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Paris-DauphineX X  T   H  0޽h ? 3ff3̙y___PPT10Y+D=' = @B + 0 *"(     x0e0e?Rectangle 2  `   N Background     `   x40e0e?Rectangle 3 `F  Archival files Must be kept a long time At lowest possible cost Emphasis on Providing highest reliability at lowest cost Update speed is less important Focus on multi-dimensional RAID arrays Highly reliable Very space-efficient 1  L ' % 1 L'%    H  0޽h ? 3ff3̙y___PPT10Y+D=' = @B +" 0 (      x0e0e?Rectangle 2  `   `A two-dimensional RAID array     x   C *Group 17"f B  \Z>??Line 4P @ B  \Z>??Line 5@ B  V>??Line 6@Y pQ2  bP??Oval 78F>6___PPT9 iD11(( " d   Q2   b< ??Oval 8 0F>6___PPT9 iD12(( " d   R2   dT??Oval 10  PF>6___PPT9 hP1(( " d   B   X>??Line 11@ @S2   d??Oval 12w0 F>6___PPT9 iD21(( " d   S2   dH??Oval 13 u % F>6___PPT9 iD22(( " d   R2  d8??Oval 15 p F>6___PPT9 hP2(( " d   R2  dA??Oval 21, w F>6___PPT9 hQ1(( " d   R2  dlK??Oval 22(, F>6___PPT9 hQ2(( " d     `TU??Text Box 18"@;  F>6___PPT9 5Four parity disks Four parity stripes Four data disks"6 " d6 6  H  0޽h ? 3ff3̙y___PPT10Y+D=' = @B +" 0 @(     x[0e0e?Rectangle 2  `   RA better array    B  ^Z>??Line 10  B @ \Z>??Line 4 b B  \Z>??Line 63 J2  dN??Oval 11 RF>6___PPT9 hP1(( " d   B  ^Z>??Line 12t K2  dr??Oval 14~ . | F>6___PPT9 iD13(( " d   K2   dP|??Oval 15 M F>6___PPT9 iD14(( " d   K2   d|??Oval 17Rk F>6___PPT9 iD34(( " d   K2   dL??Oval 18DF>6___PPT9 iD23(( " d   K2   d??Oval 193  F>6___PPT9 iD24(( " d   K2   d??Oval 20w 3 'F>6___PPT9 iD12(( " d   J2  dЮ??Oval 24 rF>6___PPT9 hP2(( " d   J2  d??Oval 25QjF>6___PPT9 hP3(( " d   J2  d4??Oval 26 b F>6___PPT9 hP4(( " d     `??Text Box 23"@ DF>6___PPT9 4Four parity disks Four parity stripes Six data disks"5 " d5 5  H  0޽h ? 3ff3̙y___PPT10Y+D=' = @B +" 0 g(  !   x0e0e?Rectangle 2  `   UCan we do better?       x0e0e?Rectangle 3 `p  :Use a three-dimensional organization Replace parity stripes by parity planes Each parity plane will contain one parity disk Place data disks will at the intersections of three parity planes L% ( <r %r   H  0޽h ? 3ff3̙y___PPT10Y+D=' = @B +"p 0  (   n   x80e0e?Rectangle 3   Parity planes , ,  and  Four data disks ,,  and A A                          R  l??Rectangle 5"@F>6___PPT9 Z$ " d   R  l??Rectangle 7"@F>6___PPT9 Z$ " d      Z'/#A  ?Object 6      x 0e0e?Rectangle 2      KExample    H  0޽h ? 3ff3̙y___PPT10Y+D=' = @B +"  0    $- (  $ $  xX*0e0e?Rectangle 3'  With np parity disks, we can protect data disks against all triple failures 2-D organizations with same number of parity disks could only protect data disks and only against all double failures O 0 <  k&       $  x\;0e0e?Rectangle 2  `   N Advantages     R $ lE??Rectangle 5"@F>6___PPT9 Z$ " d   ~ $ BA  ?Object 4  R $ lO??Rectangle 7"@F>6___PPT9 Z$ " d   ~ $ BA  ?Object 6,   f $0 s A ?5%8c8c    ?Object 12"~(  H  $ 0޽h ? 3ff3̙y___PPT10Y+D=' = @B +" , 0 C;0((  (/ (  xtW0e0e?Rectangle 4  `   cMore data disks per parity disk     d (0 s @*A ?5%8c8c    ?Object 5"$(  H ( 0޽h ? 3ff3̙y___PPT10Y+D=' = @B +"- 0 D<@,(  ,0 ,  xxa0e0e?Rectangle 2  `   d More protection at a lower cost ! ! !  d ,0 s @*A ?5%8c8c    ?Object 3"L(  H , 0޽h ? 3ff3̙y___PPT10Y+D=' = @B +" 0 0[(  0& 0  x(j0e0e?Rectangle 2  `   ZDrawback of 3-D arrays     0  xPm0e0e?Rectangle 3 `p  )More complex update procedure Each time we modify a data block, we have to update three parity blocks Not an issue for data that are rarely updated Archives, mediaV H . < H.   H 0 0޽h ? 3ff3̙y___PPT10Y+D=' = @B +"= 0 TLP4(  4+ 4  xz0e0e?Rectangle 2  `   _Handling quadruple failures     4  x 0e0e?Rectangle 3 `p  {Only a few specific quadruple failures are fatal We show that array can tolerate fraction of all quadruple failures "1 K <| |  R 4 l??Rectangle 5"@F>6___PPT9 Z$ " d   ~ 4 BA ?Object 4c*-  H 4 0޽h ? 3ff3̙y___PPT10Y+D=' = @B +"D 0 [S <(  < <  x}0e0e?Rectangle 2  `   TSelected results     <  x<0e0e?Rectangle 3 p  ?Compared the MTTDL of a 3-D array with 20 data disks and 6 parity disks with those of Two RAID arrays with 10 data disks and 3 parity disks each 60 disks using three-way mirroring to store the equivalent content of 20 data disks A 2-D array with 21 data disks and 7 parity disks under standard stochastic assumptions hV  () (VJd @  H < 0޽h ? 3ff3̙y___PPT10Y+D=' = @B +" 0 5-@D(  D D  x0e0e?Rectangle 2  `   VSystem Parameters     o D  xt0e0e?Rectangle 3 `p  Disk mean time to fail was assumed to be 100,000 hours (11 years and 5 months) Corresponds to a failure rate l of 8 to 9 percent per year High end of failure rates observed by Schroeder and Gibson and Pinheiro et al. Disk repair times varied between 12 hours and one weekVO 2 7 2OAk7&    ?  H D 0޽h ? 3ff3̙y___PPT10Y+D=' = @B +" 0 P2(  P P  x40e0e?Rectangle 2  `   TComparing MTTDLs    L P fĪ??Rectangle 3"@F>6___PPT9 Z$ " d    P N'A $??Object 4 $H P 0޽h ? 3ff3̙y___PPT10Y+D=' = @B +" 0 PT(  T T  xh0e0e?Rectangle 2  `   N Conclusion     3 T  xć0e0e?Rectangle 3 `p  g3-D RAID arrays require Fewer parity disks than comparable RAID array organizations to achieve Higher MTTDLs Sole limitation is cost of updates  <    $   * $    H T 0޽h ? 3ff3̙y___PPT10Y+D=' = @B +" 0 3+`X(  X  X  x 0e0e?Rectangle 2  `   TWork in Progress    c X  x<0e0e?Rectangle 3 `p  Can we build zero-maintenance disk arrays? Start with a 3-D RAID array Add enough spares to last several years Critical factor is failure rate of unused spares Potential for one or two MS theses Require willingness to learn Python+  <Z # $  Z#$   H X 0޽h ? 3ff3̙y___PPT10Y+D=' = @B +"$ 0 t$(  tr t S  >  r t S  `    H t 0޽h ? 3ff3̙80___PPT10.p 0  0@(  @ @  xT0e0e?Rectangle 2  `   N Our Model      S @  xd0e0e?Rectangle 3 `  }Device failures are mutually independent and follow a Poisson law A reasonable approximation Device repairs can be performed in parallel Device repair times follow an exponential law Not true but fairly robust H.-W. Kao, J.-F. Paris, T. Schwarz, S. J., and D. D. E. Long, A Flexible Simulation Tool for Estimating Data Loss Risks in Storage Arrays, Proc. MSST Symposium, May 2013.B  Z < 0 _PBZ        Z              H @ 0޽h ? 3ff3̙y___PPT10Y+D=' = @B +" 0 `Hi(  H H  x|0e0e?Rectangle 2 `   Q State Diagram    T H l??Rectangle 3"@F>6___PPT9 \&( " d    H `*??Text Box 80"@  F>6___PPT9 `State 0 is initial state a is the fraction of quadruple disk failures that result in a data loss6a dC G a  $T H n|3??Rectangle 31"@66F>6___PPT9 Z$ " d    H \ }A ?Object 30,  H H 0޽h ? 3ff3̙y___PPT10Y+D=' = @B +" 0 d(  d d fD??Rectangle 7_   l*(     d f??Rectangle 7_  l*(     d  Z\?Rectangle 2    d  ~X0e0e\?Rectangle 3 0   R    H d 0޽h ? 33  0 h(  h h fD??Rectangle 7_   l*(     h f??Rectangle 7_  l*(     h  Z\?Rectangle 2    h  ~0e0e\?Rectangle 3 0   R    H h 0޽h ? 33 0 l(  l l f̨??Rectangle 7_   l*(     l f`ר??Rectangle 7_  l*(     l  Z\?Rectangle 2    l  ~0e0e\?Rectangle 3 0   R    H l 0޽h ? 33 0 p(  p p f??Rectangle 7_   l*(     p f4??Rectangle 7_  l*(     p  Z\?Rectangle 2    p  ~0e0e\?Rectangle 3 0   R    H p 0޽h ? 33.>x[ |?3sor{Ix1kڥ+!"_Q \ MBѕoAh|-.* BxPEkZ+m9ofr҄R N~|=y};c&Glw)O]$P1Ώ Ǧ]D"B2"_^5J,B%\CՎ>X [Ę#)~E 7~n_s\qbj SU2W"ksmȑ?N3Xtp%ψuÖ;_Ě\|M`k8uuW _T.э`GНÍ _ep na`p+C&?15fua/C?ܦq9a`l! 9 C1 g0Q 020as]^+9=exr_/<[*=Ee $d@FʧmIb=C:C <;ӵ5>_'^.c5_yRpޟə?D嗓Z. d]Yh<-:rs;Zˉv3Lөs@`2W/cG-Ͽ_jgbm/ds} R~iV~/>]սd}xje.9e.rWL~F>w=;| i4. 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