Contribution to the Design & Implementation of the Highly Available Scalable and Distributed Data Structure: LH*RSRim Moussa Rim.Moussa@dauphine.fr http://ceria.dauphine.fr/rim/rim.htmlThesis Presentation in Computer Science *Distributed DatabasesThesis Supervisor: Pr. Witold Litwin Examinators: Pr. Thomas J.E. Schwarz Pr. Tor RischJury President: Pr. Grard LvyParis Dauphine University *CERIA Lab.*04th October 2004

R. Moussa, U. Paris Dauphine

OutlineIssue State of the Art LH*RS SchemeLH*RS ManagerExperimentationsLH*RS File CreationBucket RecoveryParity Bucket CreationConclusion & Future Work

R. Moussa, U. Paris Dauphine

Facts Volume of Information of 30% /yearTechnologyNetwork Infrastructure >> Gilder Law, bandwidth triples every year.Evolution of PCs storage & computing capacities>> Moore Law, the latters double every 18 months.Bottleneck of Disks Accesses & CPUsNeed of Distributed Data Storage SystemsSDDSs: LH*, RP* High Throughput

R. Moussa, U. Paris Dauphine

Facts Frequent & Costly Failures>> Stat. Published by the Contingency Planning Research in 1996: the cost of service interruption/h case of brokerage application is $6,45 million.Need of Distributed & Highly-Available Data Storage Systems Multicomputers >> Modular Architecture >> Good Price/ Performance Tradeoff

R. Moussa, U. Paris Dauphine

State of the Art Parity Calculus(+) Good Response Time, Mirors are functional(-) High Storage Overhead (n if n repliquas)Data Replication Criteria to evaluate Erasure-resilient Codes: Encoding Rate (Parity Volume/ Data Volume) Update Penality (Parity Volumes) Group Size used for Data Reconstruction Encoding & Decoding Complexity Recovery Capabilitties

R. Moussa, U. Paris Dauphine

Parity Schemes1-Available Schemesk-Available Schemes Binary Linear Codes: [H94] Tolerate max. 3 failuresArray Codes: EVENODD [B94 ], X-code [XB99], RDP [C+04] Tolerate max. 2 failures Reed Solomon Codes : IDA [R89], RAID X [W91], FEC [B95], Tutorial [P97], LH*RS [LS00, ML02, MS04, LMS04] Tolerate k failures (k > 3) XOR Parity Calculus : RAID Technology (level 3, 4, 5) [PGK88], SDDS LH*g [L96]

R. Moussa, U. Paris Dauphine

OutlineIssueState of the Art LH*RS SchemeLH*RS?SDDSs?Reed Solomon Codes?Encoding/ Decoding OptimizationsLH*RS ManagerExperimentations

R. Moussa, U. Paris Dauphine

LH*RS ?Distribution using Linear Hashing (LH*LH [KLR96]) LH*LH Manager[B00]Scalability & High Throughput High AvailabilityLH*: Scalable & Distributed Data StructureParity Calculus using Reed-Solomon Codes [RS63]LH*RS [LS00]

R. Moussa, U. Paris Dauphine

SDDSs Principles (1) Dynamic File Growth ClientNetworkClientData BucketsCoordinator

R. Moussa, U. Paris Dauphine

SDDSs Principles (2)(2) No Centralized Directory AccessCases de Donnes ClientFile Image

R. Moussa, U. Paris Dauphine

Reed-Solomon CodesEncodingFrom m Data Symbols Calculus of n Parity SymbolsData Representation Galois Field Fields with finite size: qClosure Propoerty: Addition, Substraction, Multiplication, Division.In GF(2w),(1) Addition (XOR)(2) Multiplication (Tables: gflog and antigflog) e1 * e2 = antigflog[ gflog[e1] + gflog[e2] ]

R. Moussa, U. Paris Dauphine

RS Encoding100000 C1,1 C1,j C1,n-m01000 0 C2,1 C2,j C2,n-m00100 0 C3,1 C3,j C3,n-m 0 0000 1 Cm,1 Cm,j Cm,n-m

R. Moussa, U. Paris Dauphine

RS Decoding100000C1,1 C1,2 C1,3 C1,n-m01000 0 C2,1 C2,2 C2,3 C2,n-m00100 0 C3,1 C3,2 C3,3 C3,n-m 0 00 0 0 1 Cm,1 Cm,2 Cm,3 Cm,n-mS1S2S3S4:SmP1P2P3: Pn-m

R. Moussa, U. Paris Dauphine

OptimizationsGalois FieldParity MatrixGF Multiplication (+)GF(216) vs. GF(28) reduces the #Symbols by 1/2 #Operations in the GF.GF(28) 1 symbol = 1 ByteGF(216) 1 symbol = 2 Bytes (-)Multiplication Tables SizeGF(28): 0,768 KoGF(216): 393,216 Ko (512 0,768)

R. Moussa, U. Paris Dauphine

Optimizations (2)Galois FieldParity MatrixGF Multiplication1st Column of 1sEncoding of the 1st PB along XOR Calculus Gain in encoding & decoding 1st Row of 1sAny update from 1st DB is processed with XOR Calculus Gain in Performance of 4% (case PB creation, m =4)0001 0001 0001 0001 eb9b 2284 0001 2284 974 0001 9e44 d7f1

R. Moussa, U. Paris Dauphine

Optimizations (3)Galois FieldParity MatrixGF MultiplicationEncodingLog Pre-calculus of the Coef. of P Matrix Improvement of 3,5%0000 0000 0000 0000 5ab5 e267 0000 e267 0dce 0000 784d 2b66 DecodingLog Pre-calculus of coef. of H-1 matrix and OK symbols vector Improvement of 4% to 8% depending on the #buckets to recoverGoal: Reduce GF Multiplication Complexity e1 * e2 = antigflog[ gflog[e1] + gflog[e2] ]

R. Moussa, U. Paris Dauphine

LH*RS -Parity Groups

Data BucketsParity Buckets

: Key; DataInsert Rankr: Rank; [Key-list ]; Parity Key r 210 210A k-Acvailable Group survive to the failure of k buckets Grouping Concept m: #data buckets k: #parity buckets

R. Moussa, U. Paris Dauphine

OutlineIssueState of the Art LH*RS SchemeLH*RS ManagerCommunicationGross Architecture5.Experimentations6.File CreationBucket Recovery

R. Moussa, U. Paris Dauphine

CommunicationTCP/IPUDPMulticastIndividual Operations (Insert, Update, Delete, Search) Record RecoveryControl MessagesPerformance

R. Moussa, U. Paris Dauphine

CommunicationTCP/IPUDPMulticastLarge Buffers TransfertNew Parity BucketsTransfer Parity Update & Record (Bucket Split)Bucket Recovery Performance & Reliability

R. Moussa, U. Paris Dauphine

CommunicationTCP/IPUDPMulticastLooking for New Data/Parity BucketsCommunication Multipoints

R. Moussa, U. Paris Dauphine

Architecture(1)TCP/IP Connection Handler Principle of Sending Credit & Message Conservation until delivery [J88, GRS97, D01]1 Bucket Recovery (3,125 MB): SDDS 2000: 6,7 s SDDS2000-TCP: 2,6 s (Hardware Config.: CPU 733MhZ machines, network 100Mbps) Before Improvement of 60%TCP/IP Connections are passive OPEN, RFC 793 [ISI81], TCP/IP under Win2K Server OS [MB00](2)Flow Control & Message Acknowledgement (FCMA)Enhancements to SDDS2000 Architecture:

R. Moussa, U. Paris Dauphine

Architecture (2)BeforeTo tag new servers (data or parity) using Multicast:(3)Dynamic IP Addressing StructurePre-defined and Static IP@s TableMulticast Group of Blank Data BucketsMulticast Group of Blank Parity BucketsCoordinatorCreated Buckets

R. Moussa, U. Paris Dauphine

Architecture (3) Multicast Listening Port UDP Sending Port TCP/IP Port UDP Listening Port UDP Listening Thread Messages QueueTCP Listening Thread Multicast listening Thread Message QueuePool of Working ThreadsNetworkACK Mgmt Threads Free ZonesMessages waiting for ACK.Not acquittedMessagesACK StructureMulticast Working Thread

R. Moussa, U. Paris Dauphine

ExperimentationPerformance Evaluation *CPU Time *Communication Time Experimental Environment*5 Machines (Pentium IV: 1.8 GHz, RAM: 512 Mb) *Ethernet Network 1 Gbps*O.S.: Win2K Server*Tested Configuration: 1 Client, A group of 4 Data Buckets, k Parity Buckets (k = 0,1,2,3).

R. Moussa, U. Paris Dauphine

OutlineIssue State of the Art LH*RS Scheme LH*RS Manager ExperimentationsFile CreationParity Update PerformanceBucket RecoveryParity Bucket Creation

R. Moussa, U. Paris Dauphine

File CreationClient OperationsPropagation of Data Record Inserts/ Updates/ Deletes to Parity Buckets. Update: Send only record. Deletes: Management of Free Ranks within Data Buckets.Data Bucket Split N1: #renaining recordsN2: #leaving recordsParity Group of the Splitting Data BucketN1+N2 Deletes + N1 Inserts Parity Group of the New Data BucketN2 Inserts

R. Moussa, U. Paris Dauphine

PerformancesConfig.Client Window = 1Client Window = 5Max Bucket Size = 10 000 records File of 25 000 records 1 record = 104 BytesNo difference GF(28) et GF(216) (we dont wait for ACKs between DBs and PBs)

R. Moussa, U. Paris Dauphine

PerformancesConfig.Client Window = 1Client Window = 5k = 0 ** k = 1 Perf. Degradation of 20%k = 1 ** k = 2 Perf. Degradation of 8%

R. Moussa, U. Paris Dauphine

Chart2

0.1410.1720.171

0.2820.3280.359

0.4380.50.531

0.5790.6560.703

0.7190.8130.89

0.8750.9841.062

1.0321.1411.25

1.1721.3131.421

1.3131.4691.625

1.4691.6411.796

1.611.7971.984

1.7661.9692.156

1.9222.1412.343

2.0632.2972.515

2.2042.4532.687

2.3442.6252.875

2.52.7813.046

2.6412.9383.234

2.7823.1093.406

2.9383.2663.593

3.1574.1564.5

3.3134.3134.687

3.4544.4694.859

3.5944.6415.046

3.754.7975.218

3.8914.9845.406

4.0475.1565.578

4.1885.3135.765

4.3295.4695.937

4.4695.6416.109

4.615.7976.296

4.755.9536.468

4.9076.1096.671

5.0476.2816.843

5.1886.4387.031

5.3296.5947.203

5.4856.7667.39

5.6256.9227.562

5.7667.0787.75

5.9227.257.921

6.0637.4068.109

6.0637.4068.109

6.2827.4068.109

6.2827.6568.406

6.2828.2819

6.3758.2819

6.5328.4539.187

6.6888.6259.375

6.8298.7819.562

6.9858.9539.75

7.1259.1099.921

7.2669.28110.109

7.4229.45310.296

7.5639.60910.484

7.7199.78110.656

7.8759.96910.843

k = 0

k = 1

k = 2

Inserted Keys

File Creation Time (sec)

7,896s

9,990s

10,963s

Chart1

000

0.1410.1720.172

0.2820.3280.359

0.4380.50.531

0.5790.6560.718

0.7190.8130.89

0.8750.9841.078

1.0321.1411.25

1.1721.3131.437

1.3131.4691.609

1.4691.6411.781

1.611.7971.968

1.7661.9692.156

1.9222.1412.328

2.0632.2972.515

2.2042.4532.687

2.3442.6252.859

2.52.7813.047

2.6412.9383.218

2.7823.1093.406

2.9383.2663.578

3.1574.1564.484

3.3134.3134.672

3.4544.4694.843

3.5944.6415.031

3.754.7975.203

3.8914.9845.39

4.0475.1565.578

4.1885.3135.75

4.3295.4695.922

4.4695.6416.109

4.615.7976.281

4.755.9536.468

4.9076.1096.64

5.0476.2816.828

5.1886.4387

5.3296.5947.187

5.4856.7667.359

5.6256.9227.547

5.7667.0787.718

5.9227.257.906

6.0637.4068.078

6.0637.4068.078

6.2827.4068.093

6.2827.6568.375

6.2828.2819

6.3758.2819

6.5328.4539.203

6.6888.6259.39

6.8298.7819.578

6.9858.9539.765

7.1259.1099.937

7.2669.28110.125

7.4229.45310.312

7.5639.60910.484

7.7199.78110.672

7.8759.96910.859

k = 0

k = 1

k = 2

Inserted keys

Insert Time (sec)

7,896

9,990

10,963

k = 0, GF[2^8]

AckEssai 1Essai 2Essai 3

KeyTotal time (sec)avg rec(ms)Total time (sec)avg rec(ms)Total time (sec)avg rec(ms)

0000000

5000.1560.3120.1710.3420.1410.282

10000.2970.2820.3120.2820.2820.282

15000.4370.2800.4680.3120.4380.312

20000.5940.3140.6090.2820.5790.282

25000.7340.2800.7650.3120.7190.280

30000.8910.3140.9210.3120.8750.312

35001.0310.2801.0620.2821.0320.314

40001.1720.2821.2180.3121.1720.280

45001.3280.3121.3590.2821.3130.282

50001.4690.2821.5150.3121.4690.312

55001.6250.3121.6560.2821.6100.282

60001.7660.2821.8120.3121.7660.312

65001.9220.3121.9680.3121.9220.312

70002.0620.2802.1090.2822.0630.282

75002.2030.2822.2650.3122.2040.282

80002.3590.3122.4060.2822.3440.280

85002.5000.2822.5460.2802.5000.312

90002.6410.2822.7030.3142.6410.282

95002.7970.3122.8590.3122.7820.282

100002.9370.2803.0000.2822.9380.312

100013.156219.0003.218218.0003.157219.000

105003.3120.3133.3750.3153.3130.313

110003.4530.2823.5150.2803.4540.282

115003.5940.2823.6710.3123.5940.280

120003.7500.3123.8120.2823.7500.312

125003.9060.3123.9530.2823.8910.282

130004.0620.3124.1090.3124.0470.312

135004.2030.2824.2500.2824.1880.282

140004.3440.2824.3900.2804.3290.282

145004.4840.2804.5460.3124.4690.280

150004.6250.2824.6870.2824.6100.282

155004.7660.2824.8280.2824.7500.280

160004.9220.3124.9680.2804.9070.314

165005.0620.2805.1250.3145.0470.280

170005.2030.2825.2650.2805.1880.282

175005.3440.2825.4060.2825.3290.282

180005.5000.3125.5620.3125.4850.312

185005.6410.2825.7030.2825.6250.280

190005.7810.2805.8430.2805.7660.282

195005.9370.3126.0000.3145.9220.312

200006.0780.2826.1400.2806.0630.282

200016.0780.0006.1400.0006.0630.303

200026.297219.0006.359219.0006.282219.000

200036.2970.0006.3590.0006.2820.314

200046.2970.0006.3590.0006.2820.314

200056.39194.0006.45394.0006.37593.000

205006.5470.3156.6250.3476.5320.317

210006.7030.3126.7650.2806.6880.312

215006.8440.2826.9210.3126.8290.282

220006.9840.2807.0620.2826.9850.312

225007.1250.2827.2180.3127.1250.280

230007.2810.3127.3750.3147.2660.282

235007.4220.2827.5150.2807.4220.312

240007.5620.2807.6560.2827.5630.282

245007.7190.3147.8120.3127.7190.312

250007.8590.2807.9530.2827.8750.312

DB 0 split0.2180.2030.219

DB 1 split0.2190.2190.219

DB 2 split0.0940.0940.094

(k = 1) + RS, GF[2^8]

AckEssai 1Essai 2Essai 3

KeyTotal time (sec)avg rec(ms)Total time (sec)avg rec(ms)Total time (sec)avg rec(ms)

0000000

5000.1560.3120.1880.3760.1560.312

10000.3280.3440.3440.3120.3280.344

15000.4840.3120.5160.3440.4840.312

20000.6410.3140.6720.3120.6560.344

25000.8130.3440.8440.3440.8120.312

30000.9690.3121.0160.3440.9840.344

35001.1410.3441.1720.3121.1410.314

40001.2970.3121.3440.3441.3120.342

45001.4530.3121.5000.3121.4690.314

50001.6250.3441.6720.3441.6410.344

55001.7810.3121.8440.3441.7970.312

60001.9530.3442.0160.3441.9690.344

65002.1250.3442.1880.3442.1410.344

70002.2810.3122.3440.3122.2970.312

75002.4380.3142.5160.3442.4690.344

80002.5940.3122.6720.3122.6410.344

85002.7500.3122.8440.3442.8120.342

90002.9220.3443.0000.3122.9690.314

95003.0780.3123.1720.3443.1410.344

100003.2500.3443.3440.3443.2970.312

100014.125875.0004.250906.0004.172875.000

105004.2810.3134.4220.3454.3440.345

110004.4530.3444.5780.3124.5000.312

115004.6090.3124.7500.3444.6720.344

120004.7660.3144.9220.3444.8280.312

125004.9380.3445.0780.3124.9840.312

130005.0940.3125.2500.3445.1560.344

135005.2500.3125.4220.3445.3120.312

140005.4060.3125.5780.3125.4690.314

145005.5780.3445.7500.3445.6410.344

150005.7340.3125.9060.3125.7970.312

155005.8910.3146.0780.3445.9530.312

160006.0470.3126.2340.3126.1250.344

165006.2190.3446.4060.3446.2810.312

170006.3750.3126.5630.3146.4370.312

175006.5310.3126.7340.3426.6090.344

180006.6880.3146.9060.3446.7660.314

185006.8590.3427.0630.3146.9370.342

190007.0160.3147.2340.3427.0940.314

195007.1880.3447.4060.3447.2500.312

200007.3440.3127.5630.3147.4220.344

200017.3440.0007.5630.0007.4220.000

200027.3440.0007.57815.0007.43715.000

200037.609265.0007.828250.0007.687250.000

200048.219610.0008.438610.0008.328641.000

200058.2190.0008.4380.0008.3280.000

205008.4220.4108.6410.4108.5000.347

210008.5780.3128.8130.3448.6560.312

215008.7500.3448.9840.3428.8280.344

220008.9220.3449.1410.3148.9840.312

225009.0780.3129.3130.3449.1410.314

230009.2660.3769.4840.3429.3120.342

235009.4380.3449.6560.3449.4840.344

240009.5940.3129.8130.3149.6410.314

245009.7660.3449.9840.3429.7970.312

250009.9220.31210.1410.3149.9690.344

DB 0 split0.8750.8900.875

DB 1 split0.8590.8600.906

DB 2 split0.2500.2500.250

(k = 1) + New Matrix, GF[2^8]

AckEssai 1Essai 2Essai 3

KeyTotal time (sec)avg rec(ms)Total time (sec)avg rec(ms)Total time (sec)avg rec(ms)

0000000

5000.1720.3440.1720.3440.1720.344

10000.3280.3120.3280.3120.3280.312

15000.5000.3440.5000.3440.5000.344

20000.6560.3120.6560.3120.6560.312

25000.8280.3440.8280.3440.8130.314

30000.9840.3120.9840.3120.9840.342

35001.1560.3441.1560.3441.1410.314

40001.3120.3121.3280.3441.3130.344

45001.4840.3441.5000.3441.4690.312

50001.6400.3121.6560.3121.6410.344

55001.8120.3441.8280.3441.7970.312

60001.9840.3441.9840.3121.9690.344

65002.1400.3122.1560.3442.1410.344

70002.3120.3442.3280.3442.2970.312

75002.4690.3142.4840.3122.4530.312

80002.6250.3122.6400.3122.6250.344

85002.7970.3442.8120.3442.7810.312

90002.9530.3122.9680.3122.9380.314

95003.1250.3443.1400.3443.1090.342

100003.2810.3123.3120.3443.2660.314

100014.156875.0004.187875.0004.156890.000

105004.3280.3454.3590.3454.3130.315

110004.4840.3124.5150.3124.4690.312

115004.6560.3444.6870.3444.6410.344

120004.8120.3124.8430.3124.7970.312

125004.9690.3145.0000.3144.9840.374

130005.1400.3425.1720.3445.1560.344

135005.2970.3145.3280.3125.3130.314

140005.4690.3445.5000.3445.4690.312

145005.6250.3125.6560.3125.6410.344

150005.7810.3125.8120.3125.7970.312

155005.9370.3125.9840.3445.9530.312

160006.1090.3446.1400.3126.1090.312

165006.2650.3126.3120.3446.2810.344

170006.4220.3146.4680.3126.4380.314

175006.5940.3446.6400.3446.5940.312

180006.7500.3126.7970.3146.7660.344

185006.9060.3126.9680.3426.9220.312

190007.0780.3447.1250.3147.0780.312

195007.2340.3127.2970.3447.2500.344

200007.4060.3447.4530.3127.4060.312

200017.4060.0007.4530.0007.4060.370

200027.4060.0007.46815.0007.4060.370

200037.656250.0007.718250.0007.656250.000

200048.281625.0008.359641.0008.281625.000

200058.2810.0008.3590.0008.2810.414

205008.4840.4108.5310.3478.4530.347

210008.6400.3128.7030.3448.6250.344

215008.7970.3148.8590.3128.7810.312

220008.9690.3449.0310.3448.9530.344

225009.1400.3429.1870.3129.1090.312

230009.2970.3149.3590.3449.2810.344

235009.4690.3449.5310.3449.4530.344

240009.6250.3129.6870.3129.6090.312

245009.7970.3449.8590.3449.7810.344

250009.9690.34410.0310.3449.9690.376

DB 0 split0.8750.8750.875

DB 1 split0.8750.8910.875

DB 0 split0.2500.2500.250

(k = 2) + New Matrix, GF[2^8]

AckEssai 1Essai 2Essai 3

KeyTotal time (sec)avg rec(ms)Total time (sec)avg rec(ms)Total time (sec)avg rec(ms)

0000000

5000.1870.3740.1720.3440.1710.342

10000.3750.3760.3590.3740.3590.376

15000.5620.3740.5310.3440.5310.344

20000.7500.3760.7180.3740.7030.344

25000.9370.3740.8900.3440.8900.374

30001.1400.4061.0780.3761.0620.344

35001.3280.3761.2500.3441.2500.376

40001.5150.3741.4370.3741.4210.342

45001.7030.3761.6090.3441.6250.408

50001.8900.3741.7810.3441.7960.342

55002.0780.3761.9680.3741.9840.376

60002.2810.4062.1560.3762.1560.344

65002.4680.3742.3280.3442.3430.374

70002.6560.3762.5150.3742.5150.344

75002.8430.3742.6870.3442.6870.344

80003.0310.3762.8590.3442.8750.376

85003.2180.3743.0470.3763.0460.342

90003.4060.3763.2180.3423.2340.376

95003.6090.4063.4060.3763.4060.344

100003.7960.3743.5780.3443.5930.374

100014.703907.0004.484906.0004.500907.000

105004.8900.3754.6720.3774.6870.375

110005.0780.3764.8430.3424.8590.344

115005.2500.3445.0310.3765.0460.374

120005.4370.3745.2030.3445.2180.344

125005.6250.3765.3900.3745.4060.376

130005.8120.3745.5780.3765.5780.344

135006.0000.3765.7500.3445.7650.374

140006.1870.3745.9220.3445.9370.344

145006.3590.3446.1090.3746.1090.344

150006.5460.3746.2810.3446.2960.374

155006.7340.3766.4680.3746.4680.344

160006.9060.3446.6400.3446.6710.406

165007.0930.3746.8280.3766.8430.344

170007.2810.3767.0000.3447.0310.376

175007.4680.3747.1870.3747.2030.344

180007.6560.3767.3590.3447.3900.374

185007.8280.3447.5470.3767.5620.344

190008.0150.3747.7180.3427.7500.376

195008.2030.3767.9060.3767.9210.342

200008.3900.3748.0780.3448.1090.376

200018.3900.0008.0780.0008.1090.405

200028.40616.0008.09315.0008.1090.405

200038.4060.0008.375282.0008.406297.000

200049.312906.0009.000625.0009.000594.000

200059.3120.0009.0000.0009.0000.450

205009.5150.4109.2030.4109.1870.378

210009.7030.3769.3900.3749.3750.376

215009.8750.3449.5780.3769.5620.374

2200010.0620.3749.7650.3749.7500.376

2250010.2500.3769.9370.3449.9210.342

2300010.4370.37410.1250.37610.1090.376

2350010.6250.37610.3120.37410.2960.374

2400010.8120.37410.4840.34410.4840.376

2450011.0000.37610.6720.37610.6560.344

2500011.1870.37410.8590.37410.8430.374

DB 0 split0.9060.9060.891

DB 1 split0.9220.9210.891

DB 2 split0.2810.2820.281

|||comparaison|||

Essai 1Essai 2Essai 3MoyenneImprovement (%)Improvement (%)

Total time (sec)Total time (sec)Total time (sec)|New MatrixGF[2^8] /GF[2^16]

k = 0, GF[2^8]7.8597.9537.8757.896

k = 0, GF[2^16]7.9078.0627.9857.9851.115

k = 1,RS, GF[2^8]9.92210.1419.96910.011

k = 1,XOR, GF[2^8]9.96910.0319.9699.9900.2097762387

k = 1,RS, GF[2^16]10.21810.06210.17210.1511.379

k = 1,XOR, GF[2^16]10.15610.15610.06210.1250.25614081181.333

k = 2, GF[2^8]11.18710.85910.84310.963

k = 2, GF[2^16]10.98410.9381110.9740.1002369236

0.23295852520.982

PerformancesConfig.Client Window = 1Client Window = 5k = 0 ** k = 1 Perf. Degradation of 37%k = 1 ** k = 2 Perf. Degradation of 10%

R. Moussa, U. Paris Dauphine

Chart1

000

0.10366666670.14066666670.161

0.20333333330.27066666670.3126666667

0.3070.4060.4633333333

0.40633333330.54666666670.6196666667

0.51033333330.67166666670.776

0.61466666670.8180.9323333333

0.71866666670.9531.0883333333

0.83333333331.08833333331.2343333333

0.9321.21333333331.3903333333

1.03633333331.35433333331.5416666667

1.14566666671.48966666671.698

1.251.63033333331.8593333333

1.36466666671.77566666672.0156666667

1.45833333331.90066666672.1716666667

1.55733333332.03633333332.3176666667

1.66133333332.16666666672.4633333333

1.7712.30233333332.6143333333

1.8752.42733333332.7656666667

1.9742.56733333332.9216666667

2.0782.7033.073

2.08333333332.7033.073

2.39066666673.98433333334.448

2.44766666674.0524.5156666667

2.51033333334.124.5886666667

2.56733333334.20833333334.6666666667

2.6254.2764.745

2.68233333334.34866666674.8176666667

2.7554.40633333334.8906666667

2.8234.4794.9633333333

2.89066666674.53633333335.0366666667

2.94266666674.60966666675.1093333333

34.67166666675.1823333333

3.04666666674.74466666675.255

3.1044.81233333335.3283333333

3.16666666674.8755.4063333333

3.2194.9485.479

3.27566666675.01566666675.5626666667

3.3285.07833333335.6353333333

3.39066666675.15133333335.7083333333

3.44266666675.2245.7916666667

3.5055.29166666675.8646666667

3.5055.29166666675.8646666667

3.5055.29166666675.8646666667

3.58833333335.29166666675.8646666667

3.67166666675.2975.8646666667

3.7555.2975.8696666667

3.95833333336.46366666677.281

4.00033333336.51533333337.328

4.0476.56766666677.37

4.08866666676.6257.4113333333

4.13033333336.6727.458

4.16666666676.7297.505

4.21866666676.78133333337.552

4.2556.82833333337.599

4.29666666676.88533333337.6563333333

4.34866666676.94266666677.7186666667

k = 0

k = 1

k = 2

Number of Inserted Keys

File Creation Time (sec)

4,349s

6,940s

7,720s

UDP listen priority = highest

without lossAVG

Ackk = 0k = 1k = 2Avg k= 0Avg k= 1Avg k = 2

KeyEssai 1Essai 2Essai 3Essai 1Essai 2Essai 3Essai 1Essai 2Essai 3

5000.0930000.1250000.1090000.1410000.1250000.1410000.1720000.188000

10000.2030000.2190000.2030000.2820000.2500000.2810000.3280000.344000

15000.2960000.3280000.3130000.4220000.3910000.4060000.5000000.500000

20000.4060000.4380000.4220000.5630000.5160000.5470000.6570000.657000

25000.5150000.5470000.5310000.7030000.6560000.6880000.8130000.813000

30000.6250000.6560000.6410000.8600000.7970000.8280000.9850000.985000

35000.7340000.7660000.7500001.0000000.9370000.9530001.1570001.157000

40000.8430000.8750000.8590001.1250001.0620001.0940001.3130001.297000

45000.9530000.9840000.9690001.2660001.2030001.2190001.4690001.454000

50001.0620001.0940001.0780001.4070001.3440001.3600001.6410001.610000

55001.1710001.2030001.1880001.5470001.4840001.5000001.7970001.766000

60001.2810001.3130001.2970001.6880001.6410001.6410001.9690001.938000

65001.4060001.4220001.4220001.8440001.7810001.7810002.1410002.094000

70001.5000001.5310001.5160001.9690001.9060001.9060002.2970002.250000

75001.6090001.6250001.6250002.1100002.0310002.0780002.4850002.407000

80001.7030001.7340001.7190002.2500002.1720002.2190002.6410002.563000

85001.8120001.8440001.8280002.3910002.2970002.3440002.8130002.719000

90001.9210001.9530001.9380002.5320002.4370002.4850002.9690002.860000

95002.0310002.0470002.0470002.6720002.5780002.6100003.1250003.016000

100002.1400002.1560002.1560002.8130002.7190002.7500003.2970003.188000

100012.1400002.1560002.1560002.8130002.7190002.7500003.2970003.188000

105002.8120002.4840002.4840003.9530004.3750003.8440004.40700017.313000

110002.8430002.5470002.5780004.0160004.4370003.9220004.53200017.391000

115002.8900002.6090002.6410004.0940004.4840003.9850004.61000017.454000

120002.9370002.6560002.6880004.1570004.5470004.0630004.70300017.579000

125002.9680002.7660002.7500004.2350004.6090004.1250004.78200017.641000

130003.0150002.8280002.8130004.3130004.6720004.2030004.87500017.719000

135003.0460002.8750002.8590004.3750004.7190004.2810004.95300017.766000

140003.0780002.9380002.9220004.4530004.7810004.3440005.04700017.829000

145003.1250002.9840002.9840004.5320004.8280004.4220005.12500017.891000

150003.1560003.0470003.0310004.6410004.8910004.4850005.21900017.938000

155003.2030003.1090003.0940004.7030004.9530004.5630005.29700018.000000

160003.2340003.1560003.1560004.7820005.0160004.6250005.39100018.063000

165003.2650003.2190003.2190004.8600005.0620004.7030005.46900018.125000

170003.3120003.2810003.2660004.9220005.1250004.7660005.56300018.172000

175003.3430003.3440003.3280005.0000005.1870004.8440005.64100018.235000

180003.3900003.3910003.3910005.0780005.2500004.9220005.73500018.297000

185003.4210003.4530003.4530005.1570005.3120004.9850005.81300018.360000

190003.4680003.5160003.5160005.2350005.3750005.0630005.90700018.422000

195003.5000003.5780003.5630005.2970005.4370005.1410006.00000018.469000

200003.5460003.6410003.6250005.3750005.5000005.2030006.07800018.532000

200013.5460003.6410003.6250005.3750005.5000005.2190006.07800018.532000

200023.5460003.6410003.6250005.3750005.5000005.2190006.07800018.532000

200033.5460003.6410003.6250005.3750005.5000005.2190006.07800018.532000

200043.5460003.6410003.6410005.3750005.5000005.2190006.07800018.532000

200053.5460003.9060003.8910005.3910005.5000005.2190006.07800018.532000

205003.5780004.1880004.0310007.2820005.7970007.0940008.04700018.594000

210003.6090004.2190004.0780007.3130005.8590007.2810008.09400018.657000

215003.6560004.2660004.1250007.3440005.8910007.3280008.14100018.719000

220003.6870004.2970004.1560007.3910005.9370007.4690008.18800018.782000

225003.7340004.3280004.2030007.4380005.9840007.5160008.21900018.844000

230003.7650004.3750004.2340007.4690006.0310007.5630008.26600018.907000

235003.8120004.4060004.2810007.5000006.0620007.6100008.34400018.969000

240003.8430004.4530004.3130007.5470006.1090007.6410008.39100019.032000

245003.8900004.4840004.3590007.5780006.1410007.6880008.45300019.079000

250003.9210004.5310004.3910007.6410006.1870007.7350008.50000019.141000

DB 0 split

DB 1 split

DB 0 split

DB 0 split

k = 0

Essai 1: 6 DBs, {DB0, DB1, DB4, DB5}: 3125 records, {DB2, DB3}: 6250 records

Essai 2: 5 DBs, {3125, 6251, 6249, 6249, 3126} records respectiv, {DB0, ,,,, DB4}

Essai 3: 4 DBs, {6251, 6250, 6249, 6250} records respectiv, {DB0, ,,,, DB3}

k = 1

Essai 1

DB0DB1DB2DB3DB4Total 1PB1Perte 1Total 2PB2Perte 2

# recs3125625062506250312562503125

# recv ins15671628012351224609243780.05%6090%

# sent to PBs1566062721235122460924391598

# forwards118000

Essai 2

DB0DB1DB2DB3TotalPB1Perte

# recs62516250624962506251

# recv ins13809625637041246250000.00%

# sent to PBs1380062503704124625000

# forwards9600

Essai 3

DB0DB1DB2DB3DB4DB5Total 1PB1Perte 1Total 2PB2Perte 2

# recs31263127624962503125312362503125

# recv ins15708573512231212587557238460.04%11440%

# sent to PBs15695572712221212587557238561144

# forwards1381000

k = 2

Essai 1

DB0DB1DB2DB3DB4Total1PB1PB2Perte 1Total 2PB3PB4Perte2

# recs312562516249624931266158615931263126

# recv ins1568662881226121660724294242980.40%6066060%

# sent to PBs3134112562245024321212487851212

# forwards147101

Essai 2

DB0DB1DB2DB3DB4DB5Total1PB1PB2Perte 1Total 2PB3PB4Perte2

# recs3127312862546252312531246254625431253125

# recv ins119621972371837051851183621310213070.06%368736870%

# sent to PBs2387739207436741037023672426437374

# forwards22120000

Trial number 2: I've tried many times I get same results (19,,,, for file creation time): --> data records losses at the client level --> so messages retransmissions

Fast + Ack [client -- DB]

without lossAVG

Ackk = 0k = 1k = 2Avg k= 0Avg k= 1Avg k = 2

KeyEssai 1Essai 2Essai 3Essai 1Essai 2Essai 3Essai 1Essai 2Essai 3

0000000000000

5000.0930.1090.1090.1250.1560.1410.1560.1560.1710.1040.140.16

10000.1720.2190.2190.2650.2810.2660.3130.3130.3120.2030.270.31

15000.2650.3280.3280.3900.4220.4060.4690.4530.4680.3070.410.46

20000.3590.4380.4220.5310.5620.5470.6250.6090.6250.4060.550.62

25000.4530.5470.5310.6560.6870.6720.7810.7660.7810.5100.670.78

30000.5470.6560.6410.7970.8440.8130.9380.9220.9370.6150.820.93

35000.6400.7660.7500.9370.9690.9531.0941.0781.0930.7190.951.09

40000.7340.8750.8911.0621.1091.0941.2501.2191.2340.8331.091.23

45000.8120.9841.0001.1871.2341.2191.4061.3751.390.9321.211.39

50000.9061.0941.1091.3281.3751.3601.5631.5311.5311.0361.351.54

55001.0151.2031.2191.4531.5161.5001.7191.6881.6871.1461.491.70

60001.1091.3131.3281.5941.6561.6411.8911.8441.8431.2501.631.86

65001.2181.4381.4381.7341.8121.7812.047221.3651.782.02

70001.2971.5471.5311.8591.9371.9062.2032.1562.1561.4581.902.17

75001.3901.6411.6411.9842.0782.0472.3602.2972.2961.5572.042.32

80001.4841.7501.7502.1252.2032.1722.5002.4532.4371.6612.172.46

85001.5781.8911.8442.2502.3442.3132.6562.5942.5931.7712.302.61

90001.6722.0001.9532.3752.4692.4382.8132.752.7341.8752.432.77

95001.7502.1092.0632.5152.6092.5782.9692.9062.891.9742.572.92

100001.8432.2192.1722.6402.7502.7193.1253.0633.0312.0782.703.07

100011.8592.2192.1722.6402.7502.7193.1253.0633.0312.0832.703.07

105002.1562.5472.4693.7034.4063.8444.8604.2344.252.3913.984.45

110002.2032.6092.5313.7654.4693.9224.9224.3134.3122.4484.054.52

115002.2652.6722.5943.8444.5313.9854.9854.3914.392.5104.124.59

120002.3122.7342.6563.9844.5784.0635.0474.4694.4842.5674.214.67

125002.3752.7972.7034.0624.6414.1255.1104.5634.5622.6254.284.75

130002.4222.8592.7664.1404.7034.2035.1724.6414.642.6824.354.82

135002.4842.9532.8284.2034.7504.2665.2354.7194.7182.7554.414.89

140002.5313.0162.9224.2814.8124.3445.2974.7974.7962.8234.484.96

145002.6253.0632.9844.3444.8594.4065.3604.8754.8752.8914.545.04

150002.6723.1253.0314.4224.9224.4855.4224.9534.9532.9434.615.11

155002.7183.1883.0944.4844.9844.5475.4855.0315.0313.0004.675.18

160002.7653.2343.1414.5625.0474.6255.5475.1095.1093.0474.745.26

165002.8123.2973.2034.6405.0944.7035.6105.1885.1873.1044.815.33

170002.8753.3593.2664.7035.1564.7665.6885.2665.2653.1674.885.41

175002.9223.4223.3134.7815.2194.8445.7505.3445.3433.2194.955.48

180002.9683.4843.3754.8595.2664.9225.8135.4385.4373.2765.025.56

185003.0153.5313.4384.9225.3284.9855.8755.5165.5153.3285.085.64

190003.0783.5943.5005.0005.3915.0635.9385.5945.5933.3915.155.71

195003.1253.6563.5475.0785.4535.1416.0165.6885.6713.4435.225.79

200003.1873.7193.6095.1565.5165.2036.0785.7665.753.5055.295.86

200013.1873.7193.6095.1565.5165.2036.0785.7665.753.5055.295.86

200023.1873.7193.6095.1565.5165.2036.0785.7665.753.5055.295.86

200033.4373.7193.6095.1565.5165.2036.0785.7665.753.5885.295.86

200043.4373.7193.8595.1565.5165.2196.0785.7665.753.6725.305.86

200053.4373.9693.8595.1565.5165.2196.0785.7665.7653.7555.305.87

205003.5934.1414.1416.4695.8757.0476.4697.7037.6713.9586.467.28

210003.6254.1884.1886.5155.9377.0946.5167.757.7184.0006.527.33

215003.6724.2504.2196.5785.9847.1416.5637.7977.754.0476.577.37

220003.7034.2974.2666.6406.0477.1886.6107.8287.7964.0896.637.41

225003.7504.3444.2976.6876.0947.2356.6567.8757.8434.1306.677.46

230003.7814.3914.3286.7346.1567.2976.7037.9227.894.1676.737.51

235003.8284.4534.3756.7976.2037.3446.7507.9697.9374.2196.787.55

240003.8594.5004.4066.8446.2507.3916.7978.0167.9844.2556.837.60

245003.8904.5474.4536.9066.3127.4386.8448.0948.0314.2976.897.66

250003.9534.6094.4846.9696.3597.5006.9068.1418.1094.3496.947.72

DB 0 split0.2500.9840.9841.0631.0621.1101.125

DB 1 split0.0930.2650.3120.2660.3430.3130.281

DB 0 split0.2650.9840.6090.9670.5941.0151.000

DB 0 split0.5470.5460.547

Configuration: toutes les entits DBs et client sont sur des machines 1,8Ghz + 1Gbps

Window Size = Working Threads in a DB = 5

PBs and other buckets if created are in the 2,6 GKz machine

k = 1

Essai 1

DB0DB1DB2DB3TotalPB1Perte

# recs62506250625062505887

# recv ins16288628612221215246321.50%

# sent to PBs1628262811222121525000

# forwards6500

Essai 2

DB0DB1DB2DB3TotalPB1Perte

# recs62506250625062506207

# recv ins13792625637201244248220.70%

# sent to PBs1378562523719124425000

# forwards7410

Essai 3

DB0DB1DB2DB3DB4Total 1PB1Perte 1Total 2PB2Perte 2

# recs3125625062496250312662503126

# recv ins15690628512221216598244020%5980%

# sent to PBs1568362811222121659824402598

# forwards74000

k = 2

Essai 1

DB0DB1DB2DB3TotalPB1PB2Perte

# recs625062516250624959575985

# recv ins1378862503727124624263242533.00%

# sent to PBs27557124947452249249995

# forwards7310

Essai 2

DB0DB1DB2DB3DB4Total1PB1PB2Perte 1Total 2PB3PB4Perte2

# recs312562506251625031246251625131243124

# recv ins1570162921226120860024400243970%6006000%

# sent to PBs3136712572244224161200487971200

# forwards166500

Essai 3

DB0DB1DB2DB3DB4Total1PB1PB2Perte 1Total 2PB3PB4Perte2

# recs312562516250624931256121611931253125

# recv ins1568362871228121360524257242520.60%6056050%

# sent to PBs3134112564245624261210487871210

# forwards115000

Fast + Ack [client -- DB]

000

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000

000

000

000

000

000

000

000

000

000

k = 0

k = 1

k = 2

Nombre de cls insres

Temps cration fichier (sec)

4,349s

6,940s

7,720s

000

000

000

000

000

000

000

000

000

000

000

000

000

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000

000

000

000

000

000

000

000

000

000

000

000

000

000

k = 0

k = 1

k = 2

Number of Inserted Keys

File Creation Time (sec)

4,349s

6,940s

7,720s

OutlineIssue State of the Art LH*RS Scheme LH*RS Manager ExperimentationsFile CreationBucket RecoveryScenarioPerformances8. Parity Bucket Creation

R. Moussa, U. Paris Dauphine

ScenarioFailure DetectionAre you Alive? Data BucketsParity BucketsCoordinator

R. Moussa, U. Paris Dauphine

Scenario (2)Waiting for Responses OKData BucketsParity BucketsOKOKOKCoordinator

R. Moussa, U. Paris Dauphine

Scenario (3)Searching Spare Buckets Wanna be Spare ? Multicast Group of Blank Data BucketsCoordinator

R. Moussa, U. Paris Dauphine

Scenario (4)Waiting for Replies Launch UDP Listening Launch TCP Listening, Launch Working Thredsl*Waiting for Confirmation* If Time-out elapsed cancel everythingI would Multicast Group of Blank Data BucketsCoordinatorI would I would

R. Moussa, U. Paris Dauphine

Scenario (5)Spare SelectionMulticast Group of Blank Data BucketsConfirmedCancellationConfirmedYou are HiredCoordinator

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Scenario (6)Parity BucketsRecover Failed BucketsRecovery Manager Selection Coordinator

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Scenario (7)Data BucketsParity BucketsRecovery ManagerSpare BucketsBuckets participating to RecoverySend me Records of rank in [r, r+slice-1] Query Phase

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Scenario (8)Decoding Phase Recovered SlicesData BucketsParity BucketsSpare BucketsBuckets participating to RecoveryRequested BuffersReconstruction PhaseRecovery ManagerIn // with Query Phase

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Performances2 DBs1 DB XORConfig.1 DB RSXOR vs. RS File Info File of 125 000 records Record Size = 100 bytes Bucket Size = 31250 records 3.125 MB Group of 4 Data Buckets (m = 4), k-Available with k = 1,2,3 Decoding * GF(216) * RS+ Decoding (RS + log Pre-calculus of H-1 and OK Symboles Vector) Recovery per Slice (adaptative to PCs storage & computing capacities)

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Performances2 DBs1 DB XORConfig.1 DB RSXOR vs. RS

SliceTotal Time (sec)CPU Time (sec)Com. Time (sec)12500,6250,2660,34831250,5880,2550,32362500,5520,2400,312156250,5620,2550,302312500,5780,2500,328

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Performances2 DBs1 DB XORConfig.1 DB RSXOR vs. RS

SliceTotal Time (sec)CPU Time (sec)Com. Time (sec)12500,7340,3490,36531250,6880,3590,32362500,6560,3540,297156250,6670,3600,297312500,6880,3600,328

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Performances2 DBs1 DB XORConfig.Time to Recover 1DB -XOR : 0,58 secXOR in GF(216) realizes a gain of 13% in Total Time (and 30% in CPU Time)Time to Recover 1DB RS : 0,67 sec1 DB RSXOR vs. RS

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Performances3 DBs2 DBsSummaryXOR vs. RS1 DB RS

SliceTotal Time (sec)CPU Time (sec)Com. Time (sec)12500,9760,5770,37531250,9320,5890,33862500,8830,5620,321156250,8750,5620,281312500,8750,5620,313

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Performances3 DBs2 DBsSummaryXOR vs. RS1 DB RS

SliceTotal Time (sec)CPU Time (sec)Com. Time (sec)12501,2810,8280,40631251,2500,8280,39062501,2110,8520,352156251,1880,8230,361312501,2030,8280,375

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Performances3 DBs2 DBsSummaryXOR vs. RS1 DB RSTime to Recover f Buckets f Time to Recover 1 Bucket Factorized Query Phase The + is Decoding Time & Time to send Recovered Buffers

fBucket Size (MB)Total Time (sec)Recovery Speed (MB/sec)1 (XOR)1 (RS)3,1250,585.380,674.6626,2500,96.9439,3751,237,62

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PerformancesGF(28) XOR in GF(28) improves decoding perf. of 60% compared to RS in GF(28).

RS/RS+ decoding in GF(216) realize a gain of 50% compared to decoding in GF(28).

3 DBs2 DBsSummaryXOR vs. RS

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Outline1.Issue2.State of the Art 3.LH*RS Scheme 4.LH*RS Manager 5.Experimentations6.File Creation7.Bucket Recovery8.Parity Bucket CreationScenarioPerformances

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ScenarioMulticast Group of Blank Parity BucketsWanna Join Group g ? Searching for a new Parity BucketCoordinator

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Scenario (2)CoordinatorI Would Launch UDP Listening Launch TCP Listening, Launch Working Thredsl*Waiting for Confirmation* If Time-out elapsed cancel everything

Waiting for Replies Multicast Group of Blank Parity BucketsI Would I Would

R. Moussa, U. Paris Dauphine

Scenario (3)You are HiredConfirmedCancellationCancellationNew Parity Bucket SelectionMulticast Group of Blank Parity BucketsCoordinator

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Scenario (4)Send me your contents ! Group of Data BucketsNew Parity BucketAuto-creation *Query Phase

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Scenario (5)Group of Data BucketsAuto-creation *Encoding PhaseNew Parity Bucket

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PerformancesMax Bucket Size : 5000 .. 50000 recordsBucket Load Factor: 62,5%Record Size: 100 octetsGroup of 4 Data BucketsEncoding GF(216) RS++ ( Log Pre-calculus & Row 1s XOR encoding to Process 1st DB buffer)XORRSXOR vs. RSConfig.GF(28)

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PerformancesXORRSXOR vs. RSConfig.GF(28)Same Encoding RateBucket Size: CPU Time 74% Total Time

Bucket SizeTotal Time (sec)CPU Time (sec)Com. Time (sec)50000.1900.1400.029100000.4290.3040.066250001.0070.7380.144500002.0621.4840.322

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PerformancesXORRSXOR vs. RSConfig.GF(28)Same Encoding RateBucket Size: CPU Time 74% Total Time

Bucket SizeTotal Time (sec)CPU Time (sec)Com. Time (sec)50000.1930.1490.035100000.4460.3280.059250001.0530.7660.153500002.1031.5310.322

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PerformancesXOR encoding speed : 2.062 secRS encoding speed: 2.103 secXOR realizes a performance gain in CPU time of 5% ( only 0,02% on Total Time)For Bucket Size = 50000 recordsXORRSXOR vs. RSConfig.GF(28)

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PerformancesXORRSXOR vs. RSConfig.GF(28) Idem GF(216), CPU Time = 3/4 Total Time XOR in GF(28) improves CPU Time by 22%

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PerformanceFile Creation Rate0.33MB/s for k = 00.25MB/s for k = 10.23MB/s for k = 2Record Insert Time0.29ms for k = 00.33ms for k = 10.36ms for k = 2

Bucket Recovery Rate4.66MB/s from 1-unavailability6.94MB/s from 2-unavailability7.62MB/s from 3-unavailabilityRecord Recovery TimeAbout 1.3msKey Search TimeIndividual> 0.24msBulk> 0.056msWintel P4, 1.8GHz, 1Gbps

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ConclusionExperiments prove:Optimizations Encoding/ DecodingArchitecture Impact on PerformanceGood Recovery Performances

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Future WorkUpdate Propagation to Parity Buckets ReliabilityPerformanceReduce Coordinator Tasks Parity DeclusteringInvestigation of New Erausure-Resilient Codes

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References[PGK88] D. A. Patterson, G. Gibson & R. H. Katz, A Case for Redundant Arrays of Inexpensive Disks, Proc. of ACM SIGMOD Conf, pp.109-106, June 1988.

[ISI81] Information Sciences Institute, RFC 793: Transmission Control Protocol (TCP) Specification, Sept. 1981, http://www.faqs.org/rfcs/rfc793.html

[MB 00] D. MacDonal, W. Barkley, MS Windows 2000 TCP/IP Implementation Details, http://secinf.net/info/nt/2000ip/tcpipimp.html[J88] V. Jacobson, M. J. Karels, Congestion Avoidance and Control, Computer Communication Review, Vol. 18, No 4, pp. 314-329. [XB99] L. Xu & J. Bruck, X-Code: MDS Array Codes with Optimal Encoding, IEEE Trans. on Information Theory, 45(1), p.272-276, 1999.[CEG+ 04] P. Corbett, B. English, A. Goel, T. Grcanac, S. Kleiman, J. Leong, S. Sankar, Row-Diagonal Parity for Double Disk Failure Correction, Proc. of the 3rd USENIX Conf. On File and Storage Technologies, Avril 2004. [R89] M. O. Rabin, Efficient Dispersal of Information for Security, Load Balancing and Fault Tolerance, Journal of ACM, Vol. 26, N 2, April 1989, pp. 335-348. [W91] P.E. White, RAID X tackles design problems with existing design RAID schemes, ECC Technologies, ftp://members.aol.com.mnecctek.ctr1991.pdf [GRS97] J. C. Gomez, V. Redo, V. S. Sunderam, Efficient Multithreaded User-Space Transport for Network Computing, Design & Test of the TRAP protocol, Journal of Parallel & Distributed Computing, 40 (1) 1997.

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References (2)[BK+ 95] J. Blomer, M. Kalfane, R. Karp, M. Karpinski, M. Luby & D. Zuckerman, An XOR-Based Erasure-Resilient Coding Scheme, ICSI Tech. Rep. TR-95-048, 1995. [LS00] W. Litwin & T. Schwarz, LH*RS: A High-Availability Scalable Distributed Data Structure using Reed Solomon Codes, p.237-248, Proceedings of the ACM SIGMOD 2000. [KLR96] J. Karlson, W. Litwin & T. Risch, LH*LH: A Scalable high performance data structure for switched multicomputers, EDBT 96, Springer Verlag.[RS60] I. Reed & G. Solomon, Polynomial codes over certain Finite Fields,Journal of the society for industrial and applied mathematics, 1960. [P97] J. S. Plank, A Tutorial on Reed-Solomon Coding for fault-Tolerance in RAID-like Systems, Software Practise & Experience, 27(9), Sept. 1997, pp 995- 1012,[D01] A.W. Dine, Contribution la Gestion de Structures de Donnes Distribues et Scalables, PhD Thesis, Nov. 2001, Universit Paris Dauphine. [B00] F. Sahli Bennour, Contribution la Gestion de Structures de Donnes Distribues et Scalables, PhD Thesis, Juin 2000, Universit Paris Dauphine. + Rfrences: http://ceria.dauphine.fr/rim/theserim.pdf

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Publications[ML02] R. Moussa, W. Litwin, Experimental Performance Analysis of LH*RS Parity Management, Carleton Scientific Records of the 4th International Workshop on Distributed Data & Structure : WDAS 2002, p.87-97. [MS04] R. Moussa, T. Schwarz, Design and Implementation of LH*RS A Highly-Available Scalable Distributed Data Structure, Carleton Scientific Records of the 6th International Workshop on Distributed Data & Structure: WDAS 2004.[LMS04] W. Litwin, R. Moussa, T. Schwarz, Prototype Demonstration of LH*RS: A Highly Available Distributed Storage System, Proc. of VLDB 2004 (Demo Session) p.1289-1292. [LMS04-a] W. Litwin, R. Moussa, T. Schwarz, LH*RS: A Highly Available Distributed Storage System, journal version submitted, under revision.

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Thank You For Your AttentionQuestions ?

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Le client a une image du fichierCalcul d1 symbole de parit (RS): m Mult GF + m-1 XORsCalcul d1 symbole de parit (XOR): m-1 XORs multiplier par le nombre de symboles/ enregA multiplier par le nombre denregistrements

Dduire le nombre de cases de donnes factices

Calcul d1 symbole de parit (RS): m Mult GF + m-1 XORsCalcul d1 symbole de parit (XOR): m-1 XORs multiplier par le nombre de symboles/ enregA multiplier par le nombre denregistrements

Dduire le nombre de cases de donnes factices

Performances de GF(2^16)Par rapport GF(2^8):

Le 1 cest lidentit

Performances de GF(2^16)Par rapport GF(2^8):

En //le aprs phase de dcodage , phase dinterrogationPerformances de GF(2^16)Par rapport GF(2^8):

Vitesses de rcuprationVitesses de rcupration