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USC Computer Science Technical Reports, no. 870 (2005)
(USC DC Other)
USC Computer Science Technical Reports, no. 870 (2005)
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Synergistic Memory Management and Disk Scheduling in the HYDRA Media Stream Recording System ∗ !"#$ %& ’( )*+ ! " # # # $ % % & ’ M/G/1 & ( % )*’ * % + & , & ( 1–3 $ -*./ 4 &0 + , 1 !" # $ % & % % ∗ !"#$ %& ’& ( ’’ ’ ) *(+ , ’& ’ * ’, ’(’ - + & ’ 2 M/G/1 & 5 6 ( % % #0 + , 1 3!. 4 5 6 7 2# 8 6( % # , 1 4 5 2 9 7 ’ 8 % 1–4,7,8 & : 7,8 / 8 & & % & & ; # & & : < & & . 2 2 0 6( % & 2# )= 3.2 % 3 ! # # & =# > 7 2 & # % # : ’ 2 ’ + -*./ 4 % 0 % & 9 10 % 2 # 2 & # 2 % # # / 2 : ? ? % : *2 % -*./ )*’ % # , Buffers Disks Data Stream Recording System ... ... % + % # 2 & 0 : : * ! n & 9 & @ 9 6( ( 9 % 9 : & Buffers Disk 2 n-1 1 n ... ... Buffers Disk 2 n-1 1 n ... ... ’ ,0 / ’ ,0 / n & $ ’ , ’ 1 n % 0 1 n 1 T R blkReq issue (i) i T R blkReq deadline (i) i D consume(S(i, j)) i i+1 ... j T playReq issue T movieStart T R blkReq finish (i) i T W blkReq issue (i) i T W blkReq deadline (i) i D fill (S(i, j)) i i+1 ... j T recordReq issue T recordStart T W blkReq finish (i) i N available (t) t T curtime T deadline T leadtime T req issue T req svrStart T req svrF in T wait T service !! T service = T req svrF in− T req svrStart T system !! T system = T wait + T service N rs N ws M MR MR(i) i i " MW λ R λ W λ λ = λ R + λ W µ R #$ µ W #$ µ r i i i " #$ µ w i i i " #$ P B % P read missdl (i) i i " B & #$ T diskRot T diskT ransfer T diskSeek h " w, v i,k i ! 0 + ’ , , < 1 ! A M A M R M W A M R (i) i i : / & # 9 & & & ’ M R @ : M R M W M R (i) i ∈ B+ N rs C A N rs N ws ( 4 D & % M W =M N ws i=1 µ w i N rs i=1 µ r i + N ws i=1 µ w i M R (i)=M µ r i N rs i=1 µ r i + N ws i=1 µ w i + µ r i µ w i & i i @ M R M R =M−M W ( 5 $ N ’% $ < : 6( 6( & -*./ ’ & ! & & % & @ /: / !"" # $% $&’$’" () &% (" *&+ ’ &, ( ’##(%" ’ 6 & 6 & 2 & % 2 & & # 0 + & , † & * . 4 + % * ()* $ + ( %, % 6( & ’ N & : ( & Play Request issue time Time movie start time Prefetch (blocks: 1, 2 , ... , N-1) Consume (block 1) Consume (block 2) ... ... Consume (block i) ... ... (T playReq issue ) (T movieStart) T R blkReq issue (N) T R blkReq issue (N +1) T R blkReq issue (N +2) T R blkReq issue (N + i− 1) T R blkReq issue (N + i) " ’ 1 ’% T playReq issue . % N− 1 D T movieStart @ T movieStart & N & N T blkReq issue (N) / ) & : * . 4 , D consume (S(i,j)) , i j i≤ j + ( i = j - + ( i>j - D consume (S(i,j)) = 0 + A T R blkReq finish (i) & i $ T R blkReq finish (i) & † 5 A / 4 1 . ’% - , , $ ∀i≥ N - T R blkReq finish (i)≤ T movieStart + D consume (S(1,i− 1)) + i & T TR blkReq deadline (i) T R blkReq issue (i) A 41 % ) . 4 4 . ’% - - % - ∀i ≥ N i $ T R blkReq issue (i) T TR blkReq deadline (i) - $ / ! T R blkReq issue (i)≥ T movieStart + D consume (S(1,i− N)) ! T TR blkReq deadline (i)≥ T R blkReq issue (i) !# T TR blkReq deadline (i)= T movieStart + D consume (S(1,i− 1)) Record start time Time Fill (block 1) Fill (block 2) ... ... Fill (block i ) Fill (block 3) ... ... (T record start ) T W blkReq issue (1) T W blkReq issue (2) T W blkReq issue (3) T W blkReq issue (i− 1) T W blkReq issue (i) " ! $ ’ 4 / T recordStart * . 4 5 D fill (S(i,j)) i j i≤ j + ( i = j - + ( i>j - D fill (S(i,j)) = 0 + A T W blkReq finish (i) & i % T W blkReq finish (i) & A / 4 7 . ’% - , , $ ∀i≥ 1 - T W blkReq finish (i)≤ T recordStart + D fill (S(1,N + i− 1)) + T TW blkReq deadline i & ! A 47 & % ) . 4 8 . ’% - - - $ T W blkReq issue (i) T TW blkReq deadline (i) i - $ / ! T recordStart + D fill (S(1,i))≤ T W blkReq issue (i) ! T TW blkReq deadline (i)≥ T W blkReq issue (i) !# T TW blkReq deadline (i)= T recordStart + D fill (S(1,i + N− 1)) - ) () ( (&& $ .(" $ $ 0 0 * . 4 E 3 * ()* $ , $ , $ $ + * . 4 F 1 * * , $ + 7 & 2 % 0 0% 0 0% 0 * . 4 + G . ’% - * 3 * 32* $ , , $ / ! T R blkReq issue (i)= T movieStart + D consume (S(1,i− N)) ! T VR blkReq deadline (i)≥ T R blkReq issue (i) !# T VR blkReq deadline (i)≤ T TR blkReq deadline (i)= T movieStart + D consume (S(1,i− 1)) * . 4 + + . ’% - * 3 . * 3.2* $ , % $ / ! T W blkReq issue (i)= T recordStart + D fill (S(1,i)) ! T VW blkReq deadline (i)≥ T W blkReq issue (i) !# T VW blkReq deadline (i)≤ T TW blkReq deadline (i)= T recordStart + D fill (S(1,i + N− 1)) @ % 44 % 48 % , 0% 0% & % & % 44 48 %, ’ T movieStart T recordStart 6( &D % 6( ! , 0 + % , % 1 2% , & * . 4 + , . ’% - . ’: * * .’*2* $ T R blkReq issue (i) , T VR blkReq deadline (i) , i T R blkReq issue (i)= T movieStart + D consume (S(1,i− N)) T VR blkReq deadline (i)= T R blkReq issue (i)+ D consume (S(i− N +1,i− 1)) , * . 4 + 1 . ’% - $ ’: * * $’*2* $ T W blkReq issue (i) , T VW blkReq deadline (i) i T W blkReq issue (i)= T recordStart + D fill (S(1,i)) T VW blkReq deadline (i)= T W blkReq issue (i)+ D fill (S(i+1,i + N− 1)) 1 8 , & A N r available (t) t * . 4 + 4 . ’% - . * /; * .* /2* $ T R blkReq issue (i) , T VR blkReq deadline (i) i T R blkReq issue (i)= T movieStart + D consume (S(1,i− N)) T VR blkReq deadline (i)= T R blkReq issue (i)+ D consume (S(i− N r available (T R blkReq issue (i)),i− 1)) 4 A N w available (t) t * . 4 + 5 . ’% - $ * /; * $* /2* $ T W blkReq issue (i) , T VW blkReq deadline (i) i T W blkReq issue (i)= T recordStart + D fill (S(1,i)) T VW blkReq deadline (i)= T W blkReq issue (i)+ D fill (S(i+1,i + N w available (T W blkReq issue (i)))) 5 , & 2 * . 4 + 7 . ’% - . ’ * .’2* $ T R blkReq issue (i) , T VR blkReq deadline (i) , i T R blkReq issue (i)= T movieStart + D consume (S(1,i− N)) T VR blkReq deadline (i)= T R blkReq issue (i)+ D consume (S(i− 1,i− 1)) 7 * . 4 + 8 . ’% - $ ’ * $’2* $ T W blkReq issue (i) , T VW blkReq deadline (i) i T W blkReq issue (i)= T recordStart + D fill (S(1,i)) T VW blkReq deadline (i)= T W blkReq issue (i)+ D fill (S(i+1,i + 1)) 8 ’((( & ) & . + . . 4 + . ’% - .’*2* , 32* + . + . . 4 , . ’% - $’*2* , 3$ 2* + . + . . 4 1 . ’% - .* /2* , 3$ 2* + . + . . 4 4 . ’% - $* /2* , 3$ 2* + . + . . 4 5 . ’% - .’2* , 3$ 2* + . + . . 4 7 . ’% - $’2* , 3$ 2* + $ /: / ("’% % ("" () ( (&& $ .(" % & & 11 % -*./ : 6( & & ’ -*./ : 6( & + 9 , 9 E * + % H< 2 I < < / : H I H I & 11 ; -*./0 + 6( , & : , % * . 4 + E % % % $ % T system $ + -*./ / T system & / 0 S ... ... ... ... ... ... ... ... 1 i Nrs 1 i Nws & & & ’ 5 & @ & & / +%.&(%1&$ $# 0’(’( $)( $ 6( & $ 2 7 $ 6( & & $ 6( 0 2# ’ 7 % # 1GJ ’ 7 10 2 % 6( & )*’ ‡ F 0 1000 2000 3000 4000 5000 6000 7000 8000 0 5 10 15 20 25 30 Response Time (us) Disk Capacity (GB) Seek Time avg 0 10 20 30 40 50 60 0 5 10 15 20 25 30 Transfer Rate (MB/s) Disk Capacity (GB) read avg. write avg. ’ 70 ’ 70 . ! "#$ % RS WS M/G/1 M/G/1/K λ λR λW λW PB µr µw & ’ & ’( ’ M/G/1/∞/Deadline ’ ) ’( ’ M/G/1/K/Deadline ’ / !1 &+( 0’(’( $)( % & ’ 5 & & ’ 8 % 0 M1 ’ & & % M/G/1/∞/Deadline & M2 ! 1 1 & &0 & & & & . ’ 8 $ . M/G/1/∞/Deadline M/G/1/K/Deadline & $ : @ M2 . ,((( M/G/1/∞/Deadline + ’ & $ & & % & % M/G/1/∞/Deadline & $ & % & P read missdl (i) i : ‡ ! *+,& ) ) - . / - . +G ,((( M/G/1/K/Deadline + ’ $ & $ & . & % & . % . M/G/1/K/Deadline & . # M W $ M W 0 +0 3 K ,0 *, $ -*./ 3 0 + *, 3 3 , ’ 3 *, % . & P B / $&&$ $# , .( %"# $% ) % $22 &! ((%& ’.&$ * . 5 + = ’ &2 , , X G X (z) - ’ X p X (n)= P(X = n) E n=0,1,2,... G X (z) G X (z)= E(z X )= ∞ n=0 p X (n)z n F * . 5 , A % , , X L X (s) + ( X f X (x) - L X (s) L X (s)= E(e −sX )= ∞ x=0 e −sx f X (x)dx +G / (% 3 "4 5 (% 3.( ( "&%2 ’&$ % T service 6( & 0 T diskSeek T diskRot T diskTransfer T service = T diskSeek + T diskRot + T diskTransfer ++ $ A T service L T service (s) T diskSeek T diskRot T diskTransfer A )& ++ L T service (s)=L T diskSeek (s)×L T diskRot (s)×L T diskT ransfer (s) +, ,(’(( % L T diskRot (s) - T diskRot -*./ T diskRot f T diskRot (x)= 1 h x ∈ [1,h] h : h ’ : h=0.004 L+5 ! * 5, L T diskRot (s) L T diskRot (s)= ∞ x=0 e −sx f T diskRot (x)dx = 1− e −sh sh +1 ++ ,(’(( % L T diskT ransfer (s) - T diskTransfer & #2 M!. 2 $ # R Dr A L L & L∈ [0,100] ’ ’ 7 R Dr L R Dr (j)= ⎧ ⎪⎨ ⎪⎩ v 1 0≤ L≤ k 1 (L∈ M + ) v w k w−1 <L≤ k w (L∈ M ) +4 w # v i k i 2# i ∈ [1,w] v 1 >··· >v w 0 <k 1 < ··· <k w = 100 [0,k 1 ] [k 1 ,k 2 ] ··· [k i−1 ,k i ] ··· [k w−1 ,k w ] # + , ··· i ··· w % w v i k i ! L f L (l)= 1 100 l∈ [0,100] B # 6( & T diskTransfer = B (α+(1− α)β)R Dr +5 α β 6 1 )& +5& * 12 f T diskT ransfer (x) )& +7 f T diskT ransfer (x)= w i=1 k i − k i−1 100 δ(x− B (α+(1− α)β)v i ) +7 % * 5, L T diskT ransfer (s) L T diskT ransfer (s)= ∞ x=0 e −sx f T diskT ransfer (x)dx = w i=1 k i − k i−1 100 × e −s B (α+(1−α)β)v i +8 ,(’(#( % L T diskSeek (s) - T diskSeek S G +GG $ : T diskSeek (j) S 13 T diskSeek = a 1 + b 1 √ S 0≤ S≤ r a 2 + b 2 S r D & 5 M/G/1 & 0 . / 0 5 + "%4 %4 $ & M/G/1 & M/G/1/∞/Deadline & ’ 5+ "% 4 %4 $ 5 G N ReqSys R (z) G N ReqSys R (z)=L T service (λ R − λ R z) (1− ρ R )(1− z) L T service (λ R − λ R z)− z ,G ρ R # ρ R = λ R µ R ,+ A µ T service ronly & & & µ R µ R = α µ T service ronly ,, @ µ T service ronly 54 α=1 L+5 β=0.6934 /7 (% 3 P B 8 &+( % $22 &! $# $.4 # $% (.$%) &% (" . M/G/1/K/Deadline 6=6+6> 14 & M W $ # A π (∞) i N ReqSys W i M/G/1/∞/Deadline . ’ π (∞) i π (∞) i = p N ReqSys W (i)= P(N ReqSys W = i) ,1 @ : =’ N ReqSys W M/G/1/∞/Deadline . G ∞ N ReqSys W (z) G ∞ N ReqSys W (z)=L T service (λ W − λ W z) (1− ρ W )(1− z) L T service (λ W − λ W z)− z ,4 ρ W ρ W = λ W µ W ,5 µ T service wonly & & & µ W µ W = 1− α µ T service wonly ,7 @ µ T service wonly 54 α=0 L+5 β=0.6934 / G ∞ N ReqSys R (z) π (∞) i @ : 6=6+6> 14 ’ N ReqSys W 0 p N ReqSys W (i)= π (∞) i 1− q k ρ W i N 0 1 2 K− 1 ,8 +1 p N ReqSys W (K)= (1− ρ W )q k 1− q k ρ W ,E q k & q k = ∞ i=K π (∞) i =1− K−1 i=0 π (∞) i ,F @ P B & M W P B = p N ReqSys W (M W ) 1G /9 (% 3 &+( % $22 &! &+& "4 () (6’("& "" &" () ( @ : & P read missdl (i) i : @ & & i : % : i ,(.(( Request issue time Current time Request deadline Request service start time Request service finish time Time Request service time Lead time Request wait time Request system time (Treq issue) (T0) (T leadtime ) (T deadline % (Treq svrStart)(Treq svrFin) (Tservice) (Twait) (Tsystem) 01 ’ ’ E 6( & T req issue & T req svrFin & @ & T system T wait + T service ( & * . 5 1 A % & T leadtime T 0 - T 0 ()* $+ T leadtime = T deadline − T 0 + A % . * + @ 5 $ ’ : ’ E T leadtime & T 0 A T req issue T deadline T system & i ’ E P read missdl (i)= P [ & i ] = P [T req issue + T system >T deadline ] 1+ A T leadtime arrival T leadtime & & ; % ’ E T deadline = T req issue + T leadtime arrival % )& 1+ P read missdl (i)= P [T system >T leadtime arrival ] 1, . T leadtime arrival i @ : T system & i # & 6,15,16 +4 ,(.(( + ! & 2 & A λ Q & T 0 A G(x) , *’ ’ M/G/1 & )*’ & T 0 λ Q G(x) & & 0 f X (x)= λ Q (1− G(x)) L(Q)≤ x≤∞ 0 x<L(Q) 11 L(Q) D : T 0 λ Q ∞ L(Q) (1− G(x))dx=1 14 ,(.(#( / $ )& 11 *’ F X (t)= t −∞ f X (x)dx = λ Q t L(Q) (1− G(x))dx L(Q)≤ t≤∞ 0 x<L(Q) 15 . T leadtime arrival T leadtime & REQ A & ; @ & A N req before (t) & REQ A t t & Q t / ’ E REQ A t T leadtime arrival − t + T req issue % )& 15 N req before (t)= Q t × λ Q t T leadtime arrival −t+T req issue L(Q t) (1− G(x))dx = λ T leadtime arrival −t+T req issue L(Q t) (1− G(x))dx 17 A Y REQ A )& 17 & REQ A T req issue+ +Y @ Y = T wait T req issue +Y T req svrStart REQ A ! T req svrStart & REQ A % )& 17 N req before (T req issue + T wait )= λ T leadtime arrival −T wait L(Q t) (1− G(x))dx=0 18 λ> 0 G(x) 1 T leadtime arrival − T wait = L(Q) ⇐⇒ T wait = T leadtime arrival − L(Q) 1E / # T leadtime arrival & ! T system = T wait + T service T system = T leadtime arrival − L(Q)+ T service 1F T system )& 1, P read missdl (i)= P T overall leadtime arrival − L(Q)+ T service >T stream i leadtime arrival 4G @ )& 1, T leadtime arrival & i $ )& 1F T leadtime arrival & % T stream i leadtime arrival T overall leadtime arrival . 2 N ReqSys R 55 Q / L(Q) 54 T service / T stream i leadtime arrival T overall leadtime arrival % )& 4G P read missdl (i) +5 7 - 7 :,(%(& (&’, Disk Access Scheduler λ rs n ws n Movie Trace Library e.g. "Twister", "Saving Private Ryan" "Charlie’s Angels" Measure & Report WorkLoad Generator Disk e.g. Seagate Cheetah X15 ... ... ... ... 2- $ 2 ’ F % $ A = & 2 1 λ =5 % & )*’ * & % A % & * * / % O . % $ A = 0 2 1 λ n rs n ws ( L+5 %11785,A * # B disk +G ! % , # : ’ ( ) * #’+,-. / (-0 / 123425 $ 6 47 ! ! 857541!3 )9 ’ :* #’+,-. / (-0 / ;4;.43 $ 6 47 ! ! 812;50!1 )(< /* #’+,-8 9 / 8328.2 $ 6 ;7 ! ! 41755!8 # 9 ( =84 # 9001;4.6( # - 1 λ 4 & B disk 8!7 #$ 9 ’ 3 - 7 % ("" $,%"$ 2(&*(( ; ) ’ +G : 0 % % 2% % 6 6 41 58 * 3* H% I 58 2 29 30 ) & T system ( 2 30 ’ +G % % 2% $ % T system 2 30 ’ +G % % ( +7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 5 10 15 20 25 30 35 40 45 50 Relative Frequency Request System Time (second) A Client (30 buffer) A Client (2 buffer) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 5 10 15 20 25 30 35 40 45 50 Relative Frequency Request System Time (second) A Client (30 buffer) A Client (2 buffer) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 5 10 15 20 25 Relative Frequency Request System Time (second) A Client (30 buffer) A Client (2 buffer) ’ +G0 % * % ’ +G0 * * % ’ +G0 ’ * 2% Tsystem ’ ) 2 ) 30 - 58 ) , 4, 5 5 * 29 % 2 ) 29 30 - 6 %) ) % 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.2 0.4 0.6 0.8 1 1.2 Relative Frequency Request System Time (second) A Client (10 buffer) A Client (2 buffer) 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.2 0.4 0.6 0.8 1 1.2 Relative Frequency Request System Time (second) A Client (10 buffer) A Client (2 buffer) 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Relative Frequency Request System Time (second) A Client (10 buffer) A Client (2 buffer) ’ ++0 % * % ’ ++0 * * % ’ ++0 ’ * 2% Tsystem ’ ) 2 ) 10 - 220 ) 4, 7( 5 * 110 % 2 ) 110 10 - 6 ) ) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 10 20 30 40 50 60 70 80 Relative Frequency Request System Time (second) A Client (30 buffer) A Client (2 buffer) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 10 20 30 40 50 60 Relative Frequency Request System Time (second) A Client (30 buffer) A Client (2 buffer) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 5 10 15 20 25 30 Relative Frequency Request System Time (second) A Client (30 buffer) A Client (2 buffer) ’ +,0 % * % ’ +,0 * * % ’ +,0 ’ * 2% Tsystem ’ ) 2 ) 30 - 54 ) , 4, 7! 3 &5 * 27 % 2 ) 27 30 - 6 ) ) 2% T system % % % 2% @ # % 2% % : 2 ’ : ’ ++ ’ +, 3* HD /I * 3* H .I 2% +8 0 10 20 30 40 50 Client Index (50%) 0 5 10 15 20 25 30 Buffer Allocation Scheme Index 0 0.2 0.4 0.6 0.8 1 Missed Deadline Probability 0 10 20 30 40 50 Client Index (50%) 0 5 10 15 20 25 30 Buffer Allocation Scheme Index 0 0.2 0.4 0.6 0.8 1 Missed Deadline Probability 0 10 20 30 40 50 Client Index (50%) 0 5 10 15 20 25 30 Buffer Allocation Scheme Index 0 0.2 0.4 0.6 0.8 1 Missed Deadline Probability ’ +10 % * % ’ +10 * * % ’ +10 ’ * 2% ’ - 58 , 4, 7 5 0 10 20 30 40 50 Client Index (50%) 0 5 10 15 20 25 30 Buffer Allocation Scheme Index 0 0.2 0.4 0.6 0.8 1 Missed Deadline Probability 0 10 20 30 40 50 Client Index (50%) 0 5 10 15 20 25 30 Buffer Allocation Scheme Index 0 0.2 0.4 0.6 0.8 1 Missed Deadline Probability 0 10 20 30 40 50 Client Index (50%) 0 5 10 15 20 25 30 Buffer Allocation Scheme Index 0 0.2 0.4 0.6 0.8 1 Missed Deadline Probability ’ +40 % * % ’ +40 * * % ’ +40 ’ * 2% ’ 1 27 2 ) 27 ) 2 30 - - 54 , 4, 7! 3 &5 @ : % % 2% & # : 58 * 3* H% I 29 : ,F 58 2 % 29 : G ,E # : 2 30 @ # : : 3 1 ( ! ’ +1 : & 58 % : ’ +1 % : & 2% ’ +1 : & % % : % 2% % 2% & % % & ’ 2% 9 : * 3* I .I ’ +4 7 3 ’&$ $# ’##(% +% .+(( # $% (.$%) &% (" . -*./ 3 3 3 3 & -*./ % $ : 0 + +E 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 60 80 100 120 140 160 180 200 220 240 260 280 Blocking Probability for Recording Streams Memory Capacity (MB) with 38 DVD Ryan Streams Partitioned Buffer Scheme (PBS) Shared Buffer Scheme (SBS) )9 ’ :* ← 03 57 → 0 0.005 0.01 0.015 0.02 0.025 0.03 0 100 200 300 400 500 600 700 800 900 1000 Blocking Probability for Recording Streams Memory Capacity (MB) with 40 DVD Ryan Streams Partitioned Buffer Scheme (PBS) Shared Buffer Scheme (SBS) 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 50 100 150 200 250 300 350 400 450 500 Blocking Probability for Recording Streams Memory Capacity (MB) with 41 DVD Twister Streams Partitioned Buffer Scheme (PBS) Shared Buffer Scheme (SBS) ) * ← 58 50 → 0 0.005 0.01 0.015 0.02 0.025 0 100 200 300 400 500 600 700 800 900 1000 Blocking Probability for Recording Streams Memory Capacity (MB) with 43 DVD Twister Streams Partitioned Buffer Scheme (PBS) Shared Buffer Scheme (SBS) 2 ) ) ) !/! 3/! 3 3 , 1 @ : ’ * 2% 2% ’ +5 : ’ +5 * 3* H .I # ! ! @ ! ! ! ’ : ’ +5 38 H .I ! ! 0.056% 76 ! : 0.128% 190 ! : * 3* H% I ’ +5 41 43 ! : 0 : ! ! % ! : : ! $ ! ! % ! : $ : $ # ! ! @ !D +F ! % & / % 5 3 3 -*./ : 6( & 7 +$$" N # $% ##(% (& () !,( *&+ ’##(% .+(( : 9 & & @ L+5 : 2% 0 10 20 30 40 50 Number of Clients 0 5 10 15 20 25 30 35 40 Number of Buffers 0 0.2 0.4 0.6 0.8 1 Missed Deadline Probability 0 10 20 30 40 50 Number of Clients 0 5 10 15 20 25 30 35 40 Number of Buffers 0 0.2 0.4 0.6 0.8 1 Missed Deadline Probability 0 50 100 150 200 Number of Clients 0 5 10 15 20 25 30 35 40 Number of Buffers 0 0.2 0.4 0.6 0.8 1 Missed Deadline Probability ’ +70 * 3* H .I ’ +70 * 3* H% I ’ +70 3* HD /I ’ , 4, 7! 3 &5 4, 7( 5 ’ +7 : & : 0 * 3* H .I * 3* H% I 3* HD /I ’ +7 ’ +7 & 0 & 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 10 20 30 40 50 60 Request Missed Deadline Probability Number of Clients (Ryan,Ronly,2Buf) Missed Deadline Probability System Utilization Factor (rho) Fraction of Disk Busy Time 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 10 20 30 40 50 60 70 Request Missed Deadline Probability Number of Clients (Twister,Ronly,2Buf) Missed Deadline Probability System Utilization Factor (rho) Fraction of Disk Busy Time 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 50 100 150 200 250 Request Missed Deadline Probability Number of Clients (VCD,Ronly,2Buf) Missed Deadline Probability System Utilization Factor (rho) Fraction of Disk Busy Time ’ +80 * 3* H .I ’ +80 * 3* H% I ’ +80 3* HD /I 8) ) ’ , 4, 7! 3 &5 4, 7( 5 @ +7 : # 1 % & ,G ’ +8 : # & / : % # # 1 % # % 54 59 222 * 3* I .I I% I 3* Charlie sAngeles ’ +8 / ’ +7 27 & * 3* I .I & 24 & * 3* I% I $ 3* ID /I 2 % : 9 & & 7/ !,$&+("" ("& $# "4 5 (6’("& %% 3 % $.("" % 6( & : χ 2 2& =22’ % 17 2 0 H 0 % 6( & : H a % 6( & : χ 2 0/0* " ’ 2& 22 k χ 2 = k i=1 (O i − E i ) 2 E i 4+ O i & i E i : & i E i = N(e −λY l − e −λY u )) 4, N Y u Y l λ 6( & ! χ 2 : ’ +E : )& 4, : ’ +E 200 * 3* H .I ’ +E 300 3* HD /I % ’ +E 200 * 3* H% I ’ ’ +E : : 200 +61 * 3* H% I +61 * 3* H .I 3* ID /I : : & & / 2& = GF5 % : χ 2 * 3* H% I * 3* H .I HD /I % : ’ +F / 2 : ,+ 0 100 200 300 400 500 600 700 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Frequency of Samples Interarrival Time (sec) Expected Value Measured Value 0 50 100 150 200 250 300 350 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Frequency of Samples Interarrival Time (sec) Expected Value Measured Value ’ +E0 200 * 3* I .I ’ +E0 300 3* 0 100 200 300 400 500 600 700 800 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Frequency of Samples Interarrival Time (sec) Expected Value Measured Value 0 50 100 150 200 250 300 350 400 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Frequency of Samples Interarrival Time (sec) Expected Value Measured Value ’ +E0 200 * 3* H% I ’ +E0 200 : 2- - 77 - (%<.&$ $# 3!. 2 & : -*./ $ : 2 ’ ,G T leadtime & & 100 ’ ,G * 3* H .I * 3* H% I 3* HD /I ) 5 H L *’I H A % I 2 3 % 149 : H .I 99 H% I # 1879 3* @ $ : & 25 50 75 & ’ ,+ : * 3* I% I @ ’ ,+ & : ’ ,+ / : ,, 0 200 400 600 800 1000 1200 1400 100 200 300 400 500 600 700 Chi-Square Statistics Number of concurrent streams VCD Saving Private Ryan Twister χ 2 ) , 4, 7! 3 &5) , 4, 7 5) 4, 7( 5 0 0.2 0.4 0.6 0.8 1 -2 -1 0 1 2 3 4 5 6 7 Fraction of request with lead time t Lead Time t,deadline=Ryan(2 buffer),cliNum=54,snapshots(149),QLen(100) LT PDF LT CDF gX pdf predicted gX CDF avg LT snapshot 0 0.2 0.4 0.6 0.8 1 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 Fraction of request with lead time t Lead Time t,deadline=Twister(2 buffer),cliNum=55,snapshots(99),QLen(100) LT PDF LT CDF gX pdf predicted gX CDF avg LT snapshot 0 0.2 0.4 0.6 0.8 1 2.5 3 3.5 4 4.5 5 5.5 6 6.5 Fraction of request with lead time t Lead Time t,deadline=VCD(2 buffer),cliNum=222,snapshots(1879),QLen(100) LT PDF LT CDF gX pdf predicted gX CDF avg LT snapshot ’ ,G0 * 3* H.I ’ ,G0 * 3* H% I ’ ,G0 3* H /I 01 ’ T LeadTime ) , 4, 7! 3 &5 54 %) , 4, 7 5 55 %) 4, 7( 5 222 % ’ 100 &D & 2 & & -*./ 9 $ 2% & M/G/1 & 2 ( : + . M > ’ H / I % 77 1 6 ( 6 1 6 6 899: ! @ ,2E ,GG1 , . . M *; ) 2 = H’2= * I (;;; ,4 55E?57F * ,GG1 ,1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 200 400 600 800 1000 1200 PDF of Wait Queue length Wait Queue length, deadline=Twister(15 buffer),cliNum=44 44 streams ) * : ← → 0 0.2 0.4 0.6 0.8 1 -15 -10 -5 0 5 10 15 20 25 30 Fraction of request with lead time t Lead Time t(second),deadline=Twister(15 buffer),cliNum=44 predicted WQ(70, %25 percentile) measured WQ(70, %25 percentile) predicted WQ(819, %50 percentile) measured WQ(819, %50 percentile) predicted WQ(989, %75 percentile) measured WQ(989, %75 percentile) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 200 400 600 800 1000 1200 1400 1600 PDF of Wait Queue length Wait Queue length, deadline=Twister(15 buffer),cliNum=59 59 streams ) * ’ ← → 0 0.2 0.4 0.6 0.8 1 -15 -10 -5 0 5 10 15 20 25 30 Fraction of request with lead time t Lead Time t(second),deadline=Twister(15 buffer),cliNum=59 predicted WQ(86, %25 percentile) measured WQ(86, %25 percentile) predicted WQ(1066, %50 percentile) measured WQ(1066, %50 percentile) predicted WQ(1312, %75 percentile) measured WQ(1312, %75 percentile) ’ 01 ’ T LeadTime - 42 - 59 , 4, 7 5 ! ’ 9 :#) ’ 1 > ’ . M H A * . I < ( ; ( (;( 899=- % / +42+8 ,GG4 4 . M > ’ $ 2 > H* I > ( ; ( (;( 899:- 1 % 2 / ,12,7 ,GG1 5 A > - 0 (/ P $ O !@0 G248+24F++G2+ 4+8 +F85 7 ! * P A# H.2% 9 % )2*2’ 9 * I 1 1 , 11,?18E ,GG+ 8 =# > H* 2" ) I 4 6% 1 +G+?+,8 ,GGG E $ = / > =# H* 3 ) I (;;; 4 ; # 7 F11?F5G * ,GG+ F ! =# . # L P H I 1 6 (&6* ( 6 +FF4 +G . # P ! H.(0 / .2 (; I 1 6 ;, , , +FF8 ++ ! / 2# A H( ’ 9 I 1, 1 #11 F+F?F17 ,GG4 +, P $ $ 1 2 " . @ P G845E ,GG, +1 . P $ H / I (;;; . 1 +8?,E +FF4 +4 P 6 / K , K !@0 G+,4E847,, ( ,F ,GG, ,4 +5 P A# H.2% 9 % I (;;; % 7??< +E7?+F5 @ - +FF7 +7 . ( ! @ P * 3 P ) > # ’ H.2% 9 %0 / % / / I P ,GGG +8 . 3 ) / % ( 8G4 7 ,GG+ ,5 = % $$# $# ( - ’(# . ’% - , , $ % ∀i≥ N - T R blkReq finish (i)≤ T movieStart + D consume (S(1,i− 1)) + $ ⇒ & 0 ∀i<N ’% N− 1 1 2 N− 1 T movieStart % T R blkReq finish (i)≤ T movieStart 41 / * 4, ∀i≥ 1 D consume (S(1,i−1))≥ 0 % )& 41 ∀i<N T R blkReq finish (i)≤ T movieStart + D consume (S(1,i− 1)) 0 ∀i ≥ N & i T R blkReq finish (i) $ i T movieStart + D consume (S(1,i−1)) % T R blkReq finish (i)≤ T movieStart + D consume (S(1,i− 1)) ! + ⇐0 $ ∀i T R blkReq finish (i) ≤ T movieStart + D consume (S(1,i− 1)) t : ∀i≥ 1 t i = T movieStart +D consume (S(1,i−1)) : i § 0 ∀i<N ’% N−1 1 2 N−1 T movieStart % t i = T movieStart + D consume (S(1,i− 1)) i≤ N 0 ∀i≥ N + i = N - t N = T movieStart + D consume (S(1,N− 1)) + - t N - 1 -2 - +++ N− 1 , + 1 T R blkReq finish (N)≤ T movieStart + D consume (S(1,N− 1)) = t N - - N , + - ∀i,i≤ k,k ≥ N - + - ∀t i ≤ t k ,k ≥ N - i , t i - - k , t k + t k+1 = T movieStart + D consume (S(1,k)) - T R blkReq finish (k+1)≤ T movieStart + D consume (S(1,k)) = t k+1 - - k+1 , t k+1 + - , , (( + - ( (( - , , + % $$# $# +($% ( " ’(’( $ @2 2 ∀i ≥ N i & T R blkReq issue (i) T TR blkReq deadline (i) &0 ! T R blkReq issue (i)≥ T movieStart + D consume (S(1,i− N)) ! T TR blkReq deadline (i)≥ T R blkReq issue (i) !# T TR blkReq deadline (i)= T movieStart + D consume (S(1,i− 1)) § 01) ti = TmovieStart + Dconsume(S(1,i−1)) ) i ) ) - - Dconsume(S(i, i)) ) ,7 !( i = N . @2 - N - N − 1 T movieStart + - T R blkReq issue (N) - % $ N T movieStart + 3 =+8- D consume (S(1,0)) = 0 + - i = N - T R blkReq issue (N)≥ T movieStart + D consume (S(1,N− N)) + i > N - T R blkReq issue (i) - $ i - i− N , + - T R blkReq issue (i)≥ T movieStart + D consume (S(1,i− N)) + !( $ , , $ + # !#( % - $ ! $ 5 =+:+ 3 1 2 3 - , , + % $$# $# ( 7 - ’(1 $ @2 & 2 ∀i≥ 1 T W blkReq finish (i)≤ T recordStart + D fill (S(1,N + i− 1)) . , , + ⇒ + ( $ - , + . @2 - N + - $- , + 3 ! $ N− 1 ¶ + - , $ N− 1 + - T W blkReq finish (i)≤ T W blkReq issue (i+1)+ D fill (S(1,N + i− 1)) 44 $ + - / T W blkReq issue (i)≥ T recordStart + D fill (S(1,i)) 45 3 ;$ == =>- T W blkReq finish (i)≤ T recordStart + D fill (S(1,N + i− 1)) 47 ¶ 1 ,8 ⇐ + . , ∀i - T W blkReq finish (i)≤ T recordStart + D fill (S(1,N + i− 1)) - + 1 t≥ T recordStart - ! + . - + +- t = T recordStart + D fill (S(1,i)) - ! + ’ $,- t ≥ T recordStart t = T recordStart + D fill (S(1,i)) - , + ( - + , - , #+ # ∀i - i≥ 1 - t = T recordStart + D fill (S(1,i)) - ! , + . , # i + 2$ 3 i≤ N i≤ N− 1 @2 - + +- N - i≤ N− 1 - + +- t≤ T recordStart + D fill (S(1,N− 1)) - N , + - - ! , + i = N 1 - T W blkReq finish (1)≤ T recordStart + D fill (S(1,N)) 48 - i = N - t = T recordStart + D fill (S(1,N)) - 1 + 1 - 1 + ( - ! , + 2$ 3 i>N ∀i - i≤ k k ≤ N - # + - i = k - t = T recordStart + D fill (S(1,k)) t k + 1 - 2 - +++ k− N +1 + i = k+1 - t k+1 - , T W blkReq finish (k− N +2)≤ T recordStart + D fill (S(1,k + 1)) 4E - k− N +2 t k+1 + 1 - , + - # i = k+1 + 3 1 2 - , , + % $$# $# +($% ( 9 " ’(. $ @2 & T W blkReq issue (i) T TW blkReq deadline (i) i &0 ! T recordStart + D fill (S(1,i))≤ T W blkReq issue (i) ! T TW blkReq deadline (i)≥ T W blkReq issue (i) !# T TW blkReq deadline (i)= T recordStart + D fill (S(1,i + N− 1)) !( $ , + - $ i - T W blkReq issue (i) T recordStart + D fill (S(1,i))≤ T W blkReq issue (i) 4F ,E !( $ , , $ + # !#( % - @2 - $ ! $ $ 5 =+<+ 3 1 2 3 - , , + / % $$# $# % $,$"&$ ’( $ @2 2% 0% , - =+79+ 1 =+78- , + ’ !- , + 3 =+78- , T R blkReq issue (i)= T movieStart + D consume (S(1,i− N)) 5G T VR blkReq deadline (i)= T R blkReq issue (i)+ D consume (S(i− N +1,i− 1)) 5+ - T VR blkReq deadline (i)= T movieStart + D consume (S(1,i− N)) + D consume (S(i− N +1,i− 1)) = T movieStart + D consume (S(1,i− 1)) = T TR blkReq deadline (i) =+= 5, 7 % $$# $# % $,$"&$ ’( $ @2 .2% 0. % , - =+77+ 1 =+77- , + ’ !- , + 3 =+7:- , T W blkReq issue (i)= T recordStart + D fill (S(1,i)) 51 T VW blkReq deadline (i)= T W blkReq issue (i)+ D fill (S(i+1,i + N− 1)) 54 - T VW blkReq deadline (i)= T recordStart + D fill (S(1,i)) + D fill (S(i+1,i + N− 1)) = T recordStart + D fill (S(1,i + N− 1)) = T TW blkReq deadline (i) =+@ 55 9 % $$# $# % $,$"&$ ,F ’(# $ @2 1% 0. % .* /2* .’*2* ! , + 3 =+7=- T VR blkReq deadline (i)= T R blkReq issue (i)+ D consume (S(i− N r available (T R blkReq issue (i)),i− 1)) 57 . @2 - , + - N r available (T R blkReq issue (i))<N− 1 58 - T VR blkReq deadline (i)<T R blkReq issue (i)+ D consume (S(i− (N− 1)),i− 1)) 5E 3 =+7- , , + > % $$# $# % $,$"&$ ’(’ $ @2 . 1% 0. % $* /2* $’*2* ! , + 3 =+7>- T VW blkReq deadline (i)= T W blkReq issue (i)+ D fill (S(i+1,i + N w available (T W blkReq issue (i)))) 5F . @2 - + - N w available (T W blkReq issue (i))≤ N− 1 7G - T VW blkReq deadline (i)≤ T W blkReq issue (i)+ D fill (S(i+1,i + N− 1)) 7+ 3 =+8- , , + ? % $$# $# % $,$"&$ / ’(, $ @2 2% 0. % .’2* .’*2* ! , + 3 =+7=- T VR blkReq deadline (i)= T R blkReq issue (i)+ D consume (S(i− 1,i− 1)) 7, . @2 - 2 - + +- N ≥ 2 + - , D consume (S(i− (N− 1),i− 1)≥ D consume (S(i− 1,i− 1)) 71 - T VR blkReq deadline (i)≤ T R blkReq issue (i)+ D consume (S(i− (N− 1)),i− 1)) 74 3 =+7- , , + 1G @ % $$# $# % $,$"&$ 7 ’(1 $ @2 .2% 0. % $’2* $’*2* ! , + 3 =+7@- T VW blkReq deadline (i)= T W blkReq issue (i)+ D fill (S(i+1,i + 2)) 75 . @2 - 2 - + +- N ≥ 2 + - , D fill (S(i+1,i + N− 1)≥ D fill (S(i+1,i + 1)) 77 - T VW blkReq deadline (i)≤ T W blkReq issue (i)+ D fill (S(i+1,i + N− 1)) 78 3 =+8- , , + 1+
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Description
Kun Fu, Roger Zimmermann. "Synergistic memory management and disk scheduling in the HYDRA media stream recording system." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 870 (2005).
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Zimmermann, Roger
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USC Computer Science Technical Reports, no. 870 (2005)
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Synergistic memory management and disk scheduling in the HYDRA media stream recording system (
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