Design and Reliability Analysis of a new Fault-tolerant Multistage Interconnection Network

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1 ICGST-CIR Journal, Volum 8, Issu, January 9 Dsign and Rliabiliy o a nw Faul-olran Mulisag Inrconncion work Rinkl Aggarwal, Lakhwindr Kaur, Himanshu Aggarwal Dparmn o Compur Scinc & Enginring, Thapar Univrsiy, aiala 7 (India) raggarwal@hapar.du Dparmn o Compur Enginring, unjabi Univrsiy, aiala 7 (India) mahalk8@yahoo.com, himagrawal@liv.com Absrac Th dsign o a suiabl inrconncion nwork or inr-procssor communicaion is on o h ky issus o h sysm prormanc. Th rliabiliy o hs nworks and hir abiliy o coninu opraing dspi ailurs ar major concrns in drmining h ovrall sysm prormanc. In his papr a nw irrgular nwork IASE (Irrgular Augmnd Shul Exchang work) has bn proposd, which is drivd rom h rgular ASE- (Augmnd Shul Exchang work). ASE- is a mulipah nwork wih limid aul olranc. Th rliabiliis o h IASE and ASE- muli-sag inrconncion nworks hav bn calculad and compard in rms o h Uppr and Lowr bounds o Man Tim To Failur (MTTF). I has bn obsrvd ha h proposd IASE mulisag inrconncion nwork provids much br aul-olranc by providing mor pahs bwn any pair o sourcdsinaion and br rliabiliy a h xpans o lil mor cos han ASE-. Kywords: Mulisag Inrconncion works, Rliabiliy, Augmnd Shul Exchang work, Irrgular Augmnd Shul Exchang work, Faul-olranc.. Inroducion Advancs in LSI and VLSI chnology ar ncouraging grar us o mulipl-procssor sysms wih procssing lmns o provid compuaional paralllism and mmory moduls o sor h daa rquird by h procssing lmns. Inrconncion works (Is) play a major rol in h prormanc o modm paralll compurs. Many aspcs o Is, such as implmnaion complxiy, rouing algorihms, prormanc valuaion, aulolranc, and rliabiliy hav bn h subjcs o rsarch ovr h yars. Thr ar many acors ha may ac h choic o appropria inrconncion nwork or h undrlying paralll compuing nvironmn [8,9]. Though crossbar is h idal I or shard mmory muliprocssor, whr inpus can simulanously g conncd o oupus, bu h hardwar cos grows asronomically. Mulisag Inrconncion works (MIs) ar rcognizd as cos-civ mans o provid programmabl daa pahs bwn uncional moduls in muliprocssor sysms. Ths nworks ar usually implmnd wih simpl modular swichs, mploying wo-inpu wo-oupu swiching lmns. Mos o h MIs proposd in h liraur hav bn consrucd wih x crossbar swichs as basic lmns, and hav n log swiching sags wih ach sag consising o / lmns, which maks h cos o his nwork as O( log), as compard o O( ) or a crossbar [6]. Th parn o inrconncion may b uniorm or non-uniorm, which classiis h MIs o b rgular or irrgular rspcivly[]. In h cas o irrgular nworks, h pah lngh varis rom any inpu o any oupu, in conras wih rgular nworks, whr i is h sam []. Faul-olranc in an inrconncion nwork is vry imporan or is coninuous opraion ovr a rlaivly long priod o im []. Many nworks hav bn dsignd and proposd o incras h aul-olranc in h liraur [,,9,,5,6,7]. rmuaion capabiliy and ohr issus rlad o rouing hav also bn xnsivly rsarchd [,5,5,6,7]. Bandwidh and ohr prormanc paramrs hav also bn sudid indph [,]. Howvr, lil anion has bn paid o h compuaion o rliabiliy o hs nworks. Rliabiliy is masurd in rms o Man Tim o Failur (MTTF), which is valuad using simpl sris-paralll probabilisic combinaions. This analysis is basd upon h lowr and uppr bounds o h nwork rliabiliy. This papr has bn organizd ino iv scions whos dails ar as ollows. 7

2 ICGST-CIR Journal, Volum 8, Issu, January 9 Scion inroducs h subjc undr sudy. Scion dscribs h srucur and dsign o nworks. Scion ocuss on h rliabiliy analysis. Scion concnras on h rliabiliy analysis o IASE. Scion 5 dscribs h cos civnss. Finally, h conclusion has bn prsnd.. Srucur and dsign o nworks. ASE- work Augmnd Shul Exchang work (ASE-) is a rgular nwork, having qual numbr o swichs in ach o h sag. ASE- nwork is consrucd rom Shul Exchang work by adding a sag o muliplxrs a h iniial sag and dmuliplxrs a las sag. I provids mulipl pahs bwn a sourc and a dsinaion. ASE- o siz wih numbr o sourcs and numbr o dsinaion consiss o log - sags whr h iniial sag consiss o / swichs o siz and h las sag consis o / swichs o siz. ASE- provids aul olranc using links bwn h conjuga pairs o swichs []. A 6 6 ASE- nwork is shown in Figur. Figur. Irrgular Augmnd Shul Exchang work. Rliabiliy Th rliabiliy analysis o hardwar [] and sowar[] ar wo vry imporan considraions. Th rliabiliy analysis hr ocuss on h hardwar rliabiliy o h nworks. Rliabiliy o ASE-, IASE nworks ar analyzd in rms o Man im o Failur (MTTF). MTTF o a MI is valuad using simpl sris-paralll probabilisic combinaions.. Sris coniguraion modl A sris coniguraion modl is consrucd by conncing all h componns in a sris sysm. This yp o coniguraion is vry snsiiv bcaus h ailur o a singl componn mak whol o h sysm ail. Th rliabiliy o a sris coniguraion modl is always wors han h poors componn in i. Sris coniguraion modl is shown in Figur. Figur. Augmnd Shul Exchang nwork (ASE-). Irrgular ASE Irrgular Augmnd Shul Exchang work (IASE) shown in Figur is drivd rom ASE- mulisag inrconncion nwork. Th swichs in h irs sag orm a loop o provid mulipl pahs i a aul occur in h nx sag. Each sourc is conncd o wo dirn swichs in ach group wih h hlp o muliplxr and ach dsinaion is conncd wih dmuliplxr. Following srucural changs hav bn mad in IASE in comparison o ASE-. ) Four swichs rmovd rom h sag (Inrmdia Sag) ) Us o x DEMUX in plac o x DEMUX ) Loops and conncions changd Figur. Sris coniguraion modl. aralll coniguraion modl In his all componns ar conncd paralll o ach ohr. In his i on componn ails han h daa can ollow anohr pah and sysm will b aciv. This yp o modl is shown in Figur. Inpu Oupu n Figur. aralll coniguraion modl 8

3 ICGST-CIR Journal, Volum 8, Issu, January 9. Sris-aralll Coniguraion modl Th wo loops in a conjuga pair ar in paralll and all h conjuga pairs o loops ar in sris as shown in Figur 5. Inpu Figur 5. Sris-aralll coniguraion modl To mak h Rliabiliy analysis racabl, w nd o hav som assumpions. W us h assumpions similar o h ons ha hav bn mad prviously in h ohr sudis o aul olran nworks [,,9,]. Th assumpions usd in h analysis on h ailur ras o h componns ar givn blow:. Swich ailur occur indpndnly in a nwork wih a ailur ra o or crossbar swichs (a rasonabl sima or is abou 6 pr hour).. Failur o h muliplxrs and dmuliplxrs also occur indpndnly wih ailur ras o m and d rspcivly.. Assuming ha h hardwar complxiy o a componn is dircly proporional o h ga couns o i, on can driv a ailur ra o h componn From h basic logic dsign o MUX and DEMUX, w can say ha numbr o gas in a m l MUX or a m DEMUX is roughly doubl o ha in a m l MUX or a m DEMUX. Basd on h ga couns o crossbar swichs, h numbr o gas in a crossbar swich is approximaly qual o ha in a MUX or a DEMUX. Thus o simpliy h analysis w can assum ha m m/ or a m MUX, whr m ailur ra o MUX or d ( m ) or m DEMUX, whr d ailur ra o DEMUX. Th adapiv rouing schm considrs a swich in h las sag and is associad DEMUX as a sris sysm, so w considr hs hr lmns as singl componn (SEd), and basd on a ga coun, a ailur ra o d can b assignd o his group o lmns. Also l and b h ailur ra or h (SE) and h swich (SE), hn basd on ga coun, and.5 and m.5.. Irrgular MIs ar inhrnly muli-pah and h MTTF nds o b calculad a all xising pah-lnghs sparaly basd upon h sris and paralll modls o rliabiliy. Oupu ASE- Rliabiliy For h rliabiliy boh h opimisic and pssimisic analysis o h nworks has bn don. Ths wr xndd o incorpora h addd complxiy o h swichs usd in h ASE-, h muliplxrs and dmuliplxrs usd a h inpu and oupu inracs o h nwork... ASE- Opimisic (Uppr bound) To obain an uppr bound or h ASE- and obsrvd ha ach sourc is conncd o wo muliplxrs and ach swich is conncd is a conjuga pair. So i w assum ha h ASE- is opraional as long as on o h wo muliplxrs aachd o a sourc is opraional and boh componns in a conjuga pair ar no auly []. Block diagram o uppr bound is shown in Figur 6. Figur 6. Uppr Bound o ASE- Rliabiliy Equaions ar: m + d R * * Opimisic MTTF R () d Opimisic ( n ).. ASE- ssimisic (Lowr Bound) A h inpu sid o h ASE-, h rouing algorihm dos no considr h muliplxrs o b an ingral par o a givn SE. For xampl, as long as on o h wo muliplxrs aachd o swich is 9

4 opraional, swich can sill b usd or rouing. Hnc, i w group wo muliplxrs wih ach swich on h inpu sid and considr hm as a sris sysm (SE m ), hn w will hav a consrvaiv sima o h rliabiliy o hs hr componns. Thir aggrgad ailur ra will b m.5. Finally, hs aggrgad componns and h swichs in h inrmdia sags can b arrangd in pairs o conjuga loops. To obain lowr bound o h ASE-, assum h nwork is aild whnvr mor han on loop has a auly lmn or mor han on swich in h las sag ails []. Th block diagram is shown in Figur 7. Figur 7. Lowr Bound o ASE- Rliabiliy Equaions ar: m ) ( n d * * ssimisic R d () ssimisic R MTTF. Rliabiliy o IASE. IASE Opimisic (Uppr bound) Uppr bound ormula o IASE and MASE is sam. Only dirnc is h valu o d, or MASE is valu is and or IASE is. Dirnc in his valu is du o h sam rason ha or MASE d mans on swich and wo dmuliplxrs (+), whras or IASE d mans on swich and wo dmuliplxrs (+). Th block diagram is shown in Figur 8. Figur 8. Block diagram o Uppr Bound IASE Rliabiliy Equaions ar: m 8 d * * * Opimisic R d () Opimisic R MTTF. IASE ssimisic (Lowr bound) For h lowr bound, ach group is considrd indpndnly and is assumd o b auly i hr is any singl aul in i. Lowr bound quaion o IASE and MASE is also sam. Only dirnc is again in h valu o d, or MASE is valu is and or IASE is. Dirnc in his valu is du o h rason ha or MASE d mans on swich and wo dmuliplxrs (+), whras or IASE d mans on swich and wo dmuliplxrs (+). Th block diagram is shown in Figur 9. ICGST-CIR Journal, Volum 8, Issu, January 9

5 ICGST-CIR Journal, Volum 8, Issu, January 9 Figur 9. Block diagram o Lowr Bound IASE Rliabiliy Equaions ar: 8 m 8 d R * * ssimisic MTTF R () d ssimisic Th Rliabiliy quaions ar solvd using Trapzoidal rul o ingraion and h rsuls ar shown in Tabl. Basd on Tabl a comparison o Rliabiliy valus o ASE- and IASE in rms o Lowr and Uppr-bounds o MTTF or various nwork sizs has bn shown in Figurs and rspcivly. work ASE- IASE Siz (Log) (LB) (UB) (LB) (UB) Tabl : MTTF valus or dirn nwork siz Figur. Lowr Bound MTTF Comparison Figur. Uppr Bound MTTF Comparison 5. Cos Ecivnss To sima h cos o a nwork h assumpion is mad ha h cos o a swich is proporional o h numbr o cross-poins wihin a swich. For xampl a x swich has 6 unis o hardwar cos whras a x swich has unis [,8,,,5,6]. Th cos uncions or ASE- and IASE ar givn in h abl. Tabl shows h daa valus o cos uncions. Th graph or hs daa valus is shown in Figur. work Cos ASE- (.5 log -) IASE (.5 log ) - Tabl. Cos Funcions work Siz Cos (Log ) ASE- IASE Tabl. Cos valus or dirn nwork siz

6 ICGST-CIR Journal, Volum 8, Issu, January 9 Figur. Cos comparison o ASE- and IASE 6. Conclusion An Irrgular (IASE) is dsignd using xising rgular Augmnd Baslin work (ASE-) I has comparaivly on mor sag. IASE is a dynamically r-rouabl and provids mulipl pahs o varying lnghs bwn a sourc-dsinaion pair. I has bn ound ha in an IASE, hr ar igh possibl pahs bwn any sourc-dsinaion pair, whras ASE- has only six such pahs. Th rliabiliy analysis shows ha IASE has br prormanc han ASE-. Thus h nw nwork IASE provids br aul-olranc and rliabiliy han h xising ASE- wih lil mor cos. 7. Glossary Rliabiliy: Rliabiliy o a sysm is h probabiliy ha i will prorm is inndd uncion saisacorily or a givn im undr sad opraing condiions. MTTF: Th MTTF o a MI is dind as h xpcd im lapsd bor som sourc is disconncd rom som dsinaion. Faul-olranc: Th abiliy o h nwork o opra vn in h prsnc o auls, alhough a a dgradd prormanc. Bandwidh: I is dind as man numbr o aciv mmory moduls in a ransr cycl o h MI. I also aks ino accoun h mmory accss conlics causd by random naur o procssor rquss. rmuaion: rmuaion passibiliy o a nwork shows ha a a paricular momn o im, i a numbr o rquss simulanously occur a sourc, how many o hm will succssully maur i.. rach h dsinaion. 8. Rrncs [] A. Sha, aramr Esimaion o Sowar Rliabiliy Growh Modls by aricl Swarm Opimizaion, ICGST-AIML Journal, Vol. 7, o.7, Jun,7, pp [] H. Aggarwal, and.k. Bansal, Rouing and ah Lngh Algorihm or cos civ Modiid Four Tr work, IEEE TECO,, pp [] Harsh Sadawari and.k Bansal., Faul olran Irrgular Augmnd Shul work WSEAS Inrnaional Conrnc on Compur Enginring and Applicaions, Gold Coas, Ausralia, Jan, 7, pp [] J. Sngupa and.k Bansal, Rliabily and prormanc masurs o rgular and irrgular Mulisag Inrconncion works, Inraional Conrnc IEEE TECO, pp [5] J. Sngupa and.k. Bansal, rormanc o Rgular and Irrgular Dynamic MIs, Inrnaional Conrnc IEEE TECO 99, Sp. 999, Chju Island, Kora, pp. 7-. [6] Jos Duao, Sudhakar Yalamanchili and i Lionl, Inrconncion works: An Enginring Approach, IEEE Compur Sociy, 997. [7] M. Lubazwski and B Couois, A Rliabl Fail-sa Sysm, aralll and Disribud Sysms, IEEE Compur Sociy, Vol. 7, o., Fb. 998, pp. 6-. [8] Laxmi Bhuyan, Yang Qing and Dharma Agrawal., rormanc o Muliprocssor Inrconncion works, IEEE Compur, Vol., Fb. 99, pp [9] iin, On analyic Bounds o Rgular and Irrgular Faul-olran Mulisag Inrconncion works, Inrnaional Conrnc on DTA, Jun 6, pp []. K. Bansal, R.C. Joshi and K. Singh, On a Faul-olran Muli-sag Inrconncion work, Inrnaional journal o Elcronics and Elcrical Enginring, Vol., o., 99, pp []. K. Bansal, R.C. Joshi, K. Singh K. and G.. Siroha, Faul-olran Augmnd Baslin Mulisag Inrconncion work, roc. Inrnaional Conrnc IEEE TECO 9, India, Aug. 99, pp. -. [] R. Aggarwal, H. Aggarwal and L. Kaur, On Bandwidh analysis o Irrgular Faul-olran Mulisag Inrconncion nworks, Inrnaional Rviw on Compurs and Sowar, Vol., o., March 8, pp [] R. Aggarwal and L. Kaur, On Rliabiliy o Faul-olran Mulisag Inrconncion works, Inrnaional Journal o Compur Scinc and Scuriy, Vol., o., Augus 8, pp. -8. [] R. Aggarwal, H. Aggarwal and L. Kaur, rormanc o o Rgular and Irrgular Mulisag Inrconncion works, Inrnaional Journal o Inormaion and Compuing Scinc, Vol., o., Dcmbr 8.

7 ICGST-CIR Journal, Volum 8, Issu, January 9 [5] Sandp Sharma, K.S. Kalhon and.k. Bansal, On a class o Mulisag Inrconncion works in paralll procssing IJCSS Inrnaional Journal o Compur Scinc and work Scuriy, Vol.8, o.5, May 8, pp [6] Sandp Sharma, K.S. Kalhon,.K. Bansal and Kawalj Singh, Improvd Irrgular Augmnd Shul Exchang Mulisag Inrconncion work, Inrnaional Journal o Compur Scinc and Scuriy, Vol., o., 8, pp. 8-. [7] Sandp Sharma, K.S. Kalhon,.K. Bansal and Kawalj Singh, Irrgular class o Mulisag Inrconncion works in aralll rocssing, Journal o Compur Scinc, Vol., o., 8, pp. -. Himanshu Aggarwal, h.d., is Radr in Compur Enginring a Univrsiy Collg o Enginring, unjabi Univrsiy, aiala. H has mor han 5 yars o aching xprinc and srvd acadmic insiuions such as Thapar Insiu o Enginring & Tchnology, aiala, Guru anak Dv Enginring Collg, Ludhiana and Tchnical Tachr's Training Insiu, Chandigarh. H is an aciv rsarchr who has suprvisd many M.Tch. Dissraions and conribud aricls in Conrncs and 8 paprs in rsarch Journals. His aras o inrs ar Inormaion Sysms, ER and aralll Compuing. Biographis Rinkl Aggarwal, B.Tch (Compur Scinc & Engg.), M.S. (Sowar Sysms), is Snior Lcurr in Compur Scinc & Enginring Dparmn a Thapar Univrsiy, aiala. Sh has mor han yars o aching xprinc and srvd acadmic insiuions such as Guru anak Dv Enginring Collg, Ludhiana and S.S.I.E.T 'Drabassi. Sh has suprvisd many M.Tch. Dissraions and conribud 5 aricls in Conrncs and 6 paprs in rsarch Journals. Hr aras o inrs ar aralll Compuing and Algorihms. Lakhwindr Kaur h.d. is Radr in Compur Enginring a Univrsiy Collg o Enginring unjabi Univrsiy, aiala. Sh has 6 yars o aching xprinc. Sh has publishd 8 rsarch paprs in Inrnaional Journals. Hr aras o inrs ar Imag procssing, aralll Compuing and Compur Graphics.