Prioritized Heterogeneous Traffic-Oriented Congestion Control Protocol for WSNs

Size: px
Start display at page:

Download "Prioritized Heterogeneous Traffic-Oriented Congestion Control Protocol for WSNs"

Transcription

1 The Inernaonal Arab Journal of Infmaon Technology, Vol. 9, No. 1, January Przed Heerogeneou Traffc-Orened Congeon Conrol Proocol f WSN Muhammad Monowar 1, Obadur ahman 2, Al-Sakb Khan Pahan 3, and Choong Seon Hong 2 1 Dearmen of Comuer Scence and Engneerng, Unvery of Chagong, Bangladeh 2 Dearmen of Comuer Engneerng, Kyung Hee Unvery, Souh Kea 3 Dearmen of Comuer Scence, Inernaonal Ilamc Unvery Malaya, Malaya Abrac: Due o he avalably of mulle enng un on a ngle rado board of he modern en moe, ome en newk need o handle heerogeneou raffc whn he ame alcaon. Th dvere raffc could have dfferen re n erm of ranmon rae, requred bandwdh, acke lo, ec. Becaue of he mul-ho ranmon characerc of h rzed heerogeneou raffc, occurrence of congeon very common and unle handled effecvely, could hwar he alcaon obecve. To addre h challenge, n h aer we rooe a Przed Heerogeneou Traffc-ened Congeon Conrol Proocol (PHTCCP) whch erfm ho-by-ho rae adumen conrollng he congeon and enure effcen rae f he rzed dvere raffc. Th roocol alo could be aled f healhcare nfrarucure. We exlo cro layer aroach o erfm he congeon conrol. Our roocol ue nra-queue and ner-queue re along wh weghed far queung f enurng feable ranmon rae of heerogeneou daa. I alo guaranee effcen lnk ulzaon by ung dynamc ranmon rae adumen. We reen dealed analy and mulaon reul wh he decron of our roocol o demonrae effecvene n handlng rzed heerogeneou raffc n Wrele Sen Newk (WSN). Keywd: Heerogeneou, congeon, ner-queue, nra-queue, eduler, en. eceved July 27, 2009; acceed May 20, Inroducon The ohcaon of varou communcaon roocol [9] and rad advancemen of Mcro-Elecro- Mechancal Syem (MEMS) echnologe [23] have creaed a grea ouny f wde-read ulzaon of varou nnovave en newk alcaon n near fuure. Today en are caable of enng me han one arameer wh he ad of mulle en board mouned on a ngle rado board. MICA2 [4] an examle of uch ye of en. ExScal moe, an exenon of MICA2, alo u mulle enng un [1, 3]. Inead of ung mulle node wh varou funconale [15], deloyng uch node mgh offer co effecve oluon f many alcaon. F examle, a volcano monng alcaon mgh requre emeraure, emc, and acouc daa from ame locaon. Several alcaon could even run mulaneouly baed on varou daa en by he mul-uroe node. Dfferen ye of daa alo mgh have dfferen level of mance and accdngly her ranmon characerc mgh dffer. In h aer, we conder a WSN where he deloyed node are mul-uroe node and hey generae heerogeneou raffc dened o he Bae Saon (BS). Varou ye of daa generaed by he en have varou re. Hence, neceary o enure dered ranmon rae f each ye of daa baed on he gven ry o mee he demand of BS. In uch a newk, he en could n fac generae mle erodc even o unredcable bur of meage. Boh of hee cae roduce convergen daa flow from ource node o he BS whch can oenally caue congeon. Congeon become even me lkely when concurren daa ranmon over dfferen rado lnk nerac wh each oher when he reng rae o he bae aon ncreae. Wh he ncreae of number of node n he newk, congeon mgh occur frequenly. Such congeon ha a evere mac on he energy effcency and alcaon Qualy of Servce (QoS) of WSN. Congeon conrol mechanm requre he conderaon of wo man ue; congeon deecon and effcen rae adumen. In TCP, congeon nferred a he recevng end baed on meou dulcae acknowledgemen whle n WSN roacve mehod are referred. A commonly ued mechanm ung buffer lengh [5, 7, 17, 20] acke ervce me [2], he rao of acke ner-arrval me and acke ervce me [21]. To deal wh he congeon, an effcen rae conrol mechanm need o be degned n der o mgae avod congeon. The end-oend [7, 14, 18] and ho-by-ho [2, 5, 17, 20, 21] raegy have been emloyed f he rae conrol n he la few year. Here, we rooe a ho-by-ho rae

2 40 The Inernaonal Arab Journal of Infmaon Technology, Vol. 9, No. 1, January 2012 conrol eme f quck recovery of congeon a he nermedae node. The re of he aer ganzed a follow. Secon 2 ae our movaon wh relevan wk. Secon 3 reen newk model, goal, and relmnare, econ 4 reen he deal of PHTCCP. Analy and mulaon reul are reened n econ 5, and econ 6 conclude he aer wh fuure reearch drecon. 2. Movaon and elaed Wk A number of revou wk have addreed he ue of congeon conrol n WSN [22]. Bu mo of he wk have deal wh he rae conrol f homogeneou alcaon. In fac, no oher wk exce STCP [7] ha condered he ue of muluroe en n he newk. STCP a generc, calable and relable ran layer roocol where a may of he funconale are mlemened a he BS. The roblem of STCP wofold: 1. I ake much me f he ource o be nofed of he congeon uaon and hu o erfm he rae reducon f congeon elmnaon. 2. The ue of exlc acknowledgemen acke no uable f WSN whch alo ncreae congeon. Furherme, STCP doe no rovde any ecfc rae reducon alghm ha addree heerogeneou raffc. CODA [20] ue boh buffer occuancy and channel load f meaurng node and lnk level congeon n he newk. I handle boh ranen and eren congeon. Fuon [5] deec congeon by meaurng he queue lengh. I conrol congeon by combnng hree echnque, ho-by-ho flow conrol, ource rae lmng, and rzed MAC. Alhough Fuon clam o acheve good hroughu and farne a hgh offered load, he non mooh rae adumen n handlng ranen congeon a he nermedae node could me u lnk ulzaon and farne. IFC [17] an nerference aware rae conrol mechanm degned f en newk. I deec ncen congeon a a node by obervng he average queue lengh and erfm drbued rae allocaon among he node. IFC would fal o enure raffc ened weghed farne and mananng a feable ranmon rae f he dvere daa a conder every flow equally. In [2], he auh rooe a ho-by-ho congeon conrol echnque, Congeon Conrol and Farne (CCF), whch ue acke ervce me o nfer he avalable ervce rae and herefe deec congeon n each nermedae en node. CCF enure mle farne. However, lack effcen ulzaon of he avalable lnk caacy when ome node do no have any raffc o end node remanng n lee mode he node whoe flow do no a hrough he congeed area. PCCP [21] a recen congeon conrol roocol f WSN whch ue ho-by-ho aroach f rae conrol. PCCP a node ry baed congeon conrol roocol whch allow en node o receve ry-deenden hroughu. However, PCCP doe no have any mechanm f handlng rzed heerogeneou raffc gnaed from a ngle node. CT [14] an end-o-end rae conrolled relable ran roocol. Alhough h eme u concurren alcaon, conder heerogeneou node nead of heerogeneou raffc generaed from a ngle node. Meover, congeon deecon erfmed baed on acke lo recovery me and rae adaaon, and rae allocaon erfmed by nk. We argue ha he nk baed congeon deecon and rae conrol lack quck recovery of congeon a requre a lea one TT o deec congeon. Bede hee, hon [19] (ue raffc redrecon o mgae congeon), EST [18] (nk baed relable rae conrol roocol) ec., alo addre he congeon conrol ue bu none of hem conder he dvere raffc gnaed and roued hrough a ngle node. Hence, he carcy of an effcen congeon conrol roocol f handlng dvere daa wh dfferen re whn a ngle node movae u o rooe PHTCCP [12]. 3. Degn Conderaon and Prelmnare In h econ, we ae varou degn conderaon. Noe ha hroughou he aer he erm rae conrol and congeon conrol are ued nerchangeably Newk Model and Aumon We conder a WSN where houand of mul-uroe node are deloyed over a ecfc arge area. We exclude he avalably of any moble node [10] a he node f WSN are uually ac f mo of he alcaon. All node are equed wh he ame number of dfferen en board mouned on a ngle rado board. Each of he node can ene dfferen ye of daa a he ame me and end hoe o BS. Fgure 1 how a model f our newk decng ngle ah and mul-ho roung. Fgure 1. Newk model, roung oology vew.

3 Przed Heerogeneou Traffc-Orened Congeon Conrol Proocol f WSN 41 All node are uoed o ue Carrer Sene Mulle Acce wh Collon Avodance (CSMA/CA) lke MAC roocol. Me abou of our MAC roocol feaure are reened n econ 4.4. We aume ha he newk rucure and he roue o BS have been eablhed by ung ome effcen roung roocol. Whle eablhng he rucure of he newk, he BS dynamcally agn ndvdual ry f each ye of daa. Durng fwardng heerogeneou daa oward he BS, each en node ranm roue daa of chldren node a well a own generaed daa. So, a any gven me, a en may ac boh a a ource node and a fwardng node. When a en ranm daa o he uream drecon, called a chld and mmedae uream node called aren. Each lnk beween any aren and chld bdreconal ha f he chld ge aren whn ranmon range, he aren alo ge he chld whn ranmon range. We denoe he number of chld node f a aren node K a C (K). A n Fgure 1, node B ha 3 chldren, C ha 1, and node H doe no have any chld. F each node n he newk, here a ngle ah o reach o he BS. Fgure 1 alo how dfferen level of hoo node f congeon. The black node.e., A and B have he hghe robably of congeon a all he dvere raffc beneah hee node n he ub-ree (ncludng he node hemelve) ravere hrough hee node. The grey node mgh alo uffer from congeon n cae of bur raffc whle he whe node have he lea obly of node level congeon Node Model Fgure 2 dec he node model of a arcular en. The congeon conrol funconaly a he ran layer ha been ranferred o he PHTCCP module n he newk layer. We have emloyed cro layer funconaly n degnng our roocol. PHTCCP module wk neracng wh he MAC layer o erfm congeon conrol funcon. The alcaon layer generae gnang daa (f a ource node) and he roue daa come from he chld node (f ha any) and ravere hrough he newk layer. We aume ha each node ha n number of equal zed ry queue f n ye of ened daa. F examle, a en node mgh ene emeraure, lgh, and humdy a he ame me. In uch a cae, here are 3 earae queue f each ye of daa. The number of queue n a node deend on he alcaon requremen. A hown n Fgure 2, a clafer ha been rovoned n he newk layer. The uroe of ung h clafer o clafy heerogeneou raffc eher generaed by he ame node ncomng from oher node. Baed on he ye of daa, hey are laced n he aoe queue. A weghed far queue eduler ha been rovoned o edule he dvere raffc wh dfferen ry from he ry queue. The ry of he raffc ha been maed o he queue wegh. PHTCCP module doe no nerfere wh he ce funconaly of he newk layer. Hence, PHTCCP ndeenden of ung any roung roocol Defnon Fgure 2. A en node model f PHTCCP. Orgnang ae: The rae a whch a node gnae daa. Denoed a f a node. Schedulng ae ( ): The edulng rae defned a how many acke he eduler edule er un me from he queue. The eduler fward he acke o he MAC layer from whch he acke are delvered o he nex node (.e., +1) along he ah oward he bae aon. The rae conrol funcon erfmed by conrollng he edulng rae whch exlaned n deal n he nex econ. Average Packe Servce ae ( ): Th he average rae a whch acke are fwarded from MAC layer. Iner-Queue Pry: We menoned earler ha he bae aon agn he re f heerogeneou raffc. Therefe, each daa queue hown n Fgure 2 ha own ry. Th ermed a Iner-Queue ry. The eduler edule he queue accdng o he ner-queue ry. I decde he ervce der of he daa acke from he queue and manage he queue accdng o her re. Th enure he daa wh hgher ry o ge hgher ervce rae. Inra Queue Pry: All he queue hown n Fgure 2 are ry queue. Pry queue are ued f gvng he roue daa me ry han gnang daa. The reaon ha; a roue daa have already ravered ome ho (), her lo would caue me waage of newk reource han ha of he gnang (ource) daa. Hence,

4 42 The Inernaonal Arab Journal of Infmaon Technology, Vol. 9, No. 1, January 2012 beer o fward hoe a oon a oble afer recevng from he mmedae downream node. We erm h ye of ry a nra-queue ry. The clafer can agn he ry beween he roue daa and gnang daa by examnng he ource addre n he acke header. 4. Our Proocol: PHTCCP In h econ, we decrbe our rooed roocol. The ma goal f our eme are: 1. Generang and ranmng he heerogeneou daa on ry ba. 2. Adung he rae whle congeon occur, and 2 o enure effcen lnk caacy ulzaon when ome node n a arcular roue are nacve n lee mode. PHTCCP ue Weghed Far Queung (WFQ) f edulng. Here, we llurae PHTCCP n deal ung everal ubecon o addre he ue of congeon deecon, nofcaon, and mgaon Congeon Deecon Mehod We ue acke ervce rao r() o meaure he congeon level a each node. Packe ervce rao defned a he rao of average acke ervce rae ( ) and acke edulng rae ( ha : Here, he acke ervce rae acke ervce me ) n each en node r ( ) = / (1). he nvere of he me nerval when a acke arrve a he MAC layer and when uccefully ranmed oward he nex ho. nclude acke wang me, collon reoluon, and acke ranmon me a MAC layer. In equaon 1, n der o oban, he average acke ervce me, calculaed ung Exonenal Weghed Movng Average fmula (EWMA). By ung EWMA, fwarded a: udaed each me a acke w n( = (1 w ) + ) (2) Where, n ) he nananeou ervce me of he ( acke ha ha u been ranmed and w a conan where, 0 < w < 1. The acke ervce rao reflec he congeon level a each en node. When h rao equal o 1, he edulng rae equal o he fwardng rae (.e., average acke ervce rae). When h rao greaer han 1, he edulng rae le han he average acke ervce rae. Boh of hee cae ndcae he decreae of he level of congeon. When le han 1, caue he queung u of acke a he MAC layer. Th alo ndcae lnk level collon. Thu, he acke ervce rao an effecve meaure o deec boh node level and lnk level congeon Imlc Congeon Nofcaon PHTCCP ue mlc congeon nofcaon. Each node ggyback acke edulng rae ; oal number of chldren, C () ; number of acve chldren a me, A )) ; and he weghed average queue lengh of acve chld node n acke header. Becaue of he broadca naure of wrele channel, all he chldren of node overhear he congeon nofcaon nfmaon. Whenever he value of r() goe below a ceran hrehold (alcaon deendan), rae adumen rocedure rggered ae Adumen PHTCCP ue ho-by-ho rae adumen f conrollng he congeon. The ouu rae of a node conrolled by adung he edulng rae,. We have aed earler ha he nfmaon of acke ervce rao f congeon deecon ggybacked n he acke header along wh oher arameer. Each node udae edulng rae f h rao goe below he hrehold f here any change n he edulng rae of aren node. The nal edulng rae e o r. n Befe reenng he rae adumen alghm, we reen he noaon and lluraon n Table 1. The enre rae adumen alghm hown n Fgure 3. Each node meaure edulng rae by callng he Calculae_Schedulng_ae() mehod. In h mehod, a fr each calculae acke ervce rao. When h rao equal o 1, mean ha he ncomng rae of acke o he MAC layer equal o he average acke ervce rae (he rae a whch acke are fwarded from MAC layer). Th he deal cae o ha no congeon occur. In h cae, reman unchanged. reman unchanged a long a he acke ervce rao doen go below he ecfed hrehold. In fac, when he acke ervce rao ( r () ) le han he ecfed hrehold value (ay noed by µ), ndcae ha he edulng rae of acke larger han he average acke ervce rae. In uch a cae, acke would be queung u a he MAC layer buffer and mgh caue buffer overflow ndcang congeon. To conrol congeon, n h cae, he edulng rae ree (decreaed) o he value of acke ervce rae.

5 Przed Heerogeneou Traffc-Orened Congeon Conrol Proocol f WSN 43 Table 1. Bac noaon ued n he aer. Schedulng rae of node Orgnang rae of node Schedulng rae of he aren of node Toal number of acve chld node of he A )) aren of node a me Toal number of chld node of he aren C ( ) of node E () Exce lnk caacy a me ϕ () α q () avg q N Wegh fac f node a me Pry f he h queue of node, where, =1,2,..,n Curren queue lengh f h queue of node, where, =1,2,..,n Weghed average queue lengh of node a me Number of queue n node Alghm: ae Adumen Inu: Each node ; Ouu: Schedulng rae, Orgnang rae Inalzaon() n = r ; r () =1; Calculae_Schedulng_ae(, ) r ( ) = / If r () < µ hen If r ( ) > 1 hen reurn = = End If β End If Dyn_ae_Ad(, A )), C( ), E( ) ) )) C( = / C( A = hen ) If ) End If If )) C( ) End If A < hen = + ϕ ( ) E( ) Calc_ExceLnkCaacy( A )), C( ) ) E ( ) = reurn E () C( ) A )) / C( ) n= 1 n= 1, / C( ) Calc_NodeWeghFac( α, q, A )) ) N = = 1 α q q avg ( ) N q avg ( ) q ϕ = avg ( ) ( ) A ( C ( )) 0 reurn ϕ () Calculae_Sourceae(, α ) ( ) α = α + α + + α 1 reurn 2 n A )) oherwe Fgure 3. ae adumen alghm. When r () reache above 1, ndcae ha he acke ervce rae greaer han he edulng rae. Hence, he edulng rae ncreaed ung, = β. Here β value choen o a value maller han bu cloe o 1. In our roocol, e o Afer deermnng he dered edulng rae, each node adu own edulng rae accdng o he edulng rae of aren node. Th done dynamcally by callng he mehod Dyn_ae_Ad(). The rae adumen deend on wo cae: when node deermne ha all he chld node of aren (ncludng elf) are acve a me, a hown n Fgure 4-a, A )) = C( ) ), hen node make adumen n edulng rae. In h cae, each node e edulng rae equal o 1 C( ) h of aren edulng rae. In Fgure 4-a, f he edulng rae of he aren node, each chld node ha he edulng rae, / 4. Th enure ha he oal edulng rae of all he chld node no greaer han he edulng rae of her aren node. When node deermne ha ome of he chld node of aren (.e., blng) are dle (Fgure 4- b) ha when A )) < C( ), agan adu edulng rae. / 4 / 4 / 4 / 4 a) All chld node are acve (black coled node). b) Two chld node are dle (whe). Fgure 4. Any of he chld node ermed a, and he grey coled node he aren of. To acheve hgher lnk ulzaon by akng advanage of exce lnk caacy, E () drbued o he acve chld node accdng o her wegh fac ϕ () a a arcular me,. ϕ () deermned dynamcally ung he Calc_NodeWeghFac() mehod. Here he wegh fac of he node deend on weghed average queue lengh a me. The weghed average queue lengh calculaed by ung he fmula: q avg ( ) N α q 1 = = N (3) Here α he ry and q he lengh f queue a me. The wegh ϕ () reflec how he exce lnk caacy o be allocaed among he acve node and nmalzed uch ha: A ( C ( ϕ ( ) = 1 (4) ))

6 44 The Inernaonal Arab Journal of Infmaon Technology, Vol. 9, No. 1, January 2012 The exce lnk caacy meaured by ung Calc_ExceLnkCaacy(). I can be calculaed by ubracng oal edulng rae of acve chld node from he oal edulng rae of all he chld node. Afer calculang he edulng rae, each node udae her accdng o he mehod Calculae_Sourceae(). The gnang rae deend on he edulng rae a well a on he ry f each ye of daa agned by he bae aon Traffc Pry Baed MAC Proocol Our MAC roocol manly baed on drbued CSMA wh TS/CTS collon avodance followng he raegy of DCF mode of The rzaon of raffc can be acheved by dfferenang Iner- Frame-Sacng (IFS) and back-off mechanm. The dea o agn h IFS and back-off o he hgher ry raffc o ha hey can acce he channel earler han lower ry raffc [8, 16]. Hence, we ado IEEE e [24] rzaon wh ome mn change. The ry f each queue maed o one MAC ry cla. Hence, each queue ha dfferen Arbraon Iner Frame Sace (AIFS), Conenon Wndow (CW), and Perence Fac (PF) value accdng o ry. Th way, we can mnmze he ner-node ry nveron uch ha hgher ry acke n one node no lkely o be blocked by a lower ry acke n anoher node. 5. Smulaon eul and Analy We erfmed exenve mulaon o evaluae he erfmance of PHTCCP n n-2 [13]. We ued veron 2.26 of he n-2 mula ung he Two ay Ground roagaon model n he ar and a ngle Omn-dreconal anenna commonly ued wh n Smulaon Parameer Table 2 how he mulaon arameer. We ued dreced dffuon [6] a he roung roocol n whch durng he demnaon of he nere meage; he BS agn ry f each raffc cla. IEEE e MAC roocol rovded n n-2 [13, 24] mula wa ued. The defaul PHY arameer a exed n n f MAC ha been choen. We ued he e arameer a ued by [11, 24] f he dvere raffc accdng o her ry. The arameer w a conrollng arameer and we emrcally e value o 0.1. We condered 3 dfferen ye of raffc gnang from a ngle node and herefe each node wa rovoned hree queue a hown n Table 2. Traffc ye 1 wa gven he hghe ry value of 3, ye 2 wa gven 2, and ye 3 wa gven he value 1. Table 2. Smulaon arameer. Parameer Value Toal Area 100 m X 100 m Number of Sen 100 Tranmon ange 30 m Maxmum Communcaon Channel 32 kb B ae Tranmon Power 5.85e-5 wa eceve Sgnal Threhold 3.152e-20 wa Daa Packe Sze 33 bye Conrol Packe Sze 3 bye Value of w n Eq Number of Queue 3 Sze of each Queue 10 acke Offered Load 4~16 acke er econd () Number of Source 10 Pry Value ued f Hgh Medum Low Queue AIFSN CWmn Cwmax Perence Fac Smulaon Tme 60 ec 5.2. Smulaon eul Threhold of Packe Servce ao Fgure 5 demonrae how o deermne he hrehold of acke ervce rao. I how he ercenage of buffer acke dro (rreecve of raffc ye) f dfferen acke ervce rao conderng dfferen acke gnang rae. I noceable ha he ncreae n he rao reduce he ercenage of acke dro. F dfferen acke gnang rae ( acke er econd), he buffer acke dro ercenage gradually goe below and reache o an almo able ae (abou 2%) when he acke ervce rao become 0.5. Th a olerable value befe nofyng any congeon. Hence, we e he value of µ o 0.5. Fgure 5. Percenage of acke dro v acke ervce rao f dfferen gnang rae o deermne he hrehold value of µ Perfmance Analy Fgure 6 llurae he mac of acke ervce rao over weghed average queue lengh, avg q () a he node cloe o he nk. I how ha he weghed average queue lengh ncreae becaue of he ncreae of acke ervce rao. Th becaue, ncreae n

7 Przed Heerogeneou Traffc-Orened Congeon Conrol Proocol f WSN 45 acke ervce rao eed u he acke ervce rae. In uch cae, edulng rae hould be ncreaed n uch a way ha doen caue any buffer overflow. Fgure 9 dec how he average acke laency of hree dfferen ye of raffc vare wh dfferen wk load. The average acke laency wa meaured from he me a acke gnae o he momen arrve a he BS. A he queung delay ha gnfcan mac on he acke laency, wh he ncreae of he offered load, acke ar queung u and laency alo ncreae bu afer ceran offered load due o he rae conrol mechanm he laency ablze. A n he fgure, raffc ye 1 uffered lowe delay due o he hghe ry han he oher wo ye of raffc whch ndcae he BS receved raffc wh dvere laency accdng o he ry agned o hem. Fgure 6. Weghed average queue lengh f dfferen acke ervce rao a he node near he nk. By eng he value of β o 0.75, a moderae queue lengh could be mananed. We ran he mulaon f 60 econd and meaured he weghed average queue lengh over me a hown n Fgure 7. Th fgure how ha he maxmum weghed average queue lengh reache o 9 acke and on an average ay n beween 3 o 5 acke hroughou he mulaon erod. Th ndcae ha PHTCCP manan moderae queue lengh o avod overflow. Fgure 7. Weghed average queue lengh over me a he node near he nk reflecng he moderae queue lengh. Fgure 8 how he number of dfferen ye of acke receved by he BS over me. A er he ry gven o dvere daa, he nk receved hghe number of raffc ye 1 acke and hen raffc ye 2 acke. Traffc ye 3 acke were he lowe n number receved hroughou he mulaon erod. Fgure 9. Average laency over dfferen offered load. Fgure 10 comare nmalzed yem hroughu among PHTCCP, CCF, No Congeon Conrol, and PCCP. The yem bandwdh nmalzed o 1. Whn he me beween 30 o 50 econd, ome node are e dle. Whn ha nerval, PHTCCP acheve hgher yem hroughu han CCF nce allocae he exce lnk caacy o he acve node. PCCP alo ha good erfmance durng ha erod becaue of ulzng he remanng caacy bu overall hroughu f PHTCCP beer han PCCP a ha he effcen rae conrol f dvere raffc. Whenever acke are ranmed whou conrollng he ranmon rae, he overall yem hroughu everely decreae whch we durng he erod of econd. Fgure 10. Nmalzed yem hroughu over me. Fgure 8. No. of heerogeneou daa receved by he BS over me. In our mulaon we defne energy effcency a: T/H where T he number of bye ranmed n he

8 46 The Inernaonal Arab Journal of Infmaon Technology, Vol. 9, No. 1, January 2012 whole newk durng a erod of me, he number of daa bye receved by he BS durng he ame me and H he average number of ho a delvered acke ravel. A maller value ndcae beer effcency. Th meauremen nclude he acual ranmon of daa, he energy wae due o collon, and he energy wae due o acke dro. In comaron wh he four eme, Fgure 11 how ha PHTCCP acheve much beer energy effcency han CCF and PCCP. Energy Effcency No Congeon Conrol CCF PHTCCP PCCP Smulaon Tme (Second) Fgure 11. Nmalzed yem hroughu over me Memy Analy Fgure 12-a how he maxmum memy requremen f dfferen acke ze (conderng 29 bye, 33 bye, 41 bye, and 64 bye acke). The memy requremen can be calculaed by ung he followng equaon: M r = N l q (5) l Where, l he acke lengh, N he oal number of queue, and q l he ze of each queue. A we have condered hree queue n oal and each queue can conan maxmum 10 acke, he memy requremen are 870, 990, 1230, and 1920 bye f acke ze of 29, 33, 41, and 64 bye reecvely. Thu how ha f acke ze of 64 bye, whch long enough f a en newk alcaon, he memy requremen le han 2 KB. Hence, f a en moe ha a lea 4KB (4096 Bye) onboard memy, he maxmum memy occuancy would be le han 50% and on an average le han 30% whch rove ha our roocol could well be ued wh curren ecfcaon of moe. Fgure 12-b how he memy requremen f dfferen number of queue conderng 33 bye acke. Wh 33-bye acke ze, even f we have mulaneouly 5 dfferen enng un (5 dfferen queue), he roocol ha 41% memy occuancy f he moe ha a lea 4 KB onboard memy. When he number of queue 3, he occuancy abou 25% of oal avalable onboard memy. a) Maxmum memy requremen conderng dfferen acke ze. Fgure 12. Memy analy. 6. Concluon and Fuure Wk b) Memy requremen (bye) and ercenage of memy allocaon f dfferen number of queue. In h aer, we have reened PHTCCP, an effcen congeon conrol mechanm f heerogeneou daa gnaed from muluroe en node. We have demonraed hrough mulaon reul and analy ha acheve: 1. Dered hroughu f dvere daa accdng o he ry ecfed by he BS. 2. Hgh lnk ulzaon. 3. Moderae queue lengh o reduce acke lo. 4. elavely low acke dro rae. Therefe, PHTCCP energy effcen and rovde lower delay. I alo feable n erm of memy requremen conderng he confguraon of oday mul-uroe moe. A our fuure wk, we would lke o wk on negrang end-o-end relably mechanm and mrovng farne f PHTCCP. Acknowledgemen Th reearch wa ued by he MKE, Kea, under he ITC u rogram uerved by he NIPA" (NIPA-2010-(C )). Dr. CS Hong he creondng auh. eference [1] Dua P., Grmmer M., Ara A., Bbyk S., and Culler D., Degn of a Wrele Sen Newk Plafm f Deecng are, andom, and Ehemeral Even, n Proceedng of he 4 h Inernaonal Symoum on Infmaon Proceng n Sen Newk, Calfna, , [2] Ee C. and Bacy., Congeon Conrol and Farne f Many-o-One oung n Sen Newk, n Proceedng of he 2 nd Inernaonal Conference on Embedded Newked Aocaon f Comung Machnery Sen Syem, USA, , [3] Gu L., Ja D., Vcare P., Yan T., Luo L., Trumala A., Cao Q., He T., Sankovc J.,

9 Przed Heerogeneou Traffc-Orened Congeon Conrol Proocol f WSN 47 Abdelzaher T., and Krogh B., Lghwegh Deecon and Clafcaon f Wrele Sen Newk n ealc Envronmen, n Proceedng of he 3 rd Inernaonal Conference on Embedded Newked Aocaon f Comung Machnery Sen Syem, USA, , [4] MICA2-Daahee, avalable a: h:// Produc/Produc-dffle/Wrele-df/MICA2-Daahee.df, la ved [5] Hull B., Jameon K., and Balakrhnan H., Mgang Congeon n Wrele Sen Newk, n Proceedng of he 2 nd Inernaonal Conference on Embedded Newked Aocaon f Comung Machnery Sen Syem, USA, , [6] Inanagonwwa C., Govndan., and Ern D., Dreced Dffuon: A Scalable and obu Communcaon Paradgm f Sen Newk, n Proceedng of 6 h Mobcom, USA, , [7] Iyer Y., Gandham S., and Venkaean S., STCP: A Generc Tran Layer Proocol f Wrele Sen Newk, n Proceedng of IEEE Inernaonal Conference on Comuer Communcaon and Newk, USA, , [8] Kanoda V., L C., Sabharwal A., Sadegh B., and Knghy E., Drbued Pry Schedulng and Medum Acce n Ad Hoc Newk, Comuer Journal of Wrele Newk, vol. 8, no. 1, , [9] Karl H. and Wllg A., Proocol and Archecure f Wrele Sen Newk, Wley, [10] Km B. and Kang S. IEEE MAC- Baed Locaon-ID Exchange Proocol f ealzng Mcro-Cell Conneconle Locaon- Awarene Servce, Comuer Journal of Scence and Engneerng, vol. 2, no. 4, , [11] Mangold S., Cho S., May P., Klen O., Herz G., and Sb L., IEEE e Wrele LAN f Qualy of Servce, n Proceedng of he Euroean Wrele, Ialy, , [12] Monowar M., ahman M., Pahan A., and Hong C., Congeon Conrol Proocol f Wrele Sen Newk Handlng Przed Heerogeneou Traffc, n Proceedng of SMPE 08 wh MobQuou, Ireland, , [13] NS-2, avalable a: h:// la ved [14] Paek J. and Govndan. CT: ae- Conrolled elable Tran f Wrele Sen Newk, n Proceedng of he 5 h Inernaonal Conference on Embedded Newked Sen Syem, Aurala, , [15] Pahan A., Heo G., and Hong C., A Secure Lghwegh Aroach of Node Memberh Verfcaon n Dene HDSN, n Proceedng of he IEEE Mlary Communcaon Conference, USA, , [16] Paara-Akom W., Krhnamurhy P., and Baneree S., Drbued Mechanm f Qualy of Servce n Wrele LAN, IEEE Wrele Communcaon, vol. 10, no. 3, , [17] angwala S., Gummad., Govndan., and Poun K., Inerference-Aware Far ae Conrol n Wrele Sen Newk, n Proceedng of he Conference on Alcaon, Technologe, Archecure, and Proocol f Comuer Communcaon, Ialy, , [18] Sankaraubramanam Y., Akan O., and Akyldz I., EST: Even-o-Snk elable Tran n Wrele Sen Newk, n Proceedng of 4 h Aocaon f Comung Machnery MobHoc, USA, , [19] Wan C., Eenman S., Cambell A., and Crowcrof J., Overload Traffc Managemen f Sen Newk, Aocaon f Comung Machnery ToSN, vol. 3, no. 4,. 4-18, [20] Wan C., Eenman S., and Cambell A., CODA: Congeon Deecon and Avodance n Sen Newk, n Proceedng of Aocaon f Comung Machnery Sen Syem, USA, , [21] Wang C., L B., Sohraby K., Danehmand M., and Hu Y., Uream Congeon Conrol n Wrele Sen Newk Through Cro-Layer Omzaon, IEEE on Seleced Area n Communcaon, vol. 25, no. 4, , [22] Wang C., L B., Sohraby K., Danehmand M., and Hu Y., A Survey of Tran Proocol f Wrele Sen Newk, IEEE Newk, vol. 20, no. 3, , [23] Warneke B. and Per K., MEMS f Drbued Wrele Sen Newk, n Proceedng of 9 h IEEE Inernaonal Conference on Elecronc, Crcu and Syem, USA, , [24] Weholer S. and Hoene C., Degn and Verfcaon of an IEEE e EDCF Smulaon Model n n-2.26, Techncal e, Telecommun Newk Grou, Techne Unvera Berln, 2003.

10 48 The Inernaonal Arab Journal of Infmaon Technology, Vol. 9, No. 1, January 2012 Muhammad Monowar receved Ph.D. degree n Comuer Engneerng n 2011 from Newkng lab, Dearmen of Comuer Engneerng, Kyung Hee Unvery (KHU), Souh Kea. He receved B.Sc. degree n Comuer Scence and Infmaon Technology (CIT) from Ilamc Unvery of Technology, Bangladeh (IUT) n He currenly an Aan rofe a Comuer Scence & Engneerng dearmen, Unvery of Chagong, Bangladeh. H reearch nere nclude Wrele Ad hoc and Sen Newk. Obadur ahman a lecurer (udy leave) a CSE Dearmen, Dhaka Unvery of Engneerng and Technology, Bangladeh. Currenly, he urung h PhD n comuer engneerng a KHU, Kea. He receved h BSc n Comuer cence and Infmaon Technology (CIT) from IUT, Bangladeh n 2003, and h MS n comuer engneerng from KHU, Kea n Choong Seon Hong receved h BS and MS n elecronc engneerng from Kyung Hee Unvery, Kea, n 1983, 1985, reecvely. He receved h PhD a Keo Unvery n He wked f he Telecommuncaon Newk Lab, KT a a en member of echncal aff and a a drec of newkng reearch eam unl Augu Snce 1999, he ha been wkng a a rofe of he School of Elecronc and Infmaon, KHU. He ha erved a a PC and an ganzng commee member f Inernaonal Conference uch a NOMS, IM, APNOMS, E2EMON, CCNC, ADSN, ICPP, DIM, WISA, BcN, and TINA. H reearch nere nclude ad hoc newk, newk ecury and newk managemen. He a member of IEEE, IPSJ, KIPS, KICS, and KIISE. Al-Sakb Khan Pahan receved h PhD degree n comuer engneerng n 2009 from Kyung Hee Unvery, Souh Kea. He receved h BSc degree n comuer cence and nfmaon echnology from Ilamc Unvery of Technology (IUT), Bangladeh n He currenly an aan rofe a Comuer Scence Dearmen n he Inernaonal Ilamc Unvery Malaya (IIUM), Malaya. H reearch nere nclude wrele en newk, newk ecury, and e-ervce echnologe. He he ed of everal ournal and book, and ganzng commee member of mulle conference/wkho. He a member of IEEE, IEEE ComSoc Bangladeh Chaer, and everal oher nernaonal ganzaon.

Inventory Management MILP Modeling for Tank Farm Systems

Inventory Management MILP Modeling for Tank Farm Systems 2 h European Sympoum on Compuer Aded Proce Engneerng ESCAPE2 S. Perucc and G. Buzz Ferrar (Edor) 2 Elever B.V. All rgh reerved. Invenory Managemen MILP Modelng for Tank Farm Syem Suana Relva a Ana Paula

More information

Using the Two-Stage Approach to Price Index Aggregation

Using the Two-Stage Approach to Price Index Aggregation Oaa Grou Meeng, 3 Ung he To-Sage Aroach o Prce Inde Aggregaon Toc: Samlng and Elemenary Aggregae; Aggregaon Aravndan Jayanha and Le Conn Abrac Th aer aee he raccal mlcaon for Naonal Sacal Offce (NSO) of

More information

PERFORMANCE ANALYSIS OF PARALLEL ALGORITHMS

PERFORMANCE ANALYSIS OF PARALLEL ALGORITHMS Software Analye PERFORMANCE ANALYSIS OF PARALLEL ALGORIHMS Felcan ALECU PhD, Unverty Lecturer, Economc Informatc Deartment, Academy of Economc Stude, Bucharet, Romana E-mal: [email protected] Abtract:

More information

A multi-item production lot size inventory model with cycle dependent parameters

A multi-item production lot size inventory model with cycle dependent parameters INERNAIONA JOURNA OF MAHEMAICA MODE AND MEHOD IN APPIED CIENCE A mul-em producon lo ze nvenory model wh cycle dependen parameer Zad. Balkh, Abdelazz Foul Abrac-In h paper, a mul-em producon nvenory model

More information

Capacity Planning. Operations Planning

Capacity Planning. Operations Planning Operaons Plannng Capacy Plannng Sales and Operaons Plannng Forecasng Capacy plannng Invenory opmzaon How much capacy assgned o each producon un? Realsc capacy esmaes Sraegc level Moderaely long me horzon

More information

An Architecture to Support Distributed Data Mining Services in E-Commerce Environments

An Architecture to Support Distributed Data Mining Services in E-Commerce Environments An Archecure o Suppor Dsrbued Daa Mnng Servces n E-Commerce Envronmens S. Krshnaswamy 1, A. Zaslavsky 1, S.W. Loke 2 School of Compuer Scence & Sofware Engneerng, Monash Unversy 1 900 Dandenong Road, Caulfeld

More information

Spline. Computer Graphics. B-splines. B-Splines (for basis splines) Generating a curve. Basis Functions. Lecture 14 Curves and Surfaces II

Spline. Computer Graphics. B-splines. B-Splines (for basis splines) Generating a curve. Basis Functions. Lecture 14 Curves and Surfaces II Lecure 4 Curves and Surfaces II Splne A long flexble srps of meal used by drafspersons o lay ou he surfaces of arplanes, cars and shps Ducks weghs aached o he splnes were used o pull he splne n dfferen

More information

Lecture 40 Induction. Review Inductors Self-induction RL circuits Energy stored in a Magnetic Field

Lecture 40 Induction. Review Inductors Self-induction RL circuits Energy stored in a Magnetic Field ecure 4 nducon evew nducors Self-nducon crcus nergy sored n a Magnec Feld 1 evew nducon end nergy Transfers mf Bv Mechancal energy ransform n elecrc and hen n hermal energy P Fv B v evew eformulaon of

More information

Multiple Periodic Preventive Maintenance for Used Equipment under Lease

Multiple Periodic Preventive Maintenance for Used Equipment under Lease Mulle Perodc Prevenve Manenance or Used Equmen under ease Paarasaya Boonyaha, Jarumon Jauronnaee, Member, IAENG Absrac Ugradng acon revenve manenance are alernaves o reduce he used equmen alures rae whch

More information

How To Calculate Backup From A Backup From An Oal To A Daa

How To Calculate Backup From A Backup From An Oal To A Daa 6 IJCSNS Inernaonal Journal of Compuer Scence and Nework Secury, VOL.4 No.7, July 04 Mahemacal Model of Daa Backup and Recovery Karel Burda The Faculy of Elecrcal Engneerng and Communcaon Brno Unversy

More information

MORE ON TVM, "SIX FUNCTIONS OF A DOLLAR", FINANCIAL MECHANICS. Copyright 2004, S. Malpezzi

MORE ON TVM, SIX FUNCTIONS OF A DOLLAR, FINANCIAL MECHANICS. Copyright 2004, S. Malpezzi MORE ON VM, "SIX FUNCIONS OF A DOLLAR", FINANCIAL MECHANICS Copyrgh 2004, S. Malpezz I wan everyone o be very clear on boh he "rees" (our basc fnancal funcons) and he "fores" (he dea of he cash flow model).

More information

How Much Can Taxes Help Selfish Routing?

How Much Can Taxes Help Selfish Routing? How Much Can Taxe Help Selfih Rouing? Tim Roughgarden (Cornell) Join wih Richard Cole (NYU) and Yevgeniy Dodi (NYU) Selfih Rouing a direced graph G = (V,E) a ource and a deinaion one uni of raffic from

More information

A Study of Discovering Customer Value for CRM:Integrating Customer Lifetime Value Analysis and Data Mining Techniques

A Study of Discovering Customer Value for CRM:Integrating Customer Lifetime Value Analysis and Data Mining Techniques A Sudy of Dcoverng Cuomer Value for CRM:Inegrang Cuomer Lfeme Value Analy and Daa Mnng echnque Ch-Wen Chen Chyan Yang Chun-Sn Ln Deparmen of Managemen Scence Naonal Chao ung Unvery Inue of Informaon Managemen

More information

An Optimisation-based Approach for Integrated Water Resources Management

An Optimisation-based Approach for Integrated Water Resources Management 20 h Euroean Symosum on Comuer Aded Process Engneerng ESCAPE20 S Perucc and G Buzz Ferrars (Edors) 2010 Elsever BV All rghs reserved An Omsaon-based Aroach for Inegraed Waer Resources Managemen Songsong

More information

GUIDANCE STATEMENT ON CALCULATION METHODOLOGY

GUIDANCE STATEMENT ON CALCULATION METHODOLOGY GUIDANCE STATEMENT ON CALCULATION METHODOLOGY Adopon Dae: 9/28/0 Effecve Dae: //20 Reroacve Applcaon: No Requred www.gpssandards.org 204 CFA Insue Gudance Saemen on Calculaon Mehodology GIPS GUIDANCE STATEMENT

More information

Anomaly Detection in Network Traffic Using Selected Methods of Time Series Analysis

Anomaly Detection in Network Traffic Using Selected Methods of Time Series Analysis I. J. Compuer Nework and Informaon Secury, 2015, 9, 10-18 Publshed Onlne Augus 2015 n MECS (hp://www.mecs-press.org/) DOI: 10.5815/jcns.2015.09.02 Anomaly Deecon n Nework Traffc Usng Seleced Mehods of

More information

Genetic Algorithm with Range Selection Mechanism for Dynamic Multiservice Load Balancing in Cloud-Based Multimedia System

Genetic Algorithm with Range Selection Mechanism for Dynamic Multiservice Load Balancing in Cloud-Based Multimedia System ISSN : 2347-8446 (Onlne) Inernaonal Journal of Advanced Research n Genec Algorhm wh Range Selecon Mechansm for Dynamc Mulservce Load Balancng n Cloud-Based Mulmeda Sysem I Mchael Sadgun Rao Kona, II K.Purushoama

More information

Temporal and Spatial Distributed Event Correlation for Network Security

Temporal and Spatial Distributed Event Correlation for Network Security Temoral and Saal Dsrbued Even Correlaon for Nework Secury Guofe Jang, Member, IEEE and George Cybenko, Fellow, IEEE Absrac - Comuer neworks roduce large amoun of evenbased daa ha can be colleced for nework

More information

Pedro M. Castro Iiro Harjunkoski Ignacio E. Grossmann. Lisbon, Portugal Ladenburg, Germany Pittsburgh, USA

Pedro M. Castro Iiro Harjunkoski Ignacio E. Grossmann. Lisbon, Portugal Ladenburg, Germany Pittsburgh, USA Pedro M. Casro Iro Harjunkosk Ignaco E. Grossmann Lsbon Porugal Ladenburg Germany Psburgh USA 1 Process operaons are ofen subjec o energy consrans Heang and coolng ules elecrcal power Avalably Prce Challengng

More information

Auto-tuning and Self-optimization of 3G and Beyond 3G Mobile Networks

Auto-tuning and Self-optimization of 3G and Beyond 3G Mobile Networks Auo-unng and Self-opmzaon of 3G and Beyond 3G Moble Nework Rdha Nar To ce h veron: Rdha Nar. Auo-unng and Self-opmzaon of 3G and Beyond 3G Moble Nework. Neworkng and Inerne Archecure. Unveré Perre e Mare

More information

The Rules of the Settlement Guarantee Fund. 1. These Rules, hereinafter referred to as "the Rules", define the procedures for the formation

The Rules of the Settlement Guarantee Fund. 1. These Rules, hereinafter referred to as the Rules, define the procedures for the formation Vald as of May 31, 2010 The Rules of he Selemen Guaranee Fund 1 1. These Rules, herenafer referred o as "he Rules", defne he procedures for he formaon and use of he Selemen Guaranee Fund, as defned n Arcle

More information

The Virtual Machine Resource Allocation based on Service Features in Cloud Computing Environment

The Virtual Machine Resource Allocation based on Service Features in Cloud Computing Environment Send Orders for Reprns o [email protected] The Open Cybernecs & Sysemcs Journal, 2015, 9, 639-647 639 Open Access The Vrual Machne Resource Allocaon based on Servce Feaures n Cloud Compung Envronmen

More information

A Model for Time Series Analysis

A Model for Time Series Analysis Aled Mahemaal Senes, Vol. 6, 0, no. 5, 5735-5748 A Model for Tme Seres Analyss me A. H. Poo Sunway Unversy Busness Shool Sunway Unversy Bandar Sunway, Malaysa [email protected] Absra Consder a me seres

More information

Circle Geometry (Part 3)

Circle Geometry (Part 3) Eam aer 3 ircle Geomery (ar 3) emen andard:.4.(c) yclic uadrilaeral La week we covered u otheorem 3, he idea of a convere and we alied our heory o ome roblem called IE. Okay, o now ono he ne chunk of heory

More information

GENETIC NEURAL NETWORK BASED DATA MINING AND APPLICATION IN CASE ANALYSIS OF POLICE OFFICE

GENETIC NEURAL NETWORK BASED DATA MINING AND APPLICATION IN CASE ANALYSIS OF POLICE OFFICE GENETIC NEURAL NETWORK BASED DATA MINING AND APPLICATION IN CASE ANALYSIS OF POLICE OFFICE LIU Han-l, LI Ln, ZHU Ha-hong of Reource and Envronmen Scence, Wuhan Unvery, 9 Luoyu Road, Wuhan, P.R.Chna, 430079

More information

A Real-time Adaptive Traffic Monitoring Approach for Multimedia Content Delivery in Wireless Environment *

A Real-time Adaptive Traffic Monitoring Approach for Multimedia Content Delivery in Wireless Environment * A Real-e Adapve Traffc Monorng Approach for Muleda Conen Delvery n Wreless Envronen * Boonl Adpa and DongSong Zhang Inforaon Syses Deparen Unversy of Maryland, Balore Couny Balore, MD, U.S.A. [email protected],

More information

Index Mathematics Methodology

Index Mathematics Methodology Index Mahemacs Mehodology S&P Dow Jones Indces: Index Mehodology Ocober 2015 Table of Conens Inroducon 4 Dfferen Varees of Indces 4 The Index Dvsor 5 Capalzaon Weghed Indces 6 Defnon 6 Adjusmens o Share

More information

MULTI-WORKDAY ERGONOMIC WORKFORCE SCHEDULING WITH DAYS OFF

MULTI-WORKDAY ERGONOMIC WORKFORCE SCHEDULING WITH DAYS OFF Proceedngs of he 4h Inernaonal Conference on Engneerng, Projec, and Producon Managemen (EPPM 203) MULTI-WORKDAY ERGONOMIC WORKFORCE SCHEDULING WITH DAYS OFF Tar Raanamanee and Suebsak Nanhavanj School

More information

Methodology of the CBOE S&P 500 PutWrite Index (PUT SM ) (with supplemental information regarding the CBOE S&P 500 PutWrite T-W Index (PWT SM ))

Methodology of the CBOE S&P 500 PutWrite Index (PUT SM ) (with supplemental information regarding the CBOE S&P 500 PutWrite T-W Index (PWT SM )) ehodology of he CBOE S&P 500 PuWre Index (PUT S ) (wh supplemenal nformaon regardng he CBOE S&P 500 PuWre T-W Index (PWT S )) The CBOE S&P 500 PuWre Index (cker symbol PUT ) racks he value of a passve

More information

Towards a Trustworthy and Controllable Peer- Server-Peer Media Streaming: An Analytical Study and An Industrial Perspective

Towards a Trustworthy and Controllable Peer- Server-Peer Media Streaming: An Analytical Study and An Industrial Perspective Towards a Trusworhy and Conrollable Peer- Server-Peer Meda Sreamn: An Analycal Sudy and An Indusral Perspecve Zhja Chen, Hao Yn, Chuan n, Xuenn u, Yan Chen* Deparmen of Compuer Scence & Technoloy, *Deparmen

More information

Management watch list $20.4B (326) and poorly performing

Management watch list $20.4B (326) and poorly performing Table of conen Execuve ummary... 3 Inegraed IT governance... 4 The foundaon for effecve negraed IT governance.... 5 Inegraed IT governance framework... 5 Implemenng negraed IT governance... 7 Sofware ool

More information

Linear Extension Cube Attack on Stream Ciphers Abstract: Keywords: 1. Introduction

Linear Extension Cube Attack on Stream Ciphers Abstract: Keywords: 1. Introduction Lnear Exenson Cube Aack on Sream Cphers Lren Dng Yongjuan Wang Zhufeng L (Language Engneerng Deparmen, Luo yang Unversy for Foregn Language, Luo yang cy, He nan Provnce, 47003, P. R. Chna) Absrac: Basng

More information

Ground rules. Guide to the calculation methods of the FTSE Actuaries UK Gilts Index Series v1.9

Ground rules. Guide to the calculation methods of the FTSE Actuaries UK Gilts Index Series v1.9 Ground rules Gude o he calculaon mehods of he FTSE Acuares UK Gls Index Seres v1.9 fserussell.com Ocober 2015 Conens 1.0 Inroducon... 4 1.1 Scope... 4 1.2 FTSE Russell... 5 1.3 Overvew of he calculaons...

More information

Insurance. By Mark Dorfman, Alexander Kling, and Jochen Russ. Abstract

Insurance. By Mark Dorfman, Alexander Kling, and Jochen Russ. Abstract he Impac Of Deflaon On Insurance Companes Offerng Parcpang fe Insurance y Mar Dorfman, lexander Klng, and Jochen Russ bsrac We presen a smple model n whch he mpac of a deflaonary economy on lfe nsurers

More information

Load Balancing in Internet Using Adaptive Packet Scheduling and Bursty Traffic Splitting

Load Balancing in Internet Using Adaptive Packet Scheduling and Bursty Traffic Splitting 152 IJCSNS Inernaonal Journal of Compuer Scence and Nework Secury, VOL.8 No.1, Ocober 28 Load Balancng n Inerne Usng Adapve Packe Schedulng and Bursy Traffc Splng M. Azah Research Scholar, Anna Unversy,

More information

HEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD

HEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD Journal of Appled Mahemacs and Compuaonal Mechancs 3, (), 45-5 HEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD Sansław Kukla, Urszula Sedlecka Insue of Mahemacs,

More information

Public Auditing for Ensuring Cloud Data Storage Security With Zero Knowledge Privacy

Public Auditing for Ensuring Cloud Data Storage Security With Zero Knowledge Privacy P Publc Audng for Ensurng Cloud Daa Sorage Secury Wh Zero Knowledge Prvacy, Wang Shao-huP P, Chang Su-qnP P, Chen Dan-weP P, Wang Zh-weP College of Comuer, Nanjng Unversy of Poss and elecommuncaons, Nanjng

More information

Matrices in Computer Graphics

Matrices in Computer Graphics Marce n Compuer Graphc Tng Yp Mah 8A // Tng Yp Mah 8A Abrac In h paper, we cu an eplore he bac mar operaon uch a ranlaon, roaon, calng an we wll en he cuon wh parallel an perpecve vew. Thee concep commonl

More information

UNIVERSITY TUITION SUBSIDIES AND STUDENT LOANS: A QUANTITATIVE ANALYSIS

UNIVERSITY TUITION SUBSIDIES AND STUDENT LOANS: A QUANTITATIVE ANALYSIS UNIVERSITY TUITION SUBSIDIES AND STUDENT LOANS: A QUANTITATIVE ANALYSIS YAAKOV GILBOA * ** AND MOSHE JUSTMAN Abrac We ue a calbraed macroeconomc model o examne he dfferen effec of unvery and uden loan

More information

COMPETING ADVERTISING AND PRICING STRATEGIES FOR LOCATION-BASED COMMERCE

COMPETING ADVERTISING AND PRICING STRATEGIES FOR LOCATION-BASED COMMERCE COMPTING ADVRTISING AND PRICING STRATGIS FOR LOCATION-BASD COMMRC Nng-Yao Pa, Insue of Informaon Managemen Naonal Chao Tung Unversy, Tawan, [email protected] Yung-Mng L, Insue of Informaon Managemen Naonal

More information

PerfCenter: A Methodology and Tool for Performance Analysis of Application Hosting Centers

PerfCenter: A Methodology and Tool for Performance Analysis of Application Hosting Centers PerfCener: A Mehodology and Tool for Performance Analyss of Applcaon Hosng Ceners Rukma P. Verlekar, Varsha Ape, Prakhar Goyal, Bhavsh Aggarwal Dep. of Compuer Scence and Engneerng Indan Insue of Technology

More information

SPC-based Inventory Control Policy to Improve Supply Chain Dynamics

SPC-based Inventory Control Policy to Improve Supply Chain Dynamics Francesco Cosanno e al. / Inernaonal Journal of Engneerng and Technology (IJET) SPC-based Invenory Conrol Polcy o Improve Supply Chan ynamcs Francesco Cosanno #, Gulo Gravo #, Ahmed Shaban #3,*, Massmo

More information

An Anti-spam Filter Combination Framework for Text-and-Image Emails through Incremental Learning

An Anti-spam Filter Combination Framework for Text-and-Image Emails through Incremental Learning An An-spam Fler Combnaon Framework for Tex-and-Image Emals hrough Incremenal Learnng 1 Byungk Byun, 1 Chn-Hu Lee, 2 Seve Webb, 2 Danesh Iran, and 2 Calon Pu 1 School of Elecrcal & Compuer Engr. Georga

More information

Analyzing Energy Use with Decomposition Methods

Analyzing Energy Use with Decomposition Methods nalyzng nergy Use wh Decomposon Mehods eve HNN nergy Technology Polcy Dvson [email protected] nergy Tranng Week Pars 1 h prl 213 OCD/ 213 Dscusson nergy consumpon and energy effcency? How can energy consumpon

More information

A binary powering Schur algorithm for computing primary matrix roots

A binary powering Schur algorithm for computing primary matrix roots Numercal Algorhms manuscr No. (wll be nsered by he edor) A bnary owerng Schur algorhm for comung rmary marx roos Federco Greco Bruno Iannazzo Receved: dae / Acceed: dae Absrac An algorhm for comung rmary

More information

Chapter 8: Regression with Lagged Explanatory Variables

Chapter 8: Regression with Lagged Explanatory Variables Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One

More information

A Heuristic Solution Method to a Stochastic Vehicle Routing Problem

A Heuristic Solution Method to a Stochastic Vehicle Routing Problem A Heursc Soluon Mehod o a Sochasc Vehcle Roung Problem Lars M. Hvaum Unversy of Bergen, Bergen, Norway. [email protected] Arne Løkkeangen Molde Unversy College, 6411 Molde, Norway. [email protected]

More information

Chapter 8 Student Lecture Notes 8-1

Chapter 8 Student Lecture Notes 8-1 Chaper Suden Lecure Noes - Chaper Goals QM: Business Saisics Chaper Analyzing and Forecasing -Series Daa Afer compleing his chaper, you should be able o: Idenify he componens presen in a ime series Develop

More information

(Im)possibility of Safe Exchange Mechanism Design

(Im)possibility of Safe Exchange Mechanism Design (Im)possbly of Safe Exchange Mechansm Desgn Tuomas Sandholm Compuer Scence Deparmen Carnege Mellon Unversy 5 Forbes Avenue Psburgh, PA 15213 [email protected] XaoFeng Wang Deparmen of Elecrcal and Compuer

More information

CALCULATION OF OMX TALLINN

CALCULATION OF OMX TALLINN CALCULATION OF OMX TALLINN CALCULATION OF OMX TALLINN 1. OMX Tallinn index...3 2. Terms in use...3 3. Comuaion rules of OMX Tallinn...3 3.1. Oening, real-ime and closing value of he Index...3 3.2. Index

More information

TSG-RAN Working Group 1 (Radio Layer 1) meeting #3 Nynashamn, Sweden 22 nd 26 th March 1999

TSG-RAN Working Group 1 (Radio Layer 1) meeting #3 Nynashamn, Sweden 22 nd 26 th March 1999 TSG-RAN Working Group 1 (Radio Layer 1) meeing #3 Nynashamn, Sweden 22 nd 26 h March 1999 RAN TSGW1#3(99)196 Agenda Iem: 9.1 Source: Tile: Documen for: Moorola Macro-diversiy for he PRACH Discussion/Decision

More information

Development of a Database Management System Design Involving Quality Related Costs

Development of a Database Management System Design Involving Quality Related Costs Develpmen a Daabae anagemen Sem Degn Invlvng Qual Relae C İnc Şenarlı*, nan Erurun**, Deha Çaman*** *. Pr. Dr., [email protected], **[email protected], ***[email protected] Çankaa Unver, Deparmen anagemen,06530,

More information

12/7/2011. Procedures to be Covered. Time Series Analysis Using Statgraphics Centurion. Time Series Analysis. Example #1 U.S.

12/7/2011. Procedures to be Covered. Time Series Analysis Using Statgraphics Centurion. Time Series Analysis. Example #1 U.S. Tme Seres Analyss Usng Sagraphcs Cenuron Nel W. Polhemus, CTO, SaPon Technologes, Inc. Procedures o be Covered Descrpve Mehods (me sequence plos, auocorrelaon funcons, perodograms) Smoohng Seasonal Decomposon

More information

Development of a Database Management System Design Involving Quality Related Costs

Development of a Database Management System Design Involving Quality Related Costs Develpmen a Daabae anagemen Sem Degn Invlvng Qual Relae C İnc Şenarlı*, nan Erurun**, Deha Çaman*** *. Pr. Dr., [email protected], **[email protected], ***[email protected] Çankaa Unver, Deparmen anagemen,06530,

More information

Mobile and Ubiquitous Compu3ng. Mul3plexing for wireless. George Roussos. [email protected]

Mobile and Ubiquitous Compu3ng. Mul3plexing for wireless. George Roussos. g.roussos@dcs.bbk.ac.uk Mobile and Ubiquious Compu3ng Mul3plexing for wireless George Roussos [email protected] Overview Sharing he wireless (mul3plexing) in space by frequency in 3me by code PuEng i all ogeher: cellular

More information

Cooperative Distributed Scheduling for Storage Devices in Microgrids using Dynamic KKT Multipliers and Consensus Networks

Cooperative Distributed Scheduling for Storage Devices in Microgrids using Dynamic KKT Multipliers and Consensus Networks Cooperave Dsrbued Schedulng for Sorage Devces n Mcrogrds usng Dynamc KK Mulplers and Consensus Newors Navd Rahbar-Asr Yuan Zhang Mo-Yuen Chow Deparmen of Elecrcal and Compuer Engneerng Norh Carolna Sae

More information

Sensor Nework proposeations

Sensor Nework proposeations 008 Inernaoal Symposum on Telecommuncaons A cooperave sngle arge rackng algorhm usng bnary sensor neworks Danal Aghajaran, Reza Berang Compuer Engneerng Deparmen, Iran Unversy of Scence and Technology,

More information

SHIPPING ECONOMIC ANALYSIS FOR ULTRA LARGE CONTAINERSHIP

SHIPPING ECONOMIC ANALYSIS FOR ULTRA LARGE CONTAINERSHIP Journal of he Easern Asa Socey for Transporaon Sudes, Vol. 6, pp. 936-951, 2005 SHIPPING ECONOMIC ANALYSIS FOR ULTRA LARGE CONTAINERSHIP Chaug-Ing HSU Professor Deparen of Transporaon Technology and Manageen

More information

Chapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m

Chapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m Chaper 2 Problems 2.1 During a hard sneeze, your eyes migh shu for 0.5s. If you are driving a car a 90km/h during such a sneeze, how far does he car move during ha ime s = 90km 1000m h 1km 1h 3600s = 25m

More information

Financial Time Series Forecasting: Comparison of Neural Networks and ARCH Models

Financial Time Series Forecasting: Comparison of Neural Networks and ARCH Models Inernaonal Research Journal of Fnance and Economcs ISSN 450-887 Issue 49 (00) EuroJournals Publshng, Inc. 00 h://www.eurojournals.com/fnance.hm Fnancal Tme Seres Forecasng: Comarson of Neural Neworks and

More information

Optimal Path Routing in Single and Multiple Clock Domain Systems

Optimal Path Routing in Single and Multiple Clock Domain Systems IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN, TO APPEAR. 1 Opimal Pah Rouing in Single and Muliple Clock Domain Syem Soha Haoun, Senior Member, IEEE, Charle J. Alper, Senior Member, IEEE ) Abrac Shrinking

More information

Performance of Multiple TFRC in Heterogeneous Wireless Networks

Performance of Multiple TFRC in Heterogeneous Wireless Networks Performance of Multiple TFRC in Heterogeneou Wirele Network 1 Hyeon-Jin Jeong, 2 Seong-Sik Choi 1, Firt Author Computer Engineering Department, Incheon National Univerity, [email protected] *2,Correponding

More information

A REVIEW OF EMPIRICAL STUDIES ON FOREIGN DIRECT INVESTMENT AND TRADE

A REVIEW OF EMPIRICAL STUDIES ON FOREIGN DIRECT INVESTMENT AND TRADE 72 Ercye Ünvere İkad ve İdar Blmler Faküle Derg, Sayı: 27, Temmuz-Aralık 26,. 71-99 A REVIEW OF EMPIRICAL STUDIES ON FOREIGN DIRECT INVESTMENT AND TRADE ABSTRACT Rahm ÇETİN * Hall ALTINTAŞ ** In he fr

More information

Hospital care organisation in Italy: a theoretical assessment of the reform

Hospital care organisation in Italy: a theoretical assessment of the reform Dartmento d Scenze Economche Unvertà d Breca Va S. Fautno 7/b 5 BESCIA Tel. 3 98885 Fax. 3 988837 e-mal: [email protected] otal care organaton n Italy: a theoretcal aement of the reform oella evagg Abtract.

More information

A robust optimisation approach to project scheduling and resource allocation. Elodie Adida* and Pradnya Joshi

A robust optimisation approach to project scheduling and resource allocation. Elodie Adida* and Pradnya Joshi In. J. Servces Operaons and Informacs, Vol. 4, No. 2, 2009 169 A robus opmsaon approach o projec schedulng and resource allocaon Elode Adda* and Pradnya Josh Deparmen of Mechancal and Indusral Engneerng,

More information

Fixed Income Attribution. Remco van Eeuwijk, Managing Director Wilshire Associates Incorporated 15 February 2006

Fixed Income Attribution. Remco van Eeuwijk, Managing Director Wilshire Associates Incorporated 15 February 2006 Fxed Incoe Arbuon eco van Eeuwk Managng Drecor Wlshre Assocaes Incorporaed 5 February 2006 Agenda Inroducon Goal of Perforance Arbuon Invesen Processes and Arbuon Mehodologes Facor-based Perforance Arbuon

More information

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins) Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer

More information

Kalman filtering as a performance monitoring technique for a propensity scorecard

Kalman filtering as a performance monitoring technique for a propensity scorecard Kalman flerng as a performance monorng echnque for a propensy scorecard Kaarzyna Bjak * Unversy of Souhampon, Souhampon, UK, and Buro Informacj Kredyowej S.A., Warsaw, Poland Absrac Propensy scorecards

More information

Analysis of intelligent road network, paradigm shift and new applications

Analysis of intelligent road network, paradigm shift and new applications CONFERENCE ABOUT THE STATUS AND FUTURE OF THE EDUCATIONAL AND R&D SERVICES FOR THE VEHICLE INDUSTRY Analyss of nellgen road nework, paradgm shf and new applcaons Péer Tamás "Smarer Transpor" - IT for co-operave

More information

Optimum Design of Magnetic Inductive Energy Harvester and its AC-DC Converter

Optimum Design of Magnetic Inductive Energy Harvester and its AC-DC Converter Otmum Degn of Magnetc nductve Energy Harveter and t AC-DC Converter Qan Sun, Sumeet Patl, Stehen Stoute, Nan-Xang Sun, Brad Lehman Deartment of Electrcal and Comuter Engneerng Northeatern Unverty Boton,

More information

OPTIMIZING PRODUCTION POLICIES FOR FLEXIBLE MANUFACTURING SYSTEM WITH NON-LINEAR HOLDING COST

OPTIMIZING PRODUCTION POLICIES FOR FLEXIBLE MANUFACTURING SYSTEM WITH NON-LINEAR HOLDING COST OPIMIZING PRODUCION POLICIE FOR FLEXIBLE MANUFACURING YEM WIH NON-LINEAR HOLDING CO ABRAC Leena Praher, Reearch cholar, Banahali Vidayaeeh (Raj.) Dr. hivraj Pundir, Reader, D. N. College, Meeru (UP) hi

More information

APPLICATION OF CHAOS THEORY TO ANALYSIS OF COMPUTER NETWORK TRAFFIC Liudvikas Kaklauskas, Leonidas Sakalauskas

APPLICATION OF CHAOS THEORY TO ANALYSIS OF COMPUTER NETWORK TRAFFIC Liudvikas Kaklauskas, Leonidas Sakalauskas The XIII Inernaonal Conference Appled Sochasc Models and Daa Analyss (ASMDA-2009) June 30-July 3 2009 Vlnus LITHUANIA ISBN 978-9955-28-463-5 L. Sakalauskas C. Skadas and E. K. Zavadskas (Eds.): ASMDA-2009

More information

Answer, Key Homework 2 David McIntyre 45123 Mar 25, 2004 1

Answer, Key Homework 2 David McIntyre 45123 Mar 25, 2004 1 Answer, Key Homework 2 Daid McInyre 4123 Mar 2, 2004 1 This prin-ou should hae 1 quesions. Muliple-choice quesions may coninue on he ne column or page find all choices before making your selecion. The

More information

Template-Based Reconstruction of Surface Mesh Animation from Point Cloud Animation

Template-Based Reconstruction of Surface Mesh Animation from Point Cloud Animation Temlae-Based Reconsrucon of Surface Mesh Anmaon from Pon Cloud Anmaon Sang Il Park and Seong-Jae Lm In hs aer, we resen a mehod for reconsrucng a surface mesh anmaon sequence from on cloud anmaon daa.

More information

HAND: Highly Available Dynamic Deployment Infrastructure for Globus Toolkit 4

HAND: Highly Available Dynamic Deployment Infrastructure for Globus Toolkit 4 HAND: Hghly Avalable Dynamc Deploymen Infrasrucure for Globus Toolk 4 L Q 1, Ha Jn 1, Ian Foser,3, Jarek Gawor 1 Huazhong Unversy of Scence and Technology, Wuhan, 430074, Chna [email protected]; [email protected]

More information

FRAMEWORK OF MEETING SCHEDULING IN COMPUTER SYSTEMS

FRAMEWORK OF MEETING SCHEDULING IN COMPUTER SYSTEMS FRAMEWORK OF MEEING CEDULING IN COMPUER YEM Goran Marnovc, Faculy of Elecrcal Engneerng, J.J. rossmayer Unversy of Ose, [email protected] ABRAC Developmen of compuer echnologes s a necessary bu no

More information

Guidelines and Specification for the Construction and Maintenance of the. NASDAQ OMX Credit SEK Indexes

Guidelines and Specification for the Construction and Maintenance of the. NASDAQ OMX Credit SEK Indexes Gudelnes and Specfcaon for he Consrucon and Manenance of he NASDAQ OMX Cred SEK Indexes Verson as of Aprl 7h 2014 Conens Rules for he Consrucon and Manenance of he NASDAQ OMX Cred SEK Index seres... 3

More information

Trading volume and stock market volatility: evidence from emerging stock markets

Trading volume and stock market volatility: evidence from emerging stock markets Invesmen Managemen and Fnancal Innovaons, Volume 5, Issue 4, 008 Guner Gursoy (Turkey), Asl Yuksel (Turkey), Aydn Yuksel (Turkey) Tradng volume and sock marke volaly: evdence from emergng sock markes Absrac

More information

II. IMPACTS OF WIND POWER ON GRID OPERATIONS

II. IMPACTS OF WIND POWER ON GRID OPERATIONS IEEE Energy2030 Alana, Georga, USA 17-18 November 2008 Couplng Wnd Generaors wh eferrable Loads A. Papavaslou, and S. S. Oren UC Berkeley, eparmen of Indusral Engneerng and Operaons esearch, 4141 Echeverry

More information

S-shaped Incentive Schemes and Pay Caps

S-shaped Incentive Schemes and Pay Caps S-haped Incenve Scheme and Pay Cap Tony Haao Cu Carlon School o Managemen Unvery o Mnneoa Jagmohan S. Rau The Wharon School Unvery o Pennylvana Mengze Sh Roman School o Managemen Unvery o Torono March

More information

Effects of Terms of Trade Gains and Tariff Changes on the Measurement of U.S. Productivity Growth *

Effects of Terms of Trade Gains and Tariff Changes on the Measurement of U.S. Productivity Growth * Effecs of Terms of Trade Gans and Tarff Changes on he Measuremen of U.S. Producvy Growh * Rober C. Feensra Unversy of Calforna-Davs and NBER Benjamn R. Mandel Federal Reserve Bank of New York Marshall

More information

WHAT ARE OPTION CONTRACTS?

WHAT ARE OPTION CONTRACTS? WHAT ARE OTION CONTRACTS? By rof. Ashok anekar An oion conrac is a derivaive which gives he righ o he holder of he conrac o do 'Somehing' bu wihou he obligaion o do ha 'Somehing'. The 'Somehing' can be

More information

Projective geometry- 2D. Homogeneous coordinates x1, x2,

Projective geometry- 2D. Homogeneous coordinates x1, x2, Projece geomer- D cknowledgemen Marc Pollefe: for allowng e ue of ecellen lde on opc p://www.c.unc.edu/~marc/mg/ Rcard arle and ndrew Zerman "Mulple Vew Geomer n Compuer Von" omogeneou coordnae omogeneou

More information

Currency Exchange Rate Forecasting from News Headlines

Currency Exchange Rate Forecasting from News Headlines Currency Exchange Rae Forecasng from News Headlnes Desh Peramunelleke Raymond K. Wong School of Compuer Scence & Engneerng Unversy of New Souh Wales Sydney, NSW 2052, Ausrala [email protected] [email protected]

More information

13. a. If the one-year discount factor is.905, what is the one-year interest rate?

13. a. If the one-year discount factor is.905, what is the one-year interest rate? CHAPTER 3: Pracice quesions 3. a. If he one-year discoun facor is.905, wha is he one-year ineres rae? = DF = + r 0.905 r = 0.050 = 0.50% b. If he wo-year ineres rae is 0.5 percen, wha is he wo-year discoun

More information

THE HEALTH BENEFITS OF CONTROLLING CARBON EMISSIONS IN CHINA 1. by Richard F. GARBACCIO; Mun S. HO; and Dale W. JORGENSON

THE HEALTH BENEFITS OF CONTROLLING CARBON EMISSIONS IN CHINA 1. by Richard F. GARBACCIO; Mun S. HO; and Dale W. JORGENSON THE HEALTH BENEFITS OF CONTROLLING CARBON EMISSIONS IN CHINA 1 by Rchard F. GARBACCIO; Mun S. HO; and Dale W. JORGENSON 1. Inroducon Ar polluon from rapd ndusralzaon and he use of energy has been recognzed

More information

Auxiliary Module for Unbalanced Three Phase Loads with a Neutral Connection

Auxiliary Module for Unbalanced Three Phase Loads with a Neutral Connection CODEN:LUTEDX/TEIE-514/1-141/6 Indusral Elecrcal Engneerng and Auomaon Auxlary Module for Unbalanced Three Phase Loads wh a Neural Connecon Nls Lundsröm Rkard Sröman Dep. of Indusral Elecrcal Engneerng

More information

Selected Financial Formulae. Basic Time Value Formulae PV A FV A. FV Ad

Selected Financial Formulae. Basic Time Value Formulae PV A FV A. FV Ad Basc Tme Value e Fuure Value of a Sngle Sum PV( + Presen Value of a Sngle Sum PV ------------------ ( + Solve for for a Sngle Sum ln ------ PV -------------------- ln( + Solve for for a Sngle Sum ------

More information