Energy-Aware Fault Tolerance in Fixed-Priority Real-Time Embedded Systems*

Transcription

1 Energy-Aware Fault Tolerance n Fxed-Prorty Real-Tme Embedded Systems Yng Zang, Krsnendu Cakrabarty and Vsnu Swamnatan Department of Electrcal & Computer Engneerng Duke Unversty, Duram, NC 778, USA Abstract We nvestgate an ntegrated approac to fault tolerance and dynamc power management n real-tme embedded systems Fault tolerance s aceved va ceckpontng and power management s carred out usng dynamc voltage scalng (DVS) We present feasblty-of-scedulng tests for ceckpontng scemes for a constant processor speed as well as for varable processor speeds DVS s ten carred out on te bass of tese feasblty analyses Expermental results sow tat compared to fault-oblvous metods, te proposed approac sgnfcantly reduces power consumpton and guarantees tmely task completon n te presence of faults Introducton Fault tolerance tecnques are needed to ensure te dependablty of embedded systems tat operate n ars envronmental condtons Tese embedded systems also operate under severe energy lmtatons In addton, many embedded systems execute real-tme applcatons tat requre strct aderence to task deadlnes In ts paper, we nvestgate an ntegrated approac tat provdes fault tolerance and dynamc power management (DPM) n ard real-tme embedded systems We extend a recent energy-aware adaptve ceckpontng sceme tat consders a sngle task n a soft real-tme system [] Dynamc voltage scalng (DVS) s a popular tecnque for reducng power consumpton durng system operaton [, 3] Fault tolerance s typcally aceved n real-tme systems troug ceckpontng [4] At eac ceckpont, te system saves ts state n a secure devce Wen a fault s detected, te system rolls back to te most recent ceckpont and resumes normal executon Te ceckpontng nterval, e, duraton between two consecutve ceckponts, must be carefully cosen to balance ceckpontng cost wt te re-executon tme DPM and fault tolerance for embedded real-tme systems ave largely been studed as separate problems n te lterature DVS tecnques for power management do not consder fault tolerance [, 3], and ceckpont placement strateges for fault tolerance do not address DPM [5, 6] It s only recently tat an attempt as been made to combne fault tolerance wt DPM [] Tere are tree man reasons for combnng DPM wt fault tolerance n real-tme embedded systems Increased de temperatures due to ger processor speeds create termal stresses on te de and undermne system relablty In order to mtgate relablty problems caused by g de temperatures, we can eter lower energy consumpton troug DPM tecnques suc as DVS, or we can adopt fault tolerance tecnques suc as ceckpontng Better stll, a combnaton of DVS and ceckpontng can be used Ts researc was sponsored n part by DARPA, and admnstered by te Army Researc Offce under Emergent Survellance Plexus MURI Award No DAAD Any opnons, fndngs, and conclusons or recommendatons expressed n ts publcaton are tose of te autors and do not necessarly reflect te vews of te sponsorng agences Te second reason s motvated by te need to meet te task deadlnes n real-tme systems If faults occur frequently, te processor speed can be scaled up dynamcally (wtn lmts mposed by ger de temperatures) and more slack can be provded to te task, wc allows more tme for rollback recovery Te trd motvaton arses from srnkng process tecnologes n te nanotecnology realm Lower processor voltages are lkely to lead to lower nose margns and more transent faults, caused n part by sngle-event upsets We frst present feasblty tests for fxed-prorty real-tme systems wt ceckpontng under constant processor speed Followng ts, we extend tese feasblty tests to varable-speed processors Based on te results of te feasblty analyses, an onlne dynamc speed-scalng sceme s furter developed to reduce energy durng task executon Te proposed approac s compared wt a fault-oblvous DVS sceme n te presence of faults Feasblty Analyss Under Constant Speed We are gven a set Γ = {τ, τ,, τ n } of n perodc real-tme tasks, were task τ s modeled by a tuple τ = (T, D, E ) Te elements of te tuple are defned as follows: T s te perod of τ, and D s ts deadlne (D T ); E s te executon tme of τ under fault-free condtons Let te ceckpontng cost be C We make te followng assumptons related to task executon and fault arrvals: () Te task set Γ s sceduled usng fxed-prorty metods suc as te rate-monotonc sceme [7]; () te task set Γ s scedulable under fault free condtons; () te prorty of tasks are n decreasng order of te ndex, e, task τ as ger prorty tan task τ j f < j; (v) eac nstance of te task s released at te begnnng of te perod; (v) te ceckpontng ntervals for a task are equal; (v) te tmes for rollback and state restoraton are zero; (v) faults are detected as soon as tey occur, and (v) no faults occur durng ceckpontng and rollback recovery In [8], a feasblty analyss s provded under te assumpton tat two successve faults arrve wt a mnmum nter-arrval tme T F Ts s not practcal for realstc applcatons, were te fault occurrence can be bursty or memoryless Terefore, we focus ere on toleratng up to a gven number of faults durng task executon No addtonal assumpton s made regardng fault arrvals Snce te task set s perodc, te total executon tme can be very g f we consder a large number of perods We terefore need to dentfy an approprate k-fault-tolerant condton for sorter tme duraton Here we provde two solutons correspondng to two dfferent fault-tolerance requrements One s to tolerate k faults for eac job, termed as job-orented fault-tolerance; te oter s to tolerate k faults wtn a yperperod (defned as te least common multple of all te task perods [7]), termed as yperperod-orented fault-tolerance We frst consder te case of a sngle job Suppose m ceckponts are nserted equdstantly to tolerate k faults n one job Te worst-case response tme R for te job s composed of tree terms: te task executon tme E, te ceckpontng cost mc, and te recovery cost ke/(m+), e R = E + mc + ke /( m +) To

2 satsfy te deadlne constrant, we must ave E + mc + ke /( m + ) D Let f ( m) = E + mc + ke /( m + ) D Te mnmum value of f(m) s obtaned for m = m = ke / C Snce m s a non-negatve nteger, we ave = max( ke / C,) m If f(m ), tere exsts equdstant ceckpontng scemes for k-fault-tolerance, and te response tme s mnmum wen m ceckponts are nserted If f(m ) >, ten no equdstant ceckpontng scemes exsts for toleratng up to k faults Te feasblty analyss for more tan one job s based on te tme-demand analyss for fxed-prorty scedulng [7] Te steps n te analyss are as followng: () Compute te response tme R for τ accordng to te equaton: + R = E R / = T E Here T and E are te perod and te executon tme of a task τ wt ger prorty tan τ Ts equaton can be solved by formng a recurrence relaton: ( j + ) j R E ( ) = + R / T E = () ) ( j ) () Te teraton s termnated eter wen R = R and R D ( j ) for some j or wen ) R > D, wcever occurs sooner In te former case, τ s scedulable; n te later case, τ s not scedulable Accordng to [7], te tme complexty of te tme-demand analyss for eac task s O(nR), were R s te rato of te largest perod to te smallest perod Job-orented fault-tolerance: toleratng k faults n eac job In ts case, we requre tat te task set can meet te deadlne requrement under te condton tat at most k faults occur durng te executon of eac job Under te worst-case condton, te addtonal tme due to ceckpontng and recovery sould be ncorporated Wen tere are m j equdstant ceckponts for eac nstance of τ j, we ave: R = ( E + mc + ke /( m + )) + = R / ( + + /( + )) T E mc ke m To mnmze all response tmes, we must ave: max( ke / C,) ( n) m = Ten we can employ te recurrence equaton as follows: ) R = ( E + m C+ ke /( m + )) + ( j) R / T ( E + m C+ ke /( m + )) = ( j + ) ( j ) j Wen R = R and R ( ) D for some j, τ s ( j + scedulable; wen R ) > D, τ s not scedulable Te total tme complexty ere s O ( n R), were R s te rato of te largest perod to te smallest perod Example : Consder a task set composed of two tasks: τ = (6, 8, 7) and τ = (8, 34, 8), and let k = 3, C = Ten m = 4 and m = 4 After applyng te recurrence equaton, we get te response tmes: R = 5 < 8; R = 33 < 34 Tus ceckpontng s feasble for ts task set f up to tree faults occur durng eac job Next we examne te case of k = 4 For ts case m = 5 and m = 5 Te response tmes are: R = 67 < 8 and R = 35 > 34 As a result, ceckpontng s not feasble f up to four faults need to be tolerated for eac job Hyperperod-orented fault-tolerance: toleratng k faults n a yperperod In [8], an algortm s presented to determne te ceckpontng nterval under te assumpton tat two successve faults arrve wt a mnmum nter-arrval tme T F Let F j, j, be te extra computaton tme needed by τ j, j, f one fault occurs durng te executon Wen tere are m j equdstant ceckponts for τ j, te response tme R for τ s expressed as follows n [8]: R / T ( E + mc) R / TF max j { F } R = ( E + mc ) + + = j, were F E /( m +) j = j j Te ceckpont s examned startng from g-prorty tasks to low-prorty tasks For eac task τ j, te algortm tres to reduce te response tme by reducng te maxmum addtonal computaton tme, e, max j { F j } Te detals n [8] are as follows: () Intally m = for n () Startng from te gest-prorty task τ, calculate te mnmum number of ceckponts m requred to make t scedulable (3) In decreasng order of task prortes, calculate te response tme R of task τ If R D, move to te next task; oterwse R needs to be reduced furter Te only way to reduce R s to add more ceckponts to decrease te re-executon tme caused by faults, e, F j, for j In fact, te parameter max j { F j } s relevant ere and sould be reduced Te task τ tat contrbutes te most to te task re-executon tme s found and one more ceckpont s added to τ Ten R s recalculated Ts process s repeated untl eter R D or te deadlne D s exceeded Wle te scedulablty test n [8] provdes useful gudelnes on task scedulablty n te presence of faults, ts drawback s tat two key ssues tat affect scedulablty are not addressed Ceckponts are added to te ger-prorty tasks n certan teratons n order to satsfy deadlne constrants for all te tasks Tese ger-prorty tasks, owever, ave met ter deadlne n earler teratons Te addton of more ceckponts to tem nevtably canges ter response tmes As a result, t s necessary to trace back to re-calculate ter response tmes and adjust ter ceckponts Ts ssue as not been addressed n [8] It s necessary to determne a bound on te number of ceckponts beyond wc te addton of ceckponts does not mprove scedulablty In [8], te scedulablty test concludes tat τ s not scedulable once R ncreases durng te addton of ceckponts However, ts does not always old We present a counterexample below Example : Consder two tasks τ = (, 8, 7999) and τ = (,, 8), and let T F =, C = We follow te steps from [8] as sown below: () Intally m = m =, and F = 7999, F = 8; () Next τ s examned: R =5998 < 8 No ceckponts are needed for τ Tus m = m = (3) Next τ s examned: R = 3999 > Snce F > F, one ceckpont s added to τ, tus m = and m = Ten F = 7999, F = 4 and max j { F j} = We recalculate te response tme R = 498 > 3999 Accordng to [8], τ s not scedulable However, ts s not correct We contnue te above step and fnd F > F, ten one more ceckpont s added to τ ; as a result m =, m = Ten F = /( + ) = , F = 4, and

3 max j { F j} = 4 We recalculate te response tme of τ and τ : R = 985 < 8 and R = 99 <, wc mples tat bot tasks are scedulable We requre ere tat te tasks meet ter deadlnes under te condton tat at most k faults occur durng a yperperod Based on te scedulablty test n [8], we solve te two aforementoned problems as follows Te response tme R for τ s expressed as: R / T ( E + mc) k max j { F } R = ( E + mc ) + + = j, were F E /( m +) j = j j Te frst problem can be solved usng a recursve metod Any tme we ncrease te number of ceckponts for a task, all te lower-prorty tasks need to be re-examned We solve te second problem by determnng a bound on te number of ceckponts suc tat f te task set cannot be made scedulable usng ts number of ceckponts, t cannot be sceduled by addng more ceckponts Bot te ceckpontng cost and te tmng constrants must be taken nto account () Analyss of a bound based on ceckpontng tradeoffs Te effect of addng more ceckponts s two-fold Frst t ncreases te executon tme due to te ceckpont cost, wc runs contrary to te goal of reducng te response tme On te oter and, t decreases re-executon due to a fault, wc elps n reducng te response tme Suppose te task executon tme s E and m ceckponts ave already been added If anoter ceckpont s now added, te reducton of re-executon tme under te k-faulttolerance requrement s smply: ke /( m + ) ke /( m + ) = ke /[( m + )( m + )] We combne te two mpacts of ceckpontng on te reexecuton tme to defne te tradeoff functon tr(m) as: tr ( m) = C ke /[( m + )( m + )] If tr ( m) <, ten addng one more ceckpont can potentally reduce te response tme; oterwse, t s not elpful snce t ncreases te task re-executon tme due to te k faults For eac task τ wt m ceckponts, we can calculate te tradeoff functon tr (m ) Solvng for tr ( ') =, we get: m ' = ( 3 + 4kE / C ) / for n Snce m ', we + m furter express t as: m ' max( ( 3 + 4kE / C ) /, ) = for + n Ts gves an upper bound on te number of ceckponts, wc s based on te tradeoff functon () Analyss of a bound based on tmng constrants Under fault-free condtons, te response tme R for task τ can be easly obtaned After ncorporatng te ceckpontng cost and tmng constrants, we ave: R + mc D, wc mples tat # m ( D R ) / C Let m = ( D R )/ C Combnng te two bounds, we defne # m = mn( m ', m ) ( n) Ten m s a tgter upper bound on te number of ceckponts requred to make τ scedulable A ceckpontng algortm ADV-CP for off-lne feasblty analyss s descrbed n Fgure, wc takes as an nput parameter te real-tme task set Γ All tasks are ntally set unscedulable Te recursve ceckpontng procedure CP(p,q) s descrbed n Fgure, were p and q are te lowest and gest ndex for te task subset under consderaton Te recursve executon of CP ( p, q) takes O( n R) m = n tme Let M = = m Addng all te cost togeter, te total complexty for te feasblty test & ceckpontng procedure s O ( n RM ), wc s only quadratc n te number of tasks n Furtermore, we note tat te complexty can be reduced f we can make M as small as possble Tat s wy we combne bot te tradeoff functon and tmng constrants to obtan a relatvely tgt bound for m 3 Feasblty Analyss wt DVS We are gven a varable-speed processor, wc s equpped wt l speeds f, f,, f l In addton, f < f j f < j Let c be te number of clock cycles tat a sngle ceckpont takes We are also gven a set Γ = {τ, τ,, τ n } of n perodc real-tme tasks, were task τ s modeled by a tuple τ = (T, D, E ) Te elements of te tuple are defned as follows: T s te perod of τ and D s ts deadlne (D T ); E s te number of computaton cycles of τ under fault-free condtons In addton to te assumptons n Secton, we assume te task set Γ s scedulable under fault free condtons at te lowest speed For te sake of smplcty of presentaton, we also assume wtout loss of generalty tat speed swtcng does not ncur extra cost n terms of tme and energy We note tat f supply voltage V dd s used for a task wt N sngle-cycle nstructons, te energy consumpton can be expressed as (α s a constant): Eng( N) = αnv dd () We also note tat te processor clock frequency f can be expressed n terms of te supply voltage V dd and tresold voltage V t as f = β ( Vdd Vt ) / Vdd, were β s a constant From above, we obtan V dd as a functon of f: Vdd ( f ) = ( Vt + f /(β )) + ( Vt + f /(β )) Vt (3) Accordng to Equaton (), energy consumpton s a functon of N and f: Eng( N, f ) = αnv dd ( f ), were V dd (f) s expressed n Equaton (3) Here we assume V t = wtout loss of generalty In our proposed sceme, speed scalng can be done for a partcular applcaton, e, all tasks for te applcaton are assgned te same speed, or at te task level, e, dfferent tasks can be assgned dfferent speed Speed scalng can also be carred out at te job level, e, dfferent jobs for a task can ave dfferent speeds Let τ ) : τ f j ( n, j l) denote te speed scalng functon, wc maps a task τ to speed f j Our am s to meet task deadlnes determnstcally, even toug k faults occur, wle mnmzng energy consumpton Frst, we need to dentfy approprate tme duraton to evaluate te energy consumpton We consder te yperperod as te tme duraton Second, te crteron of mnmzng energy consumpton needs to be clarfed Based on te applcaton requrement, we can coose eter a best-case or a worst-case energy consumpton value By best-case, we refer to te results obtaned under te fault-free condton, wle worst-case refers to te results obtaned wen all k faults occur In our work, we focus on mnmzng energy consumpton under te worst-case condton durng a yperperod Let te yperperod denoted by Ht and te number of ceckponts for τ denoted by m ; te total energy consumpton durng one yperperod s expressed as: n Total _ eng = = ( Ht / T ) Eng( E m c ke /( m ), τ )) (4) n 3

4 Procedure ADV-CP (Γ) begn for = to n do m = ; compute m ; R j = ; CP(, n) end Fgure : Advanced ceckpontng procedure Procedure CP (p, q) f (R p D p & R p+ D p+ & & R q D q ) return( task subset scedulable ); elsef (m > m & m > m & & m q > m q ) ext( task set unscedulable ); 3 else{for j = p to q do{ 3 compute R j ; 3 wle (R j > D j ) do{ 3 fnd [, j] suc tat F = max(f, F,, F j ); 3 m = m + ; 33 F = E /(m + ); 34 CP (, j);}}} Fgure : Recursve ceckpontng procedure Te off-lne feasblty analyss wt DVS provdes two mportant peces of nformaton: frst, t provdes te feasblty analyss under te worst-case scenaro; second, t provdes statc results suc as speed assgnment and ceckpont nterval, wc can be furter used for on-lne adjustment durng task executon 3 Job-orented fault-tolerance wt DVS Te worst-case response tme for task τ can be expressed as: E + + /( + ) mc ke m R E + mc + ke /( m + ) R = + (5) τ) = T τ) To mnmze all response tmes, we must ave: max( ke / C,) ( n) m = Ten we can employ te recurrence equaton as follows: ( ) ( ) /( ) j j E m c ke m R E + m c + ke /( m + ) R = + τ) = T τ) ) ( j) ( j) If R = R and R D for some j, τ s scedulable; f ) R > D, τ s not scedulable Snce te optmal number of ceckponts s fxed a pror for eac task, we need to coose approprate processor speeds to satsfy te deadlne constrant for eac task () Applcaton-level speed scalng: all tasks ave te same speed Here all tasks ave te same speed f and τ ) = τ ) = = τ n ) = f, were f {f, f,, f l } Equaton (5) s smplfed as: E /( ) m c ke m R E + m c + ke /( m + ) R = + f = T f Te teratve metod descrbed n Secton can be used ere to determne f To examne te feasblty for eac task, all possble speeds ave to be tested Tere are l possbltes n total Te lowest speed tat satsfes te tmng constrants s selected to mnmze energy consumpton () Task-level speed scalng: dfferent tasks can ave dfferent speeds To obtan an optmal soluton, we use an exaustve metod Snce eac task can be run at l speeds, tere are l n possble speed combnatons for n tasks For eac speed combnaton, te feasblty test s performed accordng to Equaton (5) Meanwle, te energy consumpton s calculated from Equaton (4) Te speed combnaton tat satsfes te tmng constrants wt te mnmum energy consumpton s cosen as te optmal soluton 3 Hyperperod-orented fault-tolerance wt DVS Te worst-case response tme for task τ can be expressed as: R = ( E + m c)/ τ ) + R / T ( E + m c) / τ ) + k max{ F = j} j were Fj = E j /[ τ j )( m j + )] (6) () Applcaton-level speed scalng: all tasks ave te same speed Here all tasks ave te same speed f and τ ) = τ ) = = τ n ) = f, were f {f, f,, f l } Equaton (6) s smplfed as: R = ( E + m c) / f + R / T ( E + m c) / f + k max{ F, = j} j were F j = E j /[ f ( m j + )] In contrast to () n Secton 3, we frst fx te speed nstead of te number of ceckponts For eac gven speed f, we examne te feasblty of te task set usng te metod n Secton If t s scedulable, te correspondng number of ceckponts for eac task can be obtaned Te energy consumpton s calculated from Equaton (4) Te lowest speed tat satsfes te tmng constrants s selected to mnmze energy consumpton () Task-level speed scalng: dfferent tasks can ave dfferent speeds To obtan an optmal soluton, we use an exaustve metod Snce eac task can be run at l speeds, tere are l n possble speed combnatons for n tasks For eac speed combnaton, te feasblty test s performed accordng to Equaton (6) Te metod n Secton s employed and te correspondng number of ceckponts s obtaned Meanwle, te energy consumpton s calculated from Equaton (4) Te speed combnaton tat satsfes te tmng constrants wt te mnmum energy consumpton s cosen as te optmal soluton 33 Job-level on-lne speed scalng As dscussed n Sectons 3 and 3, te speed assgnment and te ceckpontng nterval are determned by te off-lne feasblty analyss A statc sequence of jobs s obtaned and ter tmng parameters suc as release tmes and executon tmes are known a pror under te worst case However, f only suc statc measures are used durng run-tme, t wll not be possble to make use of dle ntervals Clearly, furter energy savng s possble troug addtonal on-lne speed scalng Te on-lne speed scalng procedure, done at te job-level, s adaptve wt respect to fault occurrence It makes use of a smple run-tme adaptaton mecansm Te key features are: Once a job completes, te release tme of te next job s adjusted dynamcally durng run-tme Te processor s run at an approprate speed suc tat eter te current job completes before ts deadlne, or before te statc release tme of te next job, wcever s sooner 4 Expermental Results In ts secton, we compare te performance of our energyaware fault-tolerance sceme wt te DVS tecnque proposed n [3], referred to as VSLP Our goal ere s to glgt te mpact of fault occurrences on a fault-oblvous DVS sceme We use te followng notaton to refer to te varous types of scemes: () JFTA: job-orented fault tolerance wt applcatonlevel speed scalng; () JFTT: job-orented fault tolerance wt task-level speed scalng; (3) HFTA: yperperod-orented fault tolerance wt applcaton-level speed scalng; (4) HFTT: yperperod-orented fault-tolerance wt task-level speed scalng 4

5 Snce te VSLP sceme as presented n [3] does not provde fault tolerance, we assume tat t smply re-executes a job wen a fault occurs Furtermore, snce JFTA s a specal case of JFTT and HFTA s a specal case of HFTT, we compare VSLP wt te JFTT and HFTT scemes For bot cases, we frst sow tat JFTT and HFTT can scedule task sets even wen VSLP cannot do so; we ten sow tat tese scemes can save more energy va ceckpontng n te presence of faults 4 JFTT vs VSLP As ponted out n [8], a system of perodc preemptable tasks, eac of wose relatve deadlne D s equal to ts perod T, s scedulable on one processor accordng to te rate monotonc algortm f and only f ts total task utlzaton s equal to or less tan In te presence of faults, snce te re-executon takes extra tme and te total task utlzaton wll be ncreased accordngly, a task set tat s scedulable under fault-free condtons may no longer be scedulable Here we construct a task set wose total utlzaton s greater tan for VSLP under faulty condtons even toug te entre task set s executed wt te gest speed, and sow tat ts task set s scedulable usng JFTT Suppose we are gven tree tasks τ = (,, ), τ = (8, 8, 3) and τ 3 = (4, 4, 4), and tree normalzed processor speeds, 8 and 6 Let a sngle ceckpont take c = 5 cycles If only k = fault occurs durng eac job, te total utlzaton for VSLP under te gest speed s found to be 33 Ts mples tat VSLP cannot scedule te task set wen one or more faults occur durng eac job However, te experments sow tat JFTT can tolerate up to 6 faults durng eac job Te speed assgnment (s, s, s 3 ) and number of ceckponts (m, m, m 3 ) for τ, τ and τ 3, and total energy consumpton are sown n Table Next we sow tat JFTT saves more energy tan VSLP n te presence of faults wen bot scemes are feasble Consder tree tasks τ = (,, 5), τ = (8, 6, ) and τ 3 = (4,, ), and tree normalzed processor speeds, 8 and 6 Let a sngle ceckpont take c = 5 cycles Te energy savng for JFTT over VSLP s sown n Table Compared to VSLP, JFTT can save up to 75% energy n te presence of faults To demonstrate te effect of ceckpontng cost, we fx te value of k and cange te value of c for te same task set used n Table Te results are sown n Table 3 4 HFTT vs VSLP We now sow tat HFTT can scedule task sets n te presence of faults, even wen VSLP fals to do so Suppose we are gven tree tasks τ = (,, ), τ = (8, 8, 3) and τ 3 = (4, 4, 4), and tree normalzed processor speeds, 8 and 6 Let a sngle ceckpont take c = 5 cycles As ndcated n Secton 4, VSLP cannot scedule ts task set wen one or more faults occur durng eac job Here altoug we examne te fault occurrence n one yperperod, te WCET value of eac task for VSLP remans te same as tat n Secton 4 As a result, VSLP stll cannot scedule ts task set f tere are any fault occurrences On te oter and, HFTT can tolerate more tan faults durng a yperperod Te speed assgnment (s, s, s 3 ) and number of ceckponts (m, m, m 3 ) for τ, τ and τ 3, and total energy consumpton are sown n Table 4 Next we sow tat HFTT saves more energy tan VSLP n te presence of faults wen bot scemes are feasble Consder tree tasks τ = (,, 5), τ = (8, 6, ) and τ 3 = (4,, ), and tree normalzed processor speeds, JFTT k (s, s, s 3) (m, m, m 3) Energy VSLP (8, 8, 8) (7, 8, 9) (8,, 8) (, 4, 6) 4473 Infeasble 6 (,, ) (7, 9, ) 653 Table : JFTT vs VSLP (Part ) k Engy_JFTT Engy_VSLP Engy_JFTT/ Engy_VSLP Table : JFTT vs VSLP (Part ) c Engy_JFTT Engy_VSLP Engy_JFTT/ Engy_VSLP Table 3: JFTT vs VSLP (Part 3) HFTT k (s, s, s 3) (m, m, m 3) Energy VSLP (6, 8, 8) (3, 3, 4) 76 4 (8,, 8) (5, 6, ) 387 Infeasble (,, ) (, 4, 9) 4785 Table 4: HFTT vs VSLP (Part ) k Engy_HFTT Engy_VSLP Engy_HFTT/ Engy_VSLP Table 5: HFTT vs VSLP (Part ) 8 and 6 Let a sngle ceckpont take c = cycles Te energy savng for HFTT over VSLP s demonstrated n Table 5 5 Conclusons We ave sown ow dynamc adaptaton for fault tolerance and power management can be carred out n embedded systems Fault tolerance s aceved va ceckpontng and power management s carred out usng DVS We ave presented 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