Testing Resource Allocation for Fault Detection and Correction Processes under Dynamic Environment

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1 Copuing Fo Nion Developen, Mh, Bhi Vipeeh s Insiue o Copue Appliions n Mngeen, Ne Delhi esing Resoue Alloion o Ful Deeion n Coeion Poesses une Dni Envionen P.K. Kpu n Vij Ku Depen o Opeionl Reseh, Univesi o Delhi, Delhi-7 pkkpu@gil.o n vij_psh@hoo.o ABSRAC he ul eeion n oeion poess is he os ipon phse in soe esing n evelopen le. A nue o soe eliili goh oels SRGMs hve een popose in een es o pue he ie lg eeen eee n oee ul nues. Bu unounel os o he oels ee isusse une si envionen. he in pupose o his ppe is o invesige n opil esoue lloion pln o ul eeion n oeion oel o iniize he os o soe uing he esing n opeionl phse une ni oniion. An eloe opiizion poli se on he opil onol heo is popose n nueil eples e illuse. he ppe lso suies he opil esoue lloion poles o vious oniions eining he ehvio o he oel pees. he epeienl esuls gel help us o ieni he oniuions o eh selee pee n is eigh. KEYWORDS SRGM,esing Eo Alloion, Coeion-Deeion Poess, Opil Conol heo, Lening Cuve Ee.. INRODUCION In he een es opue sses hve een eensivel use o nge he ople n vil sses. A ul in he soe le o huge losses in es o one n ie. hee e sevel epoe n unepoe insnes hee ilue o opue onolle sses hve esule in eenous h o soil lie. heeoe, hen n ognizion invess lge oun o one in king soe pou i ensues h he soe pou us e eple o he uses in he pevlen ke oniions. Soe evelopen n esing is pill ulisge poess, hee eh sge peos soe peeine iviies, ie o elive he en pou s pe he oien e o he usoe. his is hee esing pls n ipon ole. Soe esing is no onl poess o eugging he soe u i lso evlues he soe quli. Soe esing ines ih eve phse o SDLC. Soe eliili goh hs een ke issue in he soe inus sine i n povie signiin inoion o he ngeen uing he soe esing lie le SLC. Mheil oels knon s Soe eliili goh oels SRGM eslish he elion ong ilue osevion, ul eovl poess n soe eliili. Fo he ls hee ees, n SRGM hve een popose o su he poili h soe ill no use he ilue o pou o speiie ie une speiie oniions. his poili is union o he inpus o he uses n use o he pou, s ell s union o he eisene o uls hih is in soe. Resoues suh s npoe n CPU ie e onsue uing esing poess. he ul eeion n oeion poesses epen upon he nue n oun o esoues onsue. Mn SRGMs hve een popose o iniize he oun o esing eos uilize uing he esing le u osl une he ssupions h he elionship eeen he esing eo onsue n esing ie he len ie ollos Eponenil n Rleigh isiuion. Bsili e l [] ung e l [4], Pun[], Kpu n Gg [7] n Y e l. [6] isusse he ie epenen ehvio o esing eos in hei pionee ok. Usull, eponenil uve is use o esie he ehvio o esing esoues heneve onsue uniol,oheise Rleigh uve is use. Logisi n Weiull pe unions hve lso een use o esie esing eos. Mus e l. [8] ssue h he esoue onsupion s n eplii union o nue o uls eove n len ie. Kpu e l. [6] in hei ok hve isusse he opiizion pole o lloing esing esoues in soe hving oul suue n popose h lloion o eos shoul epen upon he size n sevei o uls. Vious uhos hve eoene h o ieen esoue onsins one n evelop e-o eeen iu nue o uls o e eove in eh oule n he eos equie. Vious popose SRGMs in ou ees onl onsie he ul eeion poess n e se on he ssupion h ul is eove ieiel s soon s i is eee. oeve, his ssupion no e esonle s he eee uls e el oee ieiel Gokhle e l [], Shneiein [], Shneiein [], Oh [9] n Xie n Zho [5].Genell, heneve ul is eee, is i is epoe, ne ignose, veiie n inll i ges oee. heeoe, he ie lg eeen eeion n oeion shoul no e neglee uing he oeling poess. ene, i is essenil o hve ieen goh oels o oeling he eeion-oeion poess. Mn esehes ephsize he signiine o he ul eeionoeion oeling. Shneiein [] is oele he

2 ul-oeion poess using onsn ele uleeion poess. Le, Xie n Zho [5] eene he Shneiein oel o oninuous vesion susiuing ie-epenen el union o he onsn el hih esues he epee ie lg o oe eee ul. Kpu e. l. [5] popose ekle oel inopoing ie epenen lg union uing oeling o epenen ul eeion poess. Y e l [7] in hei eseh ok isusse he ie lg eeen o sge poess ilue n eovl king onsn eovl e. Le ung n Lin [] in hei eseh ppe isusse he epenen o uls n ie lg eeen ilue osevion n ul eovl. hough, ove ls hi es n SRGMs hve een popose o iniize he ol eos epeniues uing esing phse o SDLC u osl une he si ssupion. In his ile e hve ie o invesige n opil esoue lloion pln o iniize he os o soe uing he esing phse using ul eeion n oeion oel une ni oniions. Epeienl esuls sho h he popose eok o inopoe eugging ie lg o SRGM hs il ue opil isiuion o eo poli. he ppe lso suies he opil esoue lloion poles o vious oniions eining he ehvio o he oel pees.. PROBLEM DESCRIPION he in ojeive o soe esing is eeion n oeion o uls eoe he elese o he soe in he ke. Genell heneve ilue is ieniie he ul oeion e equies peio o ie o loe he ul n oi soe oes oingl o eove i. hus, he ie lg eeen eeion n oeion is oon epeiene in soe esing. In genel, his ie lg is he ie el eeen he ul eeion n oeion poesses. he eovl ie o ul epens on vious os suh s he nue o he eee uls, he oplei o he uls, suul oplei o he soe, he skill o he oeion pesonnel, e. hus he oeion lg n e ignoe. Soe uls hih e eee u no oee sill ein in he soe. hese len uls e use he oeion lg n ele he elionship eeen he ul eeion n oeion poesses. In his eseh ppe e eoen h esing, ieniiion n oeion o ul shoul e viee s siulneous iviies. Ou in ojeive is o onsu siple, suue oel o onuen esing, ieniiion n eugging ih vie o gin insighs. o evelop he heil oel e hve ssue h uing he Soe esing Lie Cle SLC, hee e sepe es o eeing, loing n oeing he uls pesen in he soe. A e ieniies he nue o uls using ilue o soe, seon e loes o ees he uls n he hi e is eoves he eee uls. heeoe, he ie ol esoues n poin o ie n e ivie ino hee poions, n hee, is he uen eo onsupion o esing pupose ie, n is he eos onsue o eeion o he uls n poin o ie n is he uen eo onsupion ue o i ul ie he esoue lloion oel is epie in he igue. Figue : Alloion o ol esoues o solve he ni opiizion poles o esoue lloion pole, e hve use opil onol heo ppoh n ssue h soe esing n eugging n un onoinl. Opil onol heo hs een epe iel s ehnique o solve he ni opiizion poles in n es o engineeing, ngeen, eonois, e. Opil onol heo eouples nil sse ove he ie ino siple si opiizion poles ie insne n he eonoi insighs n e viee o he nlil esuls [4]. he onol viles hee n nge he evoluion o sse in suh h n opil ouoe hee, iniu os is hieve he en o he ie hoizon. In he ppe he elion eeen ilue es o soe n os o eese his e is oele vious pes o lening uves ee. We egin ou nlsis sing genel oel ih ve e ssupions. he noions use in he nlsis e s ollos: : he plnning peio. : ol esoues uilize uing he SDLC n poin o ie. : Resoues uilize uing he SDLC o esing pupose n poin o ie. : Resoues uilize uing he SDLC o i ug n poin o ie.

3 esing Resoue Alloion o Ful Deeion n Coeion Poesses une Dni Envionen : Resoues uilize uing he SDLC o eeion pupose n poin o ie., : ol os pe uni ie o uulive ul eee is ih eeion eos., :ol os pe uni ie o uulive ul oee is eugging eos : ol os o esing pe uni ie. : Iniil ul onen pesen in he soe.. MODEL DEVELOPMEN. FAUL DEECION AND CORRECION MODELING Une he iel ssupion o insnneous n pee ul eovl, he epee nue o uls oee is he se s he epee nue o uls eee. oeve, i e ke ino onsieion he ie equie o oeion, he epee nue o uls oee n given ie is less hn he epee nue o uls eee. o popose ul eeionoeion oel e ssue h he eovl o ul is one e ul is eee. ene, he eovl is one in o sges. In he is sge, he esing e ieniies he uls. In he seon sge, nohe eugging e eoves he ul using h ilue. o egin ih, le e he oun o ul pesen in he soe, enoes he epee nue o uls eee ill ie, n enoes he epee nue o uls eove ill ie. heeoe i is esonle o ssue he olloing ieenil equions o eeion n oeion poess. n hee, Whee n e he ul eeion n oeion e espeivel.. COS OPIMIZAION MODELING No suppose he soe i ns o iniize he ol epeniue ove he inie plnning hoizon. hus, he ol os n poin o ie uing he esing phse o SDLC is he su o esing os,eeion os n eugging os.heeoe, heill he oel n e epesene s in,,, n ; ; suje o hee,, 4. OPIMAL SOLUION o solve he pole, Miu piniple n e pplie. he uen vlue ilonin is s ollos [4]: he ilonin o he sse se equion, is eine s,,,,,, n µ e he join viles sho os o hee, n espeivel hih sis he olloing ieenil equion. 4 ih he nsvesli oniion, Siill 5 he nsvesli oniion, he join vile epesens he pe uni hnge in he i.e. n ojeive union o sll hnge in e inepee s ginl vlue o uls eee ie.siill n e inepee s ginl vlue o ul eove ie. hus he ilonin is he su o

4 uen os n he uue os. In sho, epesens he insnneous ol os o he i ie. he olloing e he neess oniions hol o n opil soluion: ; 6 7 he ohe opili oniions e n Fo he ove opili oniions, e hve * 8 An * 9 heeoe * Ineging 4 ih he nsvesli oniion, e hve he uue os o eeing one oe ul o he soe Siill ineging 5 ih he nsvesli oniion, e hve he uue os o eoving one oe ul o he soe No king ie eivive o 6, e hve ie eivive o 7 iplies 4 he equions n 4 n e ien in he olloing i o 5 Fo 5 e n ie P Q P Whee P An Q 5. SPECIAL CASES We no eine he ehvio o he os opil onol oel popose in he equion hnging he os o eeion n os o eugging. We hve onsiee o ses: 5.. CASE In his seion e hve ssue h he ol os pe uni o uulive ul eee n he ol os pe uni o uulive ul eove ie e onsn. i.e. n Fo onsn ul eeion n ul eovl union, he os opil onol pole n e ien s

5 esing Resoue Alloion o Ful Deeion n Coeion Poesses une Dni Envionen in, n ; ; suje o hee 6 he ilonin o he ove pole is given 7 hee is he join vile, hih sis he olloing ieenil equions. 8, ih he nsvesli oniion.solving he equion8 ogehe ih he einl oniion, e ge 9 Siill is he join vile, hih sis olloing ieenil equions. Solving he ieenil equion ogehe ih he einl oniion, We ge, Sine ilonin 7 is line in onol vile n.heeoe e hve he olloing opil poli o n une e ine hih iize he ojeive union: i i i n une e in e i i i 5.. CASE In his seion, e inoue he onep o lening uve phenoenon in he os unions. Lening uve phenoenon in soe ul oeion is onene ih he ie h hen ne ul hs o e eugge o he is ie i is likel h he eugging e involve ill no hieve iu eiien ieiel. Repeiion o he sk ill ke he people oe onien n knolegele n ill evenull esul in oe eiien n pi opeion. Evenull he lening poess ill sop e oninuous iiion. I ses h oe oen sk is peoe; he loe ill e he os o oing i. In his ppe, i is ssue h eh ie uulive volue o ul eee ineses, vlue e oss inluing inision, eugging e. ll onsn n peile peenge. In his seion e hve onsiee eeion os n eugging os ollos lening ee phenoenon Pegels [], hih e o he o, hee, is he se eeion os. Also,, hee os o eugging. he ilonin o he ove se n e ien s is he se 4 he olloing e he neess oniion hol o n opil soluion: ; 5 he join viles given he olloing ieenil equion 6 log An log 7 Solving 5,e ge

6 8 9 heeoe he phsil inepeion o he ove equion8 is h he opil poli o eeing eo is equl o he h oo o he io o ol os o eeing n iing pe uni ugs o pe uni se os o eeion uliplie he nue o eos eove ie. 6. NUMERICAL ANALYSIS In his seion, he vious opil poliies hs een esie on he popose oel using nueil eple. he pupose o his su is o ge soe insigh ino he esul n lso o su he ip o hnge in eos on he popose os oel n he oesponing opil os oel. Sevel siulion uns ee onue using vious pee vlues; esuls onvege quikl n ee sle. o o so, e hve onsiee he Pegels [] o o lening uve o eine he eeion n oeion os unions. Fis soe se vlues ee onsiee n hen ieen oel pees ee vie iniviull. he se vlues e s ollos:...,. 4 5 he epee nue o ul eee n oee is shon in Figue n Figue. Iniill, e oin he nue o ul eee o vious vlues o. he epee nue o uls eee eeses s eeses. Finll, he vlue o s se o e.8. he uulive nue o uls oee ineses s he eugging eos ineses n ollos s-shpe uve. Fo he nlsis i hs een seen h s e keep on inesing he eugging eos, he ie uion o hieving he esie gol i.e. iizing he nue o oee uls eues s. he esul lso inie h inesing he eugging eos eues he ol eugging os n hene ol os. his siuion ise, ue o he epeiene uve phenoenon. CONCLUSION In his ppe e hve suie n opil esoue lloion pln o iniize he os o soe hen ul eeion/oeion poess is o sge poess. Using opil onol heoei ppoh e hve oine nue o poliies o eeion eo n oeion eo o he ieen os union. An nlsis o ieen ul eovl segies is lso isusse. We esie eho o opue he os o he soe uing esing phse king ino onsieion. he esuls ee veiie using siulion ehnique. FUURE SCOPE he oel is se upon he si ssupion h n poin o ie he ol esoues is ie s esul one vile is epenen on he ohe o viles. ene onolling he o viles ill uoill onol he hi one. Also, i hs een onsiee h he pe uni esing os is onsn houghou he esing peio unions, u in pie his e union o ie. ene i is ve ipon o onsie ie epenen esing os union o opiizion pupose. Finll he oel n e eene in sevel s i.e. inopoing he ohe ipee eugging soe eliili goh oels. Figue : Nue o uls vs. ie

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