss of realtme capacty lmts for ealne Monotonc an Earlest ealne Frst scheulng algorthms. 5.) Loa balance traffc Loa balance traffc refers to the traffc pattern where every noe has the same noe utlzaton.

5 crtcal capacty Equvalently every neghborhoo utlzaton becomes the same. More precsely, every neghborhoo utlzaton equals the lowest boun of all neghborhoo utlzatons, etermne by the upper boun on neghborhoo sze u. We enote ths common boun on neghborhoo utlzaton by. Let be the upper boun on the path length. Therefore, from (), Solvng for we get (3) (4) From (5) nb FP u (5) Path Length() M EF Fg Real tme communcaton capacty 6) Convergecast traffc Convergecast refers to the traffc pattern n whch noes transmt ata to a common ata aggregaton pont or base- Where n s the number of noes n the network. ow we obtan the real tme capacty for EF from () EF nb u (6) (7) Fgure shows a comparson of the real-tme capacty lmt epressons for M an EF. The fgure shows that the real-tme capacty lmt for M approaches that for EF as the path length ncreases. Ths behavor of the curves can be eplane as follows: as paths get larger, Therefore nb u. FP EF eghbourhoo Sze Smulaton Analytcal Fg Effect of rao raus, 8 noes staton (Fgure 3). There may be a number of ata aggregaton ponts strbute n the network. In such a case, the traffc s estne to the nearest ata aggregaton pont. The ata aggregaton ponts form the bottleneck. The

6 noes n the neghborhoo of the ata aggregaton ponts are loae the most. In the followng, we erve an appromate epresson for real tme capacty lmt for convergecast. Base Staton Fgure 3 Convergrcast traffc Let be the number of ata aggregaton ponts n the network. We conser the traffc sent to an arbtrary ata aggregaton pont. Let be largest path length of the packets estne to. Snce all traffc ens up at the ata aggregaton pont, at steay state, the total amount of traffc generate for must equal the total amount that m R can be elvere to. Let be the average ensty of noes n the area of one rao range R. The number of noes locate hops away from the ata aggregaton pont s appromate by the prouct of the area of the rng m R R ( ) R an the noe ensty ( )m whch s equal to noes. Therefore, the average noe utlzaton, an hence neghborhoo utlzaton, ecreases wth stance from the aggregaton pont. If we enote the utlzaton at the ata aggregaton pont to be, then the utlzaton of the th hop noes s ( ) m. Therefore, from the feasblty conton for M s ( ) ( ) ( ) m ( ) ( ) m ( ) m ( ) m ( ) m ( ) m ( ) ( ) m m (8) Inequalty (8) s nonlnear n. We present a close form epresson that appromates the eact soluton below. From (5),

7 B / FP (9) where s soluton of (8). ow we obtan the real-tme capacty for EF. From (), m To obtan the sum the Euler s constant (.587) (), we note that s gven by / /3/ log () S' /.From S' ( log ).Furthermore, S S' / /3/ Therefore, log k S / log / log k / log / log k.5 log We get by pluggng (3) nto () as: m.5 log From (5) () (3) (4) Where the seres appromaton gets better as. Let S = ' an let EF B (.5log ) (5) EF M Mamum Path length() Fgure 4 Real tme communcaton capacty for convergecast traffc.

8 Fgure 4 presents a graph of the real-tme capacty lmt for Man EF scheulng algorthms. The values were obtane usng numercal soluton of the capacty epressons erve above. The plot shows that the relatve fference n the capacty epressons get mnshe as ncreases. Ths can be reasone by notng that n (8), the secon term can be appromate by unty, gven that <. Upon ths appromaton, (8) becomes same as the boun on for EF FP B (.5log ) (6) 6.) Convergecast vs. Loa-balance Traffc In the followng, we compare the real-tme capacty lmts obtane for loa balance traffc an convergecast traffc. For the purpose of comparson, we use the epressons for EF snce the appromate close form epressons for M resemble that for EF. Let CC an be the real-tme capacty lmts for the loa balance an convergecast cases respectvely. Then, for the smlar path lengths, namely BL CC ' we have n(.5log m (7) m Snce s appromately the number of noes nse one aggregaton pont oman, m n / BL CC. Therefore.5log ) BL (8) Ths rato becomes when. Ths s to be epecte snce each transmsson eclues m noes of the neghborhoo n both traffc topologes. For larger values of, the capacty lmt for loa balance case s larger than that for the convergecast snce the absence of bottleneck n the earler case allows the recepton of larger amount of traffc at the estnaton per unt tme. The gan, however, s only logarthmc. The reason for ths phenomenon s that for the loa balance traffc, the ntersecton of fferent flows, an hence nterference grows wth the path sze. But, for the convergecast traffc, the traffc flow s raal, an hence the nterference s not much of an ssue at larger hop stances from ata aggregaton ponts. 7) Evaluaton We mplemente a smulator J-sm to evaluate the pessmsm n the capacty epressons. The smulator constructs a network of sensor noes of a user-specfe sze n a perturbe gr structure. The rao layer s mplemente as a smplfe sk moel of a specfe raus (range). The snks are strbute unformly across the network. We generate traffc at each non-snk noe such that each packet was assgne a ealne at ranom from a preselecte set. All packets were sent to ther nearest snk. Packet contenton was resolve n prorty orer. Only those noes were allowe to transmt who were not wthn the rao range of another noe that was alreay scheule to receve a transmsson. Tes between smultaneously arrvng same prorty packets were broken at ranom. We mplemente a shortest path routng scheme n whch the neghborng noe nearest to the snk was chosen as the net hop. If ths noe was blocke ue to another transmsson, the packet was not scheule untl that transmsson was over. The MAC layer mplements ealne monotonc prortzaton for meum arbtraton. All packets were checke for ealne msses. All packets were checke for ealne msses. If there was a mss, the actual capacty consumpton of all n-transt traffc was compute by multplyng each n transt packet by the traverse hop count an normalzng by the en-to-en ealne. Each run was repeate 5 tmes wth fferent ranomze workloas. The mnmum capacty consumpton at whch a ealne mss occurre was recore, an s shown on the plots as crtcal capacty. Fgures show the effect of ncreasng the rao raus, shown on the top horzontal as, on realtme capacty n a network of 8 noes. Observe that ncreasng the rao raus also ncreases the neghborhoo sze (.e., the number of noes wthn the rao range), shown on the

9 ealne Mss Rate(%) Crtcal Capacty Crtcal Capacty bottom horzontal as. The number of snks was kept at. Fgures 5 an 6 repeat the eperments for networks of 8 an 6 noes respectvely, ths tme varyng the number of snks. The rao range s kept constant at a neghborhoo sze of noes. As before, a very close match s observe between smulaton an analyss. Capacty grows wth the number of snks because ata collecton bottlenecks are allevate Smulaton Analytc Smulaton Analytc o of Snks o of Snks Fgure 5 Effect of the number of snks, Fgure 6 Effect of the number of snks, 8 noes 6 noes Fnally, Fgure 7 shows the sharp ncrease n the mss rato n a network of 8 noes that occurs when capacty s eceee. In ths curve, the network workloa s ncrease past the capacty boun. The mss rato s then plotte aganst the capacty requrements of the workloa shown on the horzontal as. Each pont n the fgure correspons to a sngle eperment. Two sets of ata ponts are shown for two fferent rao ranges that correspon to neghborhoos of noes an 4 noes respectvely RT Capacty eman eghborhoo Sze eghborhoo Sze 4 Fgure 7 Mss rate as a functon of real tme capacty eman 8) Conclusons In ths paper we presente real-tme capacty lmt epressons uner the suffcent scheulablty conton. We erve lmtng epressons for large networks. We saw that uner such lmtng crcumstances, the real-tme capacty lmts for ealne monotonc an earlest ealne frst scheulng algorthms ten to agree on a common value. We showe that for convergecast, the real-tme capacty ncreases as the square root of the number of noes. Ths mples estence of mnshng return an

10 hence favors multple smaller networks as oppose to a large one. We fn that the realtme capacty obtane analytcally agrees wth that obtane usng smulaton wthn 3-4% n general. The agreement gets better as the effectve ensty ncreases. References pages IEEE Computer Socety Press, Los Alamtos, CA, 4. [] T. P. Baker. Multprocessor EF an ealne monotonc scheulablty analyss. In Proc. of the 4th IEEE Real-Tme Systems Symposum (RTSS 3),pages 9. IEEE Computer Socety Press, Los Alamtos, CA, 3. [] P. Gupta an P. R. umar. The capacty of wreless networks. Informaton Theory, IEEE Transactons on, 46():388 44,March. [] Tarek Abelzaher,. Shash Prabh, an Raghu ran. On real-tme capacty lmts of multhop wreless sensor networks. In Proceengs of the 5th IEEE Real-Tme Systems Symposum (RTSS 4). IEEE Computer Socety Press, Los Alamtos, CA, 4. [3] Tng Yan, Tan He, an John A. Stankovc. fferentate survellance for sensor networks. In SenSys 3: Proceengs of the st nternatonal conference on Embee networke sensor systems, pages 5 6, ew York, Y, USA, 3. ACM Press. [4] Qng Cao, Tng Yan, John Stankovc, an Tarek Abelzaher. Analyss of target etecton performance for wreless sensor networks. In strbute Computng n Sensor Systems, Frst IEEE Internatonal Conference, Proc. of (COSS 5), pages Sprnger, 5. [5] Tng Yan. Analyss Approaches for Prectng Performance of Wreless Sensor etworks. Ph thess, Unversty of Vrgna, 6. [6] Jean-Yves Le Bouec an Patrck Thran. etwork calculus: a theory of etermnstc queung systems for the Internet. Sprnger-Verlag ew York, Inc., ew York,Y, USA,. [7]. Shash Prabh an Tarek F. Abelzaher. Energy conservng ata cache placement n sensor networks. The ACM Transactons on Sensor etworks, ():78 3, ovember 5. [8] Ans oubaa, Maro Alves, an Euaro Tovar. Moelng an worst-case mensonng of clustertree wreless sensor networks. In Proceengs of the 7 th IEEE Real-Tme Systems Symposum (RTSS 6), pages 4 4, Los Alamtos, CA, USA, 6. IEEE Computer Socety. [9] Tarek Abelzaher, Gautam Thaker, an Patrck Larer. A feasble regon for meetng aperoc en-to-en ealnes n resource ppelnes. In Proceengs of the 4th Internatonal Conference on strbute Computng Systems(ICCS 4),