Dynamic workload. Example: video playing. Example: phone call. Mpeg decoding. Other causes of overloads

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Dynamic workload Several applicaions (e.g.

signal, decodes i, and ransfers packes o he speaker buffer for reproducion. Voice sampling, daa encoding, speech enhancemen, and packe ransmission hrough he modem.

consising ino 3 ypes of frames: I frames (Iner-frames) include he enire conen of a picure; B frames, (Backwards predicive) look backwards a he I frames and frames; frames (redicive) looks forward a

1 Dynamic workload Several applicaions (e.g., mulimedia sysems) are characerized by highly variable compuaional requiremens: load avg ime Example: phone call I consiss a leas of 2 periodic asks, execued every 20 ms: modem RX TX Receives audio signal, decodes i, and ransfers packes o he speaker buffer for reproducion. Voice sampling, daa encoding, speech enhancemen, and packe ransmission hrough he modem. processor C i-min Overall CU bandwidh: 30-65% C i-min = ms (silence) C i-max = 3 ms = 5 ms (silence) C i-max = 0 ms Example: video playing MEG sandard encodes frames in "Group of icures" (GO), consising ino 3 ypes of frames: I frames (Iner-frames) include he enire conen of a picure; B frames, (Backwards predicive) look backwards a he I frames and frames; frames (redicive) looks forward a he frame, consanly comparing frame conen. AL sandard: frame rae = 25 fps decoding ime: 2-20 ms I-frames can ake 0 imes more han B-frames Mpeg decoding Oher causes of overloads robabiliy densiy Frame execuion imes disribuion for Sar Wars Opimisic sysem design (based on average raher han wors-case behavior) Malfuncioning of inpu devices (sensors may send sequence of inerrups in burss) Variaions in he environmen Simulaneous arrivals of evens Decoding ime (s) Excepions raised by he kernel

2 Load definiions Insananeous load () Sof aperiodic asks: Hard periodic asks: C U n i C T i i Does no consider pas or fuure acivaions, bu only curren jobs: Generic RT applicaion: if g(, 2 ) is he processor demand in [, 2 ], hen: g(, max, ) Maximum processor demand among hose inervals from he curren ime and he deadlines of all acive asks. ( ) Insananeous load () g(, dk ) max k d k max k di dk d k c ( ) i Insananeous load () We can have a mos one deadline for each acive ask k, hence: ( ) k di dk ( ) max ( ) k d k c ( ) i k Example Load and design assumpions (4) = 2/4 = load Sysem designed under wors-case assumpios load Sysem designed under average-case assumpios 2 2 (4) = 5/6 = () 3 (4) = 7/9 = 0.78 (4) = ime 0 ime 2

3 redicabiliy vs. efficiency A maer of cos efficiency UNSAFE Opimisic design predicabiliy Allocaed resources SAFE essimisic design High predicabiliy and low efficiency means wasing resources high cos i can be jusified only for very criical sysems High efficiency in resource usage requires a he sysem o: handle and olerae overloads adap for graceful degradaion plan for excepion handling mechanisms Definiions Definiions Overrun: Siuaion in which a ask exceeds is expeced uilizaion. Execuion Overrun The ask compuaion ime exceeds is expeced value: Overload: Siuaion in which () >. Transien Overload max > bu avg ermanen Overload avg > Acivaion Overrun The nex ask acivaion occurs before is expeced ime: expeced inerarrival ime 0 ime 0 ime Consequences of overruns A ask overrun may no cause an overload: Consequences of overruns Consider he following applicaions wih U < : overrun Bu in general may delay he execuion of oher asks, causing a deadline miss: deadline miss (2/4) 2 (2/6) overrun 8 3 (/2)

Consequences of overruns U < bu sporadic overruns can preven 3 o run: Example of overload In engine conrol,

(2/4) early compleion 4 execuion overrun 8 2 6 20 The acivaion rae of hese asks is proporional o he angular

handling Resource Reservaion Reacive vs. roacive Local vs.

Reservaion: Resource pariion Resource enforcemen a mechanism o bound he resource consumpion of a ask se o limi

$0 % 4 20 % To implemen Resource Reservaion we have o: reserve a fracion of he processor bandwidh o a se of$

4 Consequences of overruns U < bu sporadic overruns can preven 3 o run: Example of overload In engine conrol, some asks are acivaed a specific angles of he crankshaf. (2/4) early compleion 4 execuion overrun The acivaion rae of hese asks is proporional o he angular velociy of he engine: 2 (2/6) C u() = 2 3 (/2) 2 * * = 2 C Load conrol mehods Overrun handling Overload handling Resource Reservaion Reacive vs. roacive Local vs. Global roviding emporal isolaion Resource Reservaion Transien overloads can be handled hrough Resource Reservaion: Resource pariion Resource enforcemen a mechanism o bound he resource consumpion of a ask se o limi he inerference caused o oher asks. 0 % 4 20 % To implemen Resource Reservaion we have o: reserve a fracion of he processor bandwidh o a se of asks; preven he ask se o use more han he reserved fracion. 45 % % Each ask receives a bandwidh i and behaves as i were execuing alone on a slower processor of speed i A mechanism ha prevens a ask o consume more han is reserved amoun. If a ask execues more, i is delayed, preserving he resource for oher asks. 4

5 rioriies vs. Reservaions rioriies vs. Reservaions rioriized Access READY QUEUE 2 3 rioriized Access 2 3 Resource Reservaion 2 3 = 2 = = % 30% 20% 2 3 Resource Reservaion % 30% 20% Benefis of Resource Reservaion Implemening RR. Resource allocaion is easier han prioriy mapping. 2. I provides emporal isolaion: overruns occurring in a reservaion do no affec oher asks. Imporan for modulariy and scalabiliy 2b 2a Ready queue scheduler CU 3. Simpler schedulabiliy analysis: Response imes only depends on he applicaion demand and he amoun of reserved resource. 4. Easier probabilisic approach Fixed prioriies Dynamic prioriies scheduler RM/DM EDF Sporadic Server CBS Analysis under RR 2b 2 2a 3 3 If a processor is pariioned ino n reservaions, we mus have ha: n A i i Ready queue CU scheduler U lub where A is he adoped scheduling algorihm. Types of reservaions HARD: when he budge is exhaused, he is blocked unil he nex budge replenishmen. SOFT: when he budge is exhaused, he remains acive bu a a lower prioriy level. Noe ha a HARD reservaion (Q s, s ) guaranees a mos a budge Q s every period s a SOFT reservaion (Q s, s ) guaranees a leas a budge Q s every period s 5

6 Sof CBS The original CBS formulaion implemens a SOFT reservaion: In fac, more he Q s uniscanbeexecuedin an inerval s if he processor is available. roblem wih sof reservaions The use of idle imes from a can cause irregular job execuions and long delays: s s s s s s s 5 6 Q s = 3 s = 9 Q s = s = 3 long delay Example wih Hard CBS Hierarchical scheduling The deadline aging problem can be avoided by suspending he when q s =0and recharging he budge a d s : Resource reservaion can be used o develop hierarchical sysems, where each componen is implemened wihin a reservaion: 6 Applicaion Applicaion N d 0 5 d d 2 d 3 d 4 d 5 d 6 s q s Local Scheduler Componen Local Scheduler Componen N CBS: Q s =, T s = Global Scheduler Compuing laform Hierarchical scheduling Hierarchical scheduling In general, a componen can also be divided in oher sub-componens Global scheduler: he one managing he sysem ready queue Local schedulers: he ones managing he s queues Server S 4 Server S Local Scheduler Local Scheduler 9 8 Local scheduler 3 2 Local scheduler Local Scheduler Componen Local Scheduler Componen N Global Scheduler Compuing laform S 4 S 3 S Global scheduler CU 6

7 Hierarchical Analysis Analysis under RR Global analysis: Servers mus be schedulable by he global scheduler running on he physical plaform. Local analysis: Applicaions mus be scheduled by he local schedulers running on he componens. Applicaion Local Scheduler Componen Global Scheduler Compuing laform Applicaion N Local Scheduler Componen N rocessor Demand Crierion (under EDF) Workload Analysis (under fixed prioriies): D i,..., n 0, D ] : ( i dbf ( ) Timing behavior of he applicaion W i ( ) processing ime available in [0,] Analysis under RR Under EDF, he analysis of an applicaion wihin a reservaion is done hrough he rocessor Demand Crierion: 0, dbf ( ) Under Fixed rioriy Sysems (FS), he analysis is done hrough he Workload Analysis: i,..., n (0, Di ] : W i ( ) Analysis under RR To describe he ime available in a reservaion, we need o idenify, for any inerval [0,], he minimum ime allocaed in he wors-case siuaion. Supply bound funcion sbf(): minimum amoun of ime available in reservaion R k in every ime inerval of lengh. The difference is ha in an inerval of lengh he processor is only parially available. Example: Saic ime pariion Example of reservaion providing 4 unis every 0 (bandwidh = 0.4). Analysis under RR Hence he rocessor Demand Crierion can be reformulaed as follows: sbf() 8 4 0, dbf ( ) sbf ( ) sbf() dbf()

8 Analysis under RR A simpler sufficien es, can be done by replacing sbf() wih a lower bound, called supply lower-bound funcion slbf(): 0, dbf ( ) slbf ( ) sbf() slbf() dbf() Supply lower-bound funcion A supply bound funcion has he following form: slbf() slbf ( ) max{0, ( )} = bandwidh = service delay Deriving and Given a generic supply funcion sbf(), he bandwidh is he equivalen slope compued for long inervals: sbf ( ) lim sbf() Deriving and While he delay is he highes inersecion wih he ime axis of he line of slope ouching he sbf(): sbf ( ) sup 0 sbf() sbf() sbf() sbf() Example: eriodic Server For a periodic wih budge Q s and period s running a he highes prioriy, we have: Q s s Qs s Q s s For a periodic wih budge Q s and period s running a unknown prioriy, we have: Q s sbf() Example: eriodic Server s Q s 2( s Qs ) s Q s Q s s Q s 2( s Q s ) 8

9 Observaion I is worh comparing he following supply funcions: Supply funcion of a full processor Supply funcion of a fluid pariion wih bandwidh Supply funcion of a real pariion wih bandwidh of a periodic Q, In a periodic wih bandwidh, we have ha: Q 2( Q) 2( ) Observaion The delay is proporional o he period Observaion Noe ha, for a given bandwidh, reducing reduces he delay and improves schedulabiliy, ending o a fluid reservaion, bu Taking overhead ino accoun If is he conex swich overhead, we have: Q smaller periods generaes higher runime overhead smaller Allocaed bandwidh: Effecive bandwidh: eff Q Q 2( ) eff 0 min min 2 min ( ) 2 Effecive bandwidh Hence reducing he period reduces he delay, bu also reduces he effecive bandwidh eff ha can be exploied: eff eff Reservaion inerface Noe ha he (, ) parameers offer an alernaive inerface, which is independen of he implemenaion mechanism (saic pariions or Q- ): QoS Qo / QoS 3 9

Example of sporadic wase Bandwidh allocaion error demanded bandwidh Bandwidh allocaion error Demanded Bandwidh Allocaed Bandwidh allocaed bandwidh avg bandwidh allocaion error Resource is insufficien

10 Example of sporadic wase Bandwidh allocaion error demanded bandwidh Bandwidh allocaion error Demanded Bandwidh Allocaed Bandwidh allocaed bandwidh avg bandwidh allocaion error Resource is insufficien (applicaion is delayed) ime under uilized correcly uilized over uilized ime The applicaion demands less (resource is wased) Resource Reclaiming Budge reclaiming Unused bandwidh in a reservaion can be used o saisfy exra occasional needs in anoher reservaion: R R2 CASH: Capaciy Sharing algorihm When a job finishes and q s >0, he residual budge is pu in a global queue of spare capaciies (he CASH queue), wih a deadline equal o he deadline. A firs uses he capaciy in he CASH queue wih he earlies deadline d q d s, oherwise q s is used. Idle imes consume he capaciy in he CASH queue wih he earlies deadline. Capaciy Sharing algorihm Handling wrong allocaions There are siuaions in which he reservaion error is caused by a wrong bandwidh allocaion: resource needs any reservaion is no appropriae safe bu no efficien efficien bu no enough CASH queue 2 ime 0

Need for adapiviy In hese cases, he only soluion is o design he sysem o be adapive so ha reservaions can be changed based on runime requiremens: resource needs Adapive QoS Managemen Reservaion

assigned reservaion: C i i T i Local olicy Reservaion Real-Time Sysem probes R 2b Shared Resources 2 2a 3 3 Ready queue scheduler CU Tasks are usually no independen: hey share resources!

11 Need for adapiviy In hese cases, he only soluion is o design he sysem o be adapive so ha reservaions can be changed based on runime requiremens: resource needs Adapive QoS Managemen Reservaion parameers can be changed a run ime by a Reservaion Manager: demand Reservaion Manager QoS Qo ime QoS 3 Local adapaion A local adapaion approach is also possible for a ask o comply wih he assigned reservaion: C i i T i Local olicy Reservaion Real-Time Sysem probes R 2b Shared Resources 2 2a 3 3 Ready queue scheduler CU Tasks are usually no independen: hey share resources! Examples: Daa Srucures, eripheral Devices, Common Memory Areas Resource sharing may break isolaion: 2 roblems wih Reservaions normal blocking due o reasource sharing T s wai exra blocking due o budge exhausion deadline miss

12 roblems wih Reservaions Resource sharing may break isolaion: wai The major problem is ha he resource is locked bu no ask is acually using i deadline miss Reacive approaches ossible approaches Le he budge finishes and reac wih a given sraegy: Overrun Wihou payback Wih payback roxy execuion (BWI) 2 T s roacive approaches reven he budge o finish inside a criical secion: Check and wai (SIRA) Check and recharge (BROE) Overrun wihou ayback Overrun wihou ayback When he budge exhauss inside a criical secion, do nohing. Le k be he lengh of he criical secion o be enered. In he wors-case he consumes Q s + k budge unis Isolaion is broken! wai wai k 2 2 Ts Ts The budge goes negaive k Overrun wih ayback When he budge exhauss inside a criical secion, do nohing. ayback a he nex budge replenishmen. roxy Execuion When he budge exhauss inside a criical secion, inheri he bandwidh of anoher Isolaion is broken! wai Noe ha he wors-case bandwidh consumpion does no change 2 2 wai S The budge goes negaive Ts Budge payback 2 wai Ts 2

13 roacive Approaches Le k be he lengh of he criical secion o be enered, and q s be he budge of he a he lock ime; roacive approaches are based on a budge check before locking he resource (i.e., q s k?); The scheduler requires he knowledge of k a run-ime. SIRA Check and wai If (q s k ) hen ener, else wai for he nex replenishmen. Noe ha off-line we mus guaranee ha Q s max{ k }. checking poin wai q s k? NO q s k? YES 2 T s SIRA enalizes he response-ime of he ask wishing o access he resource; oenially insers idle-ime (unused budge). Check and recharge BROE If (q s k ) hen ener, else recharge he budge a full value and proporionally pospone he deadline. Noe ha off-line we mus guaranee ha Q s max{ k }. checking poin wai checking poin wai 2 T s 2 BROE erforms beer han SIRA in mos siuaions; BROE works only wih EDF-scheduled reservaion s. BROE BROE is designed o guaranee a bounded-delay pariion (, ). A budge recharge of X ime unis reflecs as a proporional deadline shif of X/ 2 checking poin wai 2 Ts X/ 3

BROE Noe ha a deadline shif of X/ guaranees ha he never consumes a bandwidh higher han, provided ha Q x D D i j ji Q In fac, since D The deadline incremen D ha guaranees a bandwidh wih a budge (Q +

14 BROE Noe ha a deadline shif of X/ guaranees ha he never consumes a bandwidh higher han, provided ha Q x D D i j ji Q In fac, since D The deadline incremen D ha guaranees a bandwidh wih a budge (Q + x) can be found by imposing: hus: Q x Q x x D D D BROE design goals rovide an efficien soluion o he problem of budge depleion inside a criical secion; Avoid budge overruns; BROE Guaranee a maximum bandwidh consumpion equal o =Q/; Guaranee a maximum service delay = 2( Q) o he served asks (bounded-delay pariion). BROE: bandwidh guaranee When he budge is no enough o complee he criical secion, BROE performs a full budge replenishmen; To guaranee real-ime workload execuing upon a reservaion, he mus ensure a bounded-delay service To conain he bandwidh, he budge replenishmen mus be refleced in a proporional deadline posponemen; Q = 2( Q) Q To bound he service delay, he mus be suspended unil a proper ime. The budge replenishmen and he corresponding deadline posponemen can easily resul in a violaion of he wors-case delay = 2( Q), if no properly handled. Consider a BROE wih Q=4and =8; accesses a resource having =2; 4

15 Consider a BROE wih Q=4and =8; accesses a resource having =2; Consider a BROE wih Q=4and =8; accesses a resource having =2; The wors-case delay = 2( Q) is violaed! The wors case he delay can be poenially unbounded! > 2( Q) = 8 = 8 = 8 How o solve his problem? The idea is o preven he o execue oo earlier wih respec o is deadline, afer a budge replenishmen. For how long he mus be suspended? > 2( Q) = 8 = 8 = 8 This execuion mus be delayed The slack is greaer han (-Q) = 8 = 8 How o compue ime r such ha he bandwidh in [ r, d] is exacly? q ( ) d r r q() d How o compue ime r such ha he bandwidh in [ r, d] is exacly? q ( ) d r r q() d explici suspension d - r r 8 6 explici suspension d - r r d r d 5

16 Noe ha, hanks o he suspension, he wors-case service delay is sill = 2( Q): Thanks o he suspension, he wors-case delay is no violaed. Depending on he execuion sae, BROE decides o suspend he or no explici suspension 2( Q) no suspension is needed 6 < 2( Q) = 8 = 8 = 8 BROE Resource Access olicy BROE: rules Consider a BROE having budge Q and period. The curren budge a ime is denoed as q(). When a ask accesses a resource R k, of lengh k a ime : if (q() k ), ener he criical secion (here is enough budge); else compue a recharging ime r = d q()/ If ( < r ), he is suspended unil r, he budge is replenished o Q and he deadline is posponed o d = r + BROE: consrains The BROE resource access policy can work only wih EDF due o he proporional deadline shif. The suppor for F is currenly an open problem; To perform he budge check, BROE requires he specificaion of he wors-case holding ime for he shared resources; BROE is inrinsically designed for he wors-case: he budge check can cause a scheduling decision ha could be unnecessary. Oherwise he budge is immediaely replenished o Q and he deadline is posponed o d = r + BROE: recap The BROE is a scheduling mechanism providing resource reservaion including he suppor for shared resources Hard reservaion implemening he Hard-CBS algorihm; Resource access proocol ha guaranees boh bandwidh isolaion and bounded-delay o he served applicaion. Resource Holding Time In general, he BROE budge check has o be performed using he Resource Holding Time (RHT) of a shared resource; RHT = budge consumed from he lock of a resource unil is unlock 6

17 Resource Holding Time In general, he BROE budge check has o be performed using he Resource Holding Time (RHT) of a shared resource; Resource Holding Time Inerference from high-prioriy ask has o be accouned in he budge consumed when a resource is locked RHT = budge consumed from he lock of a resource unil is unlock s 2 lock unlock s 2 lock unlock RHT budge Resource Holding Time RHT = Criical Secion WCET + Wors-case Inerference The inerference is caused by he ask preempions Resource Holding Time If resources are accessed in a non-preempive manner, he RHT is equal o he wors-case criical secion lengh; Trade-off: lower hreshold for he budge check, bu greaer ask blocking due o non-preempive blocking non-preempive blocking s 2 lock unlock s 2 lock unlock RHT RHT BROE: example Consider 2 BROE s: (Q =4, =8) (Q 2 =5, 2 = 0) 2 r r 20 6 S r

An off-line multiprocessor real-time scheduling algorithm to reduce static energy consumption

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