-
Peer Pressure: Distributed Recovery in GnutellaPedram KeyaniBrian LarsonMuthukumar Senthil
Computer Science DepartmentStanford University
-
IntroductionGnutella is a P2P file sharing protocolThe issue we are addressing is distributed recovery from malicious attacks in GnutellaOur solution is a mechanism for proactive failure detection and recoveryOur experimental process and modelsThe fruits of our labor: RESULTS!
-
Failure in GnutellaFailure of nodes in Gnutella can be caused by any number of reasonsFailure of 4% of the most highly connected nodes in Gnutella fragments the network to the point where it is unusable by anyone The exact details of this are outlined in work done by Stefan Saroiu
-
Scale Free Networks (Gnutella, Internet)Abide by power law where# of nodes of degree N is proportional to N -lambdaLambda is observed to be roughly 2.3Scale Free networks are highly resilient to large scale random failures but weak for malicious attacks on the most highly connected well known nodes
Chart1
5
1.0153154954
0.3995683852
0.2061731111
0.2061731111
0.1234067725
0.0811375946
0.0569173291
0.0418661509
0.0319309789
0.0250593617
Number of Neighbors
Number of Nodes
Power Law Distribution K=5, Lambda = 2.3
Sheet1
15
21.0153154954
30.3995683852
40.2061731111
40.2061731111
50.1234067725
60.0811375946
70.0569173291
80.0418661509
90.0319309789
100.0250593617
110.0201264338
120.0164760514
130.0137056707
140.0115578092
150.009861889
160.0085014703
170.0073949882
180.0064840035
190.0057258072
200.0050886316
210.0045484731
220.004086936
230.0036897418
240.0033456781
Sheet1
0
0
0
0
0
0
0
0
0
0
0
Number of Neighbors
Number of Nodes
Power Law Distribution K=5, Lambda = 2.3
Sheet2
Sheet3
-
Exponential NetworksConnections between nodes are randomNo preferential connections ensures no node holds the entire network togetherThey react the same way to malicious attacks and random failures
-
Scale Free and Exponential
-
Our HypothesisIn order to allow Gnutella to recover from malicious attacks nodes must plan for failures by discovering and maintaining backup connections to form an exponential network. These backups will be used to replace dead neighbors in the case of a malicious attack.
-
Recovery MethodBuild and maintain a virtual exponential network connecting all the nodesAccomplish this through random node discoveryDetect malicious attacks on active networkSwitch over to exponential network
-
Random Node DiscoveryProblem: no centralized name authority to give a truly random nodeSolution: use random walks through the network to arrive at random nodeRandom Discovery Ping (RDP) is forwarded to only one of a nodes neighbors, selected in such a way to give a random distributionRDPs use a hop count of 20, roughly equal to the network diameter
-
Maintenance of Virtual Exponential NetworkEach node discovers N random nodes, where N is the minimum number of connections the node wants to maintainThen periodically ping these nodes to make sure they are aliveDiscover new neighbors to replace them should they die
-
Failure DetectionRandom failures result in loss of 1st degree neighborsMalicious attacks result in greater loss of 2nd degree neighbors than 1st degreeKeep a history (30 seconds) of 1st and 2nd degree neighbor lossIf 2nd degree loss exceeds 1st degree loss and a threshold (50%), mark as malicious
-
Reacting to FailuresFor each neighbor lost, replace it with a node from the virtual exponential networkOnly nodes local to an attack will switch, preserving the rest of the network structureDo not attempt to discover additional random nodes during an attackWhen attack is deemed to be over, return to normal operations
-
P2P SimulatorGeneralized P2P network simulatorHandles message routing, time managementSupport for bringing nodes up or down, injecting failures, loggingAlso created a compatible Gnutella client, and our enhanced Gnutella clientAbout 5k lines of Java
-
Modeling GnutellaNo standard way to do thisProtocol only specifies message formatsClients free to implement other aspectsSome degree of standardizationWe used the most common client in our simulation model - Bearshare
-
BootstrappingHow do nodes connect in our simulation?Defunct www.gnutellahosts.comMaintain list of highly-available, well-connected nodesClients connect by receiving one of these nodesBearshare clients do something similarConnect to service pubic.bearshare.netKeep a range of neighbors (3-10)
-
Uptime DistributionHow long do nodes stay up in our simulation?Modeled by a power law functionMost nodes are up for a short period of time, few are up for a long periodMany users just sign off after getting their contentMost users are dialup usersWithin a reasonable time slice, nodes have uptimes following the power law distribution
-
Our ExperimentsRan with recovery method and without No failures just ran our simulator without removing any nodes (control)Malicious attack on most highly connected nodes
-
Malicious AttackRan the experiment for 10 minutesWe removed 5% of the most highly connected nodes over a 5 minute interval in the middleRepresentative of a coordinated distributed attack on the network
-
MetricsLarge number of metrics that we could have usedWe picked metrics that measureHow partitioned the network isHow useful the network is in sending queries
-
Size of Largest Connected ComponentLargest set of nodes V, where any vm and vn V have a path between each otherMeasures the number of nodes that can potentially communicate with each otherCan get any data from any other node
-
# of Connected ComponentsNumber of separate pieces of the networkIf number of CCs is large then the network is heavily partitionedNot possible to retrieve content between CCsWant to monitor this number to make sure it is not increasing
-
Nodes Reachable Within 6 HopsSum of number of 1st, 2nd . . ., 6th degree neighbors of a nodeEnd to end measurement of how many nodes you can reach with a queryTypically queries are forwarded about 6 nodesRough estimate of the number of nodes a user can search.
-
Results Largest CC
Chart1
0.99983459820.00005494960.00005494960.99983497560.0000385410.000038541
0.99985973030.00002429940.00002429940.99982977260.00005331970.0000533197
0.99982982270.00006040870.00006040870.99980469770.00007255430.0000725543
0.99974460040.00006412060.00006412060.99982975740.00004682460.0000468246
0.99986959150.00005910450.00005910450.99981503340.00006493090.0000649309
0.99980460850.00006779960.00006779960.99986483990.0000389090.000038909
0.99987468520.00004216830.00004216830.99984495430.00004471040.0000447104
0.9998395520.00004605320.00004605320.99981468880.00008295720.0000829572
0.99982450610.000067720.000067720.99980479990.00005150880.0000515088
0.99980444990.00005774810.00005774810.99987479340.00003945010.0000394501
0.99982977240.0000605650.0000605650.99982474960.00004680490.0000468049
0.9998544820.0000665350.0000665350.99980992440.00006143540.0000614354
0.99981964220.00003643980.00003643980.99982973510.00006267530.0000626753
0.99320055340.00308886160.00308886160.33273752650.03531952740.0353195274
0.9965893140.00158189120.00158189120.23730294030.0191217420.019121742
0.99760707750.00186783290.00186783290.18582906440.03519528060.0351952806
0.99888470970.00056877830.00056877830.14214210730.032063460.03206346
0.99939845240.00042094510.00042094510.10021101760.02190499350.0219049935
0.99985329250.00006168910.00006168910.08397148570.02205775160.0220577516
0.99972614630.00007590190.00007590190.07378161880.01385080340.0138508034
0.99971568020.00008410.00008410.06690181110.01349456210.0134945621
0.99966434550.00007144250.00007144250.06387852140.01292318370.0129231837
0.99947431350.0004561040.0004561040.05362399410.01249720370.0124972037
0.99965293480.00004407720.00004407720.05309430110.01263263960.0126326396
0.99967286820.00008311890.00008311890.04995975960.01260103540.0126010354
0.99965671840.00009263040.00009263040.04751102180.01160186670.0116018667
0.99968700460.00006421610.00006421610.04271776390.01067691940.0106769194
0.99969182010.00006678530.00006678530.04108789520.01158211420.0115821142
0.99964456710.00009238820.00009238820.03707467940.01000440270.0100044027
0.99968543790.00006443140.00006443140.03342026490.00990901020.0099090102
0.99969003210.00005237990.00005237990.03209062720.0101978670.010197867
0.9997515370.00004494540.00004494540.03082146880.00877820410.0087782041
0.99965796420.00007854240.00007854240.02923052250.00802548920.0080254892
0.99967803250.00010798730.00010798730.02613284360.00654260110.0065426011
0.99961498890.0000484940.0000484940.02566191750.0063174990.006317499
0.99976536460.00006342530.00006342530.02569520510.00631271860.0063127186
0.99957751250.00009843070.00009843070.02507311580.00589930960.0058993096
0.999612950.0000632710.0000632710.02419786180.00543531830.0054353183
0.99952319560.00006905520.00006905520.0209883860.00317637540.0031763754
0.99956934020.00011081840.00011081840.01985000650.00246800860.0024680086
0.99965297450.00007704670.00007704670.01930733550.00255300190.0025530019
0.99960475440.00007624450.00007624450.01929850410.00254827620.0025482762
0.9995567420.0000913430.0000913430.01901165340.00278219690.0027821969
0.99987845480.00005586970.00005586970.0190351950.00278128040.0027812804
0.9998523940.00003702460.00003702460.0190261110.00277924420.0027792442
0.99985234370.00004568880.00004568880.01901628820.00276554730.0027655473
0.99985237410.00006126540.00006126540.01903540750.00276971480.0027697148
0.99985206850.00004842750.00004842750.01889918230.00294349560.0029434956
0.99985719480.00005390460.00005390460.01871769080.00300231210.0030023121
0.99985759270.00004874830.00004874830.01872692960.00300478340.0030047834
0.99985745080.00007435920.00007435920.01856325760.00282633960.0028263396
0.99987349190.00003482940.00003482940.01858259890.00283983760.0028398376
0.9998259180.00005122710.00005122710.01857468940.00284721480.0028472148
0.99989423120.00004643670.00004643670.01843247150.00292928840.0029292884
0.99984695750.00006430290.00006430290.01841725560.00292719950.0029271995
0.99985225130.00005502460.00005502460.01840999830.00291571640.0029157164
0.99981511860.0000792340.0000792340.01839787070.00289405460.0028940546
0.99979933130.00008141110.00008141110.01837324280.00290302830.0029030283
0.99981015650.00005765830.00005765830.01835556110.00291343810.0029134381
0.99985757490.00004870490.00004870490.01760818470.00291868080.0029186808
0.99980464220.00006907850.00006907850.0173186090.00295944910.0029594491
Smart Recovery
No Recovery
Time (minutes)
Percentage of Nodes
% of nodes in the largest connected component
Sheet1
0:00
0:10
0:20
0:30
0:40
0:50
1:00
1:10
1:20
1:30
1:40
1:50
start
2:10
2:20
2:30
2:40
2:50
3:00
3:10
3:20
3:30
3:40
3:50
4:00
4:10
4:20
4:30
4:40
4:50
5:00
5:10
5:20
5:30
5:40
5:50
6:00
6:10
6:20
6:30
6:40
6:50
end
7:10
7:20
7:30
7:40
7:50
8:00
8:10
8:20
8:30
8:40
8:50
9:00
9:10
9:20
9:30
9:40
9:50
10:00
Sheet1
0.99983459820.00005494960.00005494960.99983497560.0000385410.000038541
0.99985973030.00002429940.00002429940.99982977260.00005331970.0000533197
0.99982982270.00006040870.00006040870.99980469770.00007255430.0000725543
0.99974460040.00006412060.00006412060.99982975740.00004682460.0000468246
0.99986959150.00005910450.00005910450.99981503340.00006493090.0000649309
0.99980460850.00006779960.00006779960.99986483990.0000389090.000038909
0.99987468520.00004216830.00004216830.99984495430.00004471040.0000447104
0.9998395520.00004605320.00004605320.99981468880.00008295720.0000829572
0.99982450610.000067720.000067720.99980479990.00005150880.0000515088
0.99980444990.00005774810.00005774810.99987479340.00003945010.0000394501
0.99982977240.0000605650.0000605650.99982474960.00004680490.0000468049
0.9998544820.0000665350.0000665350.99980992440.00006143540.0000614354
0.99981964220.00003643980.00003643980.99982973510.00006267530.0000626753
0.99320055340.00308886160.00308886160.33273752650.03531952740.0353195274
0.9965893140.00158189120.00158189120.23730294030.0191217420.019121742
0.99760707750.00186783290.00186783290.18582906440.03519528060.0351952806
0.99888470970.00056877830.00056877830.14214210730.032063460.03206346
0.99939845240.00042094510.00042094510.10021101760.02190499350.0219049935
0.99985329250.00006168910.00006168910.08397148570.02205775160.0220577516
0.99972614630.00007590190.00007590190.07378161880.01385080340.0138508034
0.99971568020.00008410.00008410.06690181110.01349456210.0134945621
0.99966434550.00007144250.00007144250.06387852140.01292318370.0129231837
0.99947431350.0004561040.0004561040.05362399410.01249720370.0124972037
0.99965293480.00004407720.00004407720.05309430110.01263263960.0126326396
0.99967286820.00008311890.00008311890.04995975960.01260103540.0126010354
0.99965671840.00009263040.00009263040.04751102180.01160186670.0116018667
0.99968700460.00006421610.00006421610.04271776390.01067691940.0106769194
0.99969182010.00006678530.00006678530.04108789520.01158211420.0115821142
0.99964456710.00009238820.00009238820.03707467940.01000440270.0100044027
0.99968543790.00006443140.00006443140.03342026490.00990901020.0099090102
0.99969003210.00005237990.00005237990.03209062720.0101978670.010197867
0.9997515370.00004494540.00004494540.03082146880.00877820410.0087782041
0.99965796420.00007854240.00007854240.02923052250.00802548920.0080254892
0.99967803250.00010798730.00010798730.02613284360.00654260110.0065426011
0.99961498890.0000484940.0000484940.02566191750.0063174990.006317499
0.99976536460.00006342530.00006342530.02569520510.00631271860.0063127186
0.99957751250.00009843070.00009843070.02507311580.00589930960.0058993096
0.999612950.0000632710.0000632710.02419786180.00543531830.0054353183
0.99952319560.00006905520.00006905520.0209883860.00317637540.0031763754
0.99956934020.00011081840.00011081840.01985000650.00246800860.0024680086
0.99965297450.00007704670.00007704670.01930733550.00255300190.0025530019
0.99960475440.00007624450.00007624450.01929850410.00254827620.0025482762
0.9995567420.0000913430.0000913430.01901165340.00278219690.0027821969
0.99987845480.00005586970.00005586970.0190351950.00278128040.0027812804
0.9998523940.00003702460.00003702460.0190261110.00277924420.0027792442
0.99985234370.00004568880.00004568880.01901628820.00276554730.0027655473
0.99985237410.00006126540.00006126540.01903540750.00276971480.0027697148
0.99985206850.00004842750.00004842750.01889918230.00294349560.0029434956
0.99985719480.00005390460.00005390460.01871769080.00300231210.0030023121
0.99985759270.00004874830.00004874830.01872692960.00300478340.0030047834
0.99985745080.00007435920.00007435920.01856325760.00282633960.0028263396
0.99987349190.00003482940.00003482940.01858259890.00283983760.0028398376
0.9998259180.00005122710.00005122710.01857468940.00284721480.0028472148
0.99989423120.00004643670.00004643670.01843247150.00292928840.0029292884
0.99984695750.00006430290.00006430290.01841725560.00292719950.0029271995
0.99985225130.00005502460.00005502460.01840999830.00291571640.0029157164
0.99981511860.0000792340.0000792340.01839787070.00289405460.0028940546
0.99979933130.00008141110.00008141110.01837324280.00290302830.0029030283
0.99981015650.00005765830.00005765830.01835556110.00291343810.0029134381
0.99985757490.00004870490.00004870490.01760818470.00291868080.0029186808
0.99980464220.00006907850.00006907850.0173186090.00295944910.0029594491
Smart Recovery
No Recovery
Time (minutes)
Percentage of Nodes
% of nodes in the largest connected component
Sheet2
4.30.77577494560.77577494564.31.09516448881.0951644888
4.41.06151994031.06151994033.80.48890019080.4889001908
4.91.44470981331.44470981334.41.21172875621.2117287562
4.40.93312811950.93312811956.11.28854916511.2885491651
4.71.30827300291.30827300293.61.17597664941.1759766494
3.70.77577494560.77577494564.91.35317772241.3531777224
4.10.89816700190.89816700193.50.83920519830.8392051983
4.71.65407503921.65407503924.20.91464850510.9146485051
4.91.03092214041.03092214044.51.34685442741.3468544274
3.50.78670189150.78670189154.91.14843239061.1484323906
4.50.93541240230.93541240234.41.21172875621.2117287562
4.81.23268239131.23268239133.91.32125866111.3212586611
4.41.24645580651.24645580654.60.72750676440.7275067644
309.542.335209788642.335209788611.22.62631534662.6263153466
332.944.870744396944.87074439698.71.62806594971.6280659497
350.746.64181212946.6418121297.51.43878884651.4387888465
366.748.816672681248.816672681282.04521623292.0452162329
382.450.422789715350.42278971537.50.83920519830.8392051983
395.552.553318855952.55331885593.91.22050315581.2205031558
408.552.831970002452.83197000246.41.49551866171.4955186617
416.452.116950339252.11695033926.61.65794121131.6579412113
423.353.956549537553.95654953757.61.40729512581.4072951258
434.555.961188902655.96118890266.81.04531257721.0453125772
443.956.43073289256.4307328927.80.86672740180.8667274018
452.556.401831997556.40183199757.41.63199373811.6319937381
462.857.01267423357.0126742337.71.80226447221.8022644722
469.158.154650535158.154650535171.23958822911.2395882291
477.959.155949025959.155949025971.30664072151.3066407215
490.559.129102044659.12910204467.91.78799830221.7879983022
498.859.696323489459.69632348947.11.25498743111.2549874311
50658.523794658758.523794658771.01211955081.0121195508
515.857.789722004957.78972200495.80.86672740180.8667274018
525.157.331197556357.33119755637.61.52379183821.5237918382
532.258.319812191158.31981219117.22.08244263722.0824426372
540.858.446289234658.44628923468.40.93312811950.9331281195
547.760.537138436360.53713843635.41.21172875621.2117287562
557.460.634465229860.63446522989.11.90361903291.9036190329
567.959.869566362459.86956636248.41.21172875621.2117287562
57859.796482179759.796482179710.11.32125866111.3212586611
586.459.578518587259.57851858729.22.1028392322.102839232
595.159.134299185859.13429918587.61.46670057231.4667005723
604.559.329438875359.32943887538.51.43878884651.4387888465
614.759.33792741759.3379274179.41.73345480371.7334548037
611.859.948898444559.94889844453.31.05547134441.0554713444
614.460.335965789360.33596578933.80.70364756290.7036475629
616.360.724396684760.72439668473.80.86672740180.8667274018
618.561.085453732361.08545373233.81.16136767671.1613676767
620.560.796189902860.79618990283.80.91464850510.9146485051
623.361.247904011461.24790401143.71.01422594131.0142259413
625.861.034109822361.03410982233.70.9262414710.926241471
627.960.527548763160.52754876313.71.40273830291.4027383029
630.460.699192742560.69919274253.40.66625865360.6662586536
632.959.766816416859.76681641684.30.97123053970.9712305397
636.259.495069820959.495069820930.87652124270.8765212427
637.660.14891749760.1489174973.91.22050315581.2205031558
640.359.634980897359.63498089733.81.04531257721.0453125772
642.660.204242250560.20424225054.51.49694500321.4969450032
646.860.525680010260.52568001024.81.54050669121.5405066912
648.960.28023087860.2802308784.61.10099504191.1009950419
652.359.809364888259.80936488823.70.9262414710.926241471
655.159.474727583359.47472758334.71.30827300291.3082730029
No Recovery
Smart Recovery
Time (minutes)
Number of Components
Number of Connected Components
Sheet3
0.23464913310.00436961790.00436961790.23786524430.00617432790.0061743279
0.23320761040.00552288760.00552288760.23845619190.00609876010.0060987601
0.23395703480.00549518090.00549518090.23708527650.0059843580.005984358
0.23532182650.0065614030.0065614030.23844513820.00477545910.0047754591
0.23298287660.00455405430.00455405430.23610178820.00577121590.0057712159
0.2327222120.00527436090.00527436090.23579978510.00589376020.0058937602
0.23345910920.00574364360.00574364360.23670566880.00559587440.0055958744
0.23258378850.00599213090.00599213090.23782254030.00503472870.0050347287
0.23304705760.00573576110.00573576110.23844829340.00613534160.0061353416
0.23414483790.0057432410.0057432410.23860783460.00633934060.0063393406
0.23433175080.00470021890.00470021890.23631635090.00659342380.0065934238
0.23192524310.00582480430.00582480430.23890288330.00571359210.0057135921
0.2327932170.00554433910.00554433910.23733490040.006396690.00639669
0.00732213250.00035416090.00035416090.0274158420.00200416350.0020041635
0.00538154670.00023268550.00023268550.03392621970.00268352610.0026835261
0.00462740320.00025040610.00025040610.03899277050.00304748480.0030474848
0.00397102250.00023462590.00023462590.04339794870.00340409990.0034040999
0.00359712040.0002529290.0002529290.04735230120.00367983030.0036798303
0.00327394160.00022706190.00022706190.05251950510.00388120.0038812
0.00309432460.00020858620.00020858620.05594072050.00432043820.0043204382
0.00293251720.00018709580.00018709580.06023060490.00469466760.0046946676
0.00280173080.00020608280.00020608280.06391433640.00519573580.0051957358
0.00268292540.00021112630.00021112630.06812735810.0051397360.005139736
0.00256604710.00019947340.00019947340.07104753290.00534900190.0053490019
0.00251088870.00019083330.00019083330.07434040180.00584590170.0058459017
0.00239682390.00019380040.00019380040.07766227210.00566017280.0056601728
0.00232263170.00018939480.00018939480.08057586570.00585087370.0058508737
0.00225107170.00017811860.00017811860.08424126480.00624007680.0062400768
0.00218891140.00017403830.00017403830.087267830.00626123440.0062612344
0.002135410.00016445610.00016445610.08940411680.00661556950.0066155695
0.00207890810.00015885530.00015885530.09321777090.00646182410.0064618241
0.00202333730.00015917870.00015917870.09580321180.00623768670.0062376867
0.00198132910.00014796260.00014796260.09833825920.00653992210.0065399221
0.00193448580.0001435530.0001435530.10108017690.00642283360.0064228336
0.00190147370.00014407930.00014407930.10337931670.00688711830.0068871183
0.00187275670.00014225870.00014225870.10531985610.00664382590.0066438259
0.00182121870.00014218640.00014218640.10869955510.00703809450.0070380945
0.00178127650.00012201590.00012201590.11039636390.00691479030.0069147903
0.0017408370.00012145980.00012145980.11264702480.00705092790.0070509279
0.00171455140.0001133480.0001133480.11403451470.00705636840.0070563684
0.00167378950.00011183660.00011183660.11639122970.00711883770.0071188377
0.00166281110.00010869340.00010869340.11832621440.00694433520.0069443352
0.00163258010.00011355530.00011355530.12019569090.00658196010.0065819601
0.00162483130.00011052230.00011052230.123276880.00706198950.0070619895
0.00161902850.00011813050.00011813050.1222289180.00709439940.0070943994
0.00161265340.00010773280.00010773280.1216049160.00706678840.0070667884
0.00162344040.00011254130.00011254130.12003288160.0067621360.006762136
0.00161234630.00010795330.00010795330.11962683770.00653108340.0065310834
0.00160633990.00011298150.00011298150.11923385410.00671601930.0067160193
0.00161198030.00011354690.00011354690.11835598180.00679794830.0067979483
0.00160738380.00010487710.00010487710.11779428320.00684153460.0068415346
0.00159460610.00010806050.00010806050.11593353890.00645363010.0064536301
0.00160228460.00011107090.00011107090.11580086550.00652481060.0065248106
0.00159881260.00011796420.00011796420.11502062420.00664953480.0066495348
0.0016001840.00010782210.00010782210.1135189620.00644398070.0064439807
0.00158873920.00011183150.00011183150.11362617820.00639389660.0063938966
0.00159870730.00011304710.00011304710.11226382060.00653775890.0065377589
0.00159058490.00011659850.00011659850.11155994120.0063347660.006334766
0.00158937110.00010974680.00010974680.11077910590.00669510250.0066951025
0.00158623230.00011110480.00011110480.11046136920.00629453630.0062945363
0.00158769690.00011172360.00011172360.10951868510.00587700220.0058770022
No Recovery
Smart Recovery
Time (minutes)
Percentage of Nodes
Average % of nodes within 6 hops
1.950.1037092210.1037092212.30.08121132680.0812113268
1.952325840.01577391680.01577391682.301531310.0130040910.013004091
1.953678870.01496655880.01496655882.301357390.0151458140.015145814
1.953590520.01548581340.01548581342.299936020.01439586730.0143958673
1.953659860.01554898810.01554898812.301190710.01471179830.0147117983
1.95328670.01584233240.01584233242.30206940.0129134980.012913498
1.953829570.0150692160.0150692162.300477490.0133495080.013349508
1.954788830.01495036340.01495036342.301931530.01507990210.0150799021
1.954610480.01533573290.01533573292.301422760.01228129710.0122812971
1.955093470.0153484970.0153484972.301902860.01212360020.0121236002
1.955146470.01500929550.01500929552.302704810.01264109870.0126410987
1.95624110.01527774920.01527774922.30515580.01327696820.0132769682
1.955672610.01536275910.01536275912.299374460.01334313260.0133431326
1.949407030.0163621560.0163621562.385655710.01208466920.0120846692
1.924790560.01623475630.01623475632.434574660.01399855730.0139985573
1.899458830.0146119190.0146119192.434213970.00972090840.0097209084
1.879404410.01464699150.01464699152.751365420.01192319760.0119231976
1.861478410.01414329210.01414329212.895688740.01404199670.0140419967
1.845404570.01427567850.01427567852.771901820.01558512940.0155851294
1.830077590.01388990820.01388990822.744917120.02043762790.0204376279
1.815186670.01354669880.01354669882.723360530.01826282540.0182628254
1.801629210.01295176480.01295176482.709334920.0154022520.015402252
1.787863530.01221522910.01221522912.704945960.01850340250.0185034025
1.775780710.01222362170.01222362172.690584370.0133624750.013362475
1.763506470.01191443460.01191443462.673471640.01276703280.0127670328
1.751881410.01156059570.01156059572.670401190.01355871690.0135587169
1.740899590.01217064010.01217064012.669586360.01587006370.0158700637
1.729868460.01152238990.01152238992.659622250.01293701650.0129370165
1.718395040.01119737910.01119737912.645290560.01328720740.0132872074
1.708831410.01086792990.01086792992.643449090.01192074630.0119207463
1.698740910.01044465320.01044465322.638378990.01394955690.0139495569
1.688730150.01039113220.01039113222.630514430.0179193070.017919307
1.679823840.00992315180.00992315182.626762040.015752020.01575202
1.670274860.00919599520.00919599522.623787740.01556958850.0155695885
1.660993660.00983735950.00983735952.615220930.01277432180.0127743218
1.652730590.0091033310.0091033312.608704750.013884860.01388486
1.644599590.00895068180.00895068182.599120710.01427321530.0142732153
1.63518380.00827392140.00827392142.595478540.01388250310.0138825031
1.627237120.00796672440.00796672442.591830480.00745244130.0074524413
1.61929370.00766958260.00766958262.590371930.01252318210.0125231821
1.610430760.00715308960.00715308962.59129970.01373700580.0137370058
1.602827430.00660019760.00660019762.581863850.0097470320.009747032
1.595842430.00623951140.00623951142.575454150.01527021490.0152702149
1.591012370.00622176530.00622176532.555467830.01274074670.0127407467
1.588599810.00613759670.00613759672.504121510.01103129350.0110312935
1.589525510.0062860220.0062860222.493408130.0110184530.011018453
1.591006360.00614508790.00614508792.41715380.01048041810.0104804181
1.592711880.00652243280.00652243282.280763280.0068162440.006816244
1.594062610.00611043860.00611043862.277970850.00746328670.0074632867
1.595470740.00588707870.00588707872.277886130.00853262940.0085326294
1.596853390.00610127940.00610127942.277024950.00827989730.0082798973
1.598685110.00620038810.00620038812.276530060.00957547590.0095754759
1.599986880.0062153160.0062153162.270571720.00612057240.0061205724
1.601840290.00576958720.00576958722.271857760.00815321520.0081532152
1.60256870.00653324890.00653324892.268769550.00934328810.0093432881
1.604181340.00629765550.00629765552.269248850.00704313060.0070431306
1.605882370.00626224890.00626224892.267515610.00844547220.0084454722
1.607175170.00590808680.00590808682.266604270.00677518430.0067751843
1.608501670.00593929190.00593929192.267836780.00873346690.0087334669
1.610523120.00607246050.00607246052.266808740.00679198090.0067919809
1.611604280.00614966230.00614966232.264537690.0058815260.005881526
No Recovery
Smart Recovery
Time (minutes)
Pings
Average Number of Pings
-
Results Number of CCs
-
Results - % of nodes within 6 hops
Chart2
0.23464913310.00436961790.00436961790.23786524430.00617432790.0061743279
0.23320761040.00552288760.00552288760.23845619190.00609876010.0060987601
0.23395703480.00549518090.00549518090.23708527650.0059843580.005984358
0.23532182650.0065614030.0065614030.23844513820.00477545910.0047754591
0.23298287660.00455405430.00455405430.23610178820.00577121590.0057712159
0.2327222120.00527436090.00527436090.23579978510.00589376020.0058937602
0.23345910920.00574364360.00574364360.23670566880.00559587440.0055958744
0.23258378850.00599213090.00599213090.23782254030.00503472870.0050347287
0.23304705760.00573576110.00573576110.23844829340.00613534160.0061353416
0.23414483790.0057432410.0057432410.23860783460.00633934060.0063393406
0.23433175080.00470021890.00470021890.23631635090.00659342380.0065934238
0.23192524310.00582480430.00582480430.23890288330.00571359210.0057135921
0.2327932170.00554433910.00554433910.23733490040.006396690.00639669
0.00732213250.00035416090.00035416090.0274158420.00200416350.0020041635
0.00538154670.00023268550.00023268550.03392621970.00268352610.0026835261
0.00462740320.00025040610.00025040610.03899277050.00304748480.0030474848
0.00397102250.00023462590.00023462590.04339794870.00340409990.0034040999
0.00359712040.0002529290.0002529290.04735230120.00367983030.0036798303
0.00327394160.00022706190.00022706190.05251950510.00388120.0038812
0.00309432460.00020858620.00020858620.05594072050.00432043820.0043204382
0.00293251720.00018709580.00018709580.06023060490.00469466760.0046946676
0.00280173080.00020608280.00020608280.06391433640.00519573580.0051957358
0.00268292540.00021112630.00021112630.06812735810.0051397360.005139736
0.00256604710.00019947340.00019947340.07104753290.00534900190.0053490019
0.00251088870.00019083330.00019083330.07434040180.00584590170.0058459017
0.00239682390.00019380040.00019380040.07766227210.00566017280.0056601728
0.00232263170.00018939480.00018939480.08057586570.00585087370.0058508737
0.00225107170.00017811860.00017811860.08424126480.00624007680.0062400768
0.00218891140.00017403830.00017403830.087267830.00626123440.0062612344
0.002135410.00016445610.00016445610.08940411680.00661556950.0066155695
0.00207890810.00015885530.00015885530.09321777090.00646182410.0064618241
0.00202333730.00015917870.00015917870.09580321180.00623768670.0062376867
0.00198132910.00014796260.00014796260.09833825920.00653992210.0065399221
0.00193448580.0001435530.0001435530.10108017690.00642283360.0064228336
0.00190147370.00014407930.00014407930.10337931670.00688711830.0068871183
0.00187275670.00014225870.00014225870.10531985610.00664382590.0066438259
0.00182121870.00014218640.00014218640.10869955510.00703809450.0070380945
0.00178127650.00012201590.00012201590.11039636390.00691479030.0069147903
0.0017408370.00012145980.00012145980.11264702480.00705092790.0070509279
0.00171455140.0001133480.0001133480.11403451470.00705636840.0070563684
0.00167378950.00011183660.00011183660.11639122970.00711883770.0071188377
0.00166281110.00010869340.00010869340.11832621440.00694433520.0069443352
0.00163258010.00011355530.00011355530.12019569090.00658196010.0065819601
0.00162483130.00011052230.00011052230.123276880.00706198950.0070619895
0.00161902850.00011813050.00011813050.1222289180.00709439940.0070943994
0.00161265340.00010773280.00010773280.1216049160.00706678840.0070667884
0.00162344040.00011254130.00011254130.12003288160.0067621360.006762136
0.00161234630.00010795330.00010795330.11962683770.00653108340.0065310834
0.00160633990.00011298150.00011298150.11923385410.00671601930.0067160193
0.00161198030.00011354690.00011354690.11835598180.00679794830.0067979483
0.00160738380.00010487710.00010487710.11779428320.00684153460.0068415346
0.00159460610.00010806050.00010806050.11593353890.00645363010.0064536301
0.00160228460.00011107090.00011107090.11580086550.00652481060.0065248106
0.00159881260.00011796420.00011796420.11502062420.00664953480.0066495348
0.0016001840.00010782210.00010782210.1135189620.00644398070.0064439807
0.00158873920.00011183150.00011183150.11362617820.00639389660.0063938966
0.00159870730.00011304710.00011304710.11226382060.00653775890.0065377589
0.00159058490.00011659850.00011659850.11155994120.0063347660.006334766
0.00158937110.00010974680.00010974680.11077910590.00669510250.0066951025
0.00158623230.00011110480.00011110480.11046136920.00629453630.0062945363
0.00158769690.00011172360.00011172360.10951868510.00587700220.0058770022
No Recovery
Smart Recovery
Time (minutes)
Percentage of Nodes
Average % of nodes within 6 hops
Sheet1
0:00
0:10
0:20
0:30
0:40
0:50
1:00
1:10
1:20
1:30
1:40
1:50
start
2:10
2:20
2:30
2:40
2:50
3:00
3:10
3:20
3:30
3:40
3:50
4:00
4:10
4:20
4:30
4:40
4:50
5:00
5:10
5:20
5:30
5:40
5:50
6:00
6:10
6:20
6:30
6:40
6:50
end
7:10
7:20
7:30
7:40
7:50
8:00
8:10
8:20
8:30
8:40
8:50
9:00
9:10
9:20
9:30
9:40
9:50
10:00
Sheet1
0.99983459820.00005494960.00005494960.99983497560.0000385410.000038541
0.99985973030.00002429940.00002429940.99982977260.00005331970.0000533197
0.99982982270.00006040870.00006040870.99980469770.00007255430.0000725543
0.99974460040.00006412060.00006412060.99982975740.00004682460.0000468246
0.99986959150.00005910450.00005910450.99981503340.00006493090.0000649309
0.99980460850.00006779960.00006779960.99986483990.0000389090.000038909
0.99987468520.00004216830.00004216830.99984495430.00004471040.0000447104
0.9998395520.00004605320.00004605320.99981468880.00008295720.0000829572
0.99982450610.000067720.000067720.99980479990.00005150880.0000515088
0.99980444990.00005774810.00005774810.99987479340.00003945010.0000394501
0.99982977240.0000605650.0000605650.99982474960.00004680490.0000468049
0.9998544820.0000665350.0000665350.99980992440.00006143540.0000614354
0.99981964220.00003643980.00003643980.99982973510.00006267530.0000626753
0.99320055340.00308886160.00308886160.33273752650.03531952740.0353195274
0.9965893140.00158189120.00158189120.23730294030.0191217420.019121742
0.99760707750.00186783290.00186783290.18582906440.03519528060.0351952806
0.99888470970.00056877830.00056877830.14214210730.032063460.03206346
0.99939845240.00042094510.00042094510.10021101760.02190499350.0219049935
0.99985329250.00006168910.00006168910.08397148570.02205775160.0220577516
0.99972614630.00007590190.00007590190.07378161880.01385080340.0138508034
0.99971568020.00008410.00008410.06690181110.01349456210.0134945621
0.99966434550.00007144250.00007144250.06387852140.01292318370.0129231837
0.99947431350.0004561040.0004561040.05362399410.01249720370.0124972037
0.99965293480.00004407720.00004407720.05309430110.01263263960.0126326396
0.99967286820.00008311890.00008311890.04995975960.01260103540.0126010354
0.99965671840.00009263040.00009263040.04751102180.01160186670.0116018667
0.99968700460.00006421610.00006421610.04271776390.01067691940.0106769194
0.99969182010.00006678530.00006678530.04108789520.01158211420.0115821142
0.99964456710.00009238820.00009238820.03707467940.01000440270.0100044027
0.99968543790.00006443140.00006443140.03342026490.00990901020.0099090102
0.99969003210.00005237990.00005237990.03209062720.0101978670.010197867
0.9997515370.00004494540.00004494540.03082146880.00877820410.0087782041
0.99965796420.00007854240.00007854240.02923052250.00802548920.0080254892
0.99967803250.00010798730.00010798730.02613284360.00654260110.0065426011
0.99961498890.0000484940.0000484940.02566191750.0063174990.006317499
0.99976536460.00006342530.00006342530.02569520510.00631271860.0063127186
0.99957751250.00009843070.00009843070.02507311580.00589930960.0058993096
0.999612950.0000632710.0000632710.02419786180.00543531830.0054353183
0.99952319560.00006905520.00006905520.0209883860.00317637540.0031763754
0.99956934020.00011081840.00011081840.01985000650.00246800860.0024680086
0.99965297450.00007704670.00007704670.01930733550.00255300190.0025530019
0.99960475440.00007624450.00007624450.01929850410.00254827620.0025482762
0.9995567420.0000913430.0000913430.01901165340.00278219690.0027821969
0.99987845480.00005586970.00005586970.0190351950.00278128040.0027812804
0.9998523940.00003702460.00003702460.0190261110.00277924420.0027792442
0.99985234370.00004568880.00004568880.01901628820.00276554730.0027655473
0.99985237410.00006126540.00006126540.01903540750.00276971480.0027697148
0.99985206850.00004842750.00004842750.01889918230.00294349560.0029434956
0.99985719480.00005390460.00005390460.01871769080.00300231210.0030023121
0.99985759270.00004874830.00004874830.01872692960.00300478340.0030047834
0.99985745080.00007435920.00007435920.01856325760.00282633960.0028263396
0.99987349190.00003482940.00003482940.01858259890.00283983760.0028398376
0.9998259180.00005122710.00005122710.01857468940.00284721480.0028472148
0.99989423120.00004643670.00004643670.01843247150.00292928840.0029292884
0.99984695750.00006430290.00006430290.01841725560.00292719950.0029271995
0.99985225130.00005502460.00005502460.01840999830.00291571640.0029157164
0.99981511860.0000792340.0000792340.01839787070.00289405460.0028940546
0.99979933130.00008141110.00008141110.01837324280.00290302830.0029030283
0.99981015650.00005765830.00005765830.01835556110.00291343810.0029134381
0.99985757490.00004870490.00004870490.01760818470.00291868080.0029186808
0.99980464220.00006907850.00006907850.0173186090.00295944910.0029594491
Smart Recovery
No Recovery
Time (minutes)
Percentage of Nodes
% of nodes in the largest connected component
Sheet2
4.30.77577494560.77577494564.31.09516448881.0951644888
4.41.06151994031.06151994033.80.48890019080.4889001908
4.91.44470981331.44470981334.41.21172875621.2117287562
4.40.93312811950.93312811956.11.28854916511.2885491651
4.71.30827300291.30827300293.61.17597664941.1759766494
3.70.77577494560.77577494564.91.35317772241.3531777224
4.10.89816700190.89816700193.50.83920519830.8392051983
4.71.65407503921.65407503924.20.91464850510.9146485051
4.91.03092214041.03092214044.51.34685442741.3468544274
3.50.78670189150.78670189154.91.14843239061.1484323906
4.50.93541240230.93541240234.41.21172875621.2117287562
4.81.23268239131.23268239133.91.32125866111.3212586611
4.41.24645580651.24645580654.60.72750676440.7275067644
309.542.335209788642.335209788611.22.62631534662.6263153466
332.944.870744396944.87074439698.71.62806594971.6280659497
350.746.64181212946.6418121297.51.43878884651.4387888465
366.748.816672681248.816672681282.04521623292.0452162329
382.450.422789715350.42278971537.50.83920519830.8392051983
395.552.553318855952.55331885593.91.22050315581.2205031558
408.552.831970002452.83197000246.41.49551866171.4955186617
416.452.116950339252.11695033926.61.65794121131.6579412113
423.353.956549537553.95654953757.61.40729512581.4072951258
434.555.961188902655.96118890266.81.04531257721.0453125772
443.956.43073289256.4307328927.80.86672740180.8667274018
452.556.401831997556.40183199757.41.63199373811.6319937381
462.857.01267423357.0126742337.71.80226447221.8022644722
469.158.154650535158.154650535171.23958822911.2395882291
477.959.155949025959.155949025971.30664072151.3066407215
490.559.129102044659.12910204467.91.78799830221.7879983022
498.859.696323489459.69632348947.11.25498743111.2549874311
50658.523794658758.523794658771.01211955081.0121195508
515.857.789722004957.78972200495.80.86672740180.8667274018
525.157.331197556357.33119755637.61.52379183821.5237918382
532.258.319812191158.31981219117.22.08244263722.0824426372
540.858.446289234658.44628923468.40.93312811950.9331281195
547.760.537138436360.53713843635.41.21172875621.2117287562
557.460.634465229860.63446522989.11.90361903291.9036190329
567.959.869566362459.86956636248.41.21172875621.2117287562
57859.796482179759.796482179710.11.32125866111.3212586611
586.459.578518587259.57851858729.22.1028392322.102839232
595.159.134299185859.13429918587.61.46670057231.4667005723
604.559.329438875359.32943887538.51.43878884651.4387888465
614.759.33792741759.3379274179.41.73345480371.7334548037
611.859.948898444559.94889844453.31.05547134441.0554713444
614.460.335965789360.33596578933.80.70364756290.7036475629
616.360.724396684760.72439668473.80.86672740180.8667274018
618.561.085453732361.08545373233.81.16136767671.1613676767
620.560.796189902860.79618990283.80.91464850510.9146485051
623.361.247904011461.24790401143.71.01422594131.0142259413
625.861.034109822361.03410982233.70.9262414710.926241471
627.960.527548763160.52754876313.71.40273830291.4027383029
630.460.699192742560.69919274253.40.66625865360.6662586536
632.959.766816416859.76681641684.30.97123053970.9712305397
636.259.495069820959.495069820930.87652124270.8765212427
637.660.14891749760.1489174973.91.22050315581.2205031558
640.359.634980897359.63498089733.81.04531257721.0453125772
642.660.204242250560.20424225054.51.49694500321.4969450032
646.860.525680010260.52568001024.81.54050669121.5405066912
648.960.28023087860.2802308784.61.10099504191.1009950419
652.359.809364888259.80936488823.70.9262414710.926241471
655.159.474727583359.47472758334.71.30827300291.3082730029
No Recovery
Smart Recovery
Time (minutes)
Number of Components
Number of Connected Components
Sheet3
0.23464913310.00436961790.00436961790.23786524430.00617432790.0061743279
0.23320761040.00552288760.00552288760.23845619190.00609876010.0060987601
0.23395703480.00549518090.00549518090.23708527650.0059843580.005984358
0.23532182650.0065614030.0065614030.23844513820.00477545910.0047754591
0.23298287660.00455405430.00455405430.23610178820.00577121590.0057712159
0.2327222120.00527436090.00527436090.23579978510.00589376020.0058937602
0.23345910920.00574364360.00574364360.23670566880.00559587440.0055958744
0.23258378850.00599213090.00599213090.23782254030.00503472870.0050347287
0.23304705760.00573576110.00573576110.23844829340.00613534160.0061353416
0.23414483790.0057432410.0057432410.23860783460.00633934060.0063393406
0.23433175080.00470021890.00470021890.23631635090.00659342380.0065934238
0.23192524310.00582480430.00582480430.23890288330.00571359210.0057135921
0.2327932170.00554433910.00554433910.23733490040.006396690.00639669
0.00732213250.00035416090.00035416090.0274158420.00200416350.0020041635
0.00538154670.00023268550.00023268550.03392621970.00268352610.0026835261
0.00462740320.00025040610.00025040610.03899277050.00304748480.0030474848
0.00397102250.00023462590.00023462590.04339794870.00340409990.0034040999
0.00359712040.0002529290.0002529290.04735230120.00367983030.0036798303
0.00327394160.00022706190.00022706190.05251950510.00388120.0038812
0.00309432460.00020858620.00020858620.05594072050.00432043820.0043204382
0.00293251720.00018709580.00018709580.06023060490.00469466760.0046946676
0.00280173080.00020608280.00020608280.06391433640.00519573580.0051957358
0.00268292540.00021112630.00021112630.06812735810.0051397360.005139736
0.00256604710.00019947340.00019947340.07104753290.00534900190.0053490019
0.00251088870.00019083330.00019083330.07434040180.00584590170.0058459017
0.00239682390.00019380040.00019380040.07766227210.00566017280.0056601728
0.00232263170.00018939480.00018939480.08057586570.00585087370.0058508737
0.00225107170.00017811860.00017811860.08424126480.00624007680.0062400768
0.00218891140.00017403830.00017403830.087267830.00626123440.0062612344
0.002135410.00016445610.00016445610.08940411680.00661556950.0066155695
0.00207890810.00015885530.00015885530.09321777090.00646182410.0064618241
0.00202333730.00015917870.00015917870.09580321180.00623768670.0062376867
0.00198132910.00014796260.00014796260.09833825920.00653992210.0065399221
0.00193448580.0001435530.0001435530.10108017690.00642283360.0064228336
0.00190147370.00014407930.00014407930.10337931670.00688711830.0068871183
0.00187275670.00014225870.00014225870.10531985610.00664382590.0066438259
0.00182121870.00014218640.00014218640.10869955510.00703809450.0070380945
0.00178127650.00012201590.00012201590.11039636390.00691479030.0069147903
0.0017408370.00012145980.00012145980.11264702480.00705092790.0070509279
0.00171455140.0001133480.0001133480.11403451470.00705636840.0070563684
0.00167378950.00011183660.00011183660.11639122970.00711883770.0071188377
0.00166281110.00010869340.00010869340.11832621440.00694433520.0069443352
0.00163258010.00011355530.00011355530.12019569090.00658196010.0065819601
0.00162483130.00011052230.00011052230.123276880.00706198950.0070619895
0.00161902850.00011813050.00011813050.1222289180.00709439940.0070943994
0.00161265340.00010773280.00010773280.1216049160.00706678840.0070667884
0.00162344040.00011254130.00011254130.12003288160.0067621360.006762136
0.00161234630.00010795330.00010795330.11962683770.00653108340.0065310834
0.00160633990.00011298150.00011298150.11923385410.00671601930.0067160193
0.00161198030.00011354690.00011354690.11835598180.00679794830.0067979483
0.00160738380.00010487710.00010487710.11779428320.00684153460.0068415346
0.00159460610.00010806050.00010806050.11593353890.00645363010.0064536301
0.00160228460.00011107090.00011107090.11580086550.00652481060.0065248106
0.00159881260.00011796420.00011796420.11502062420.00664953480.0066495348
0.0016001840.00010782210.00010782210.1135189620.00644398070.0064439807
0.00158873920.00011183150.00011183150.11362617820.00639389660.0063938966
0.00159870730.00011304710.00011304710.11226382060.00653775890.0065377589
0.00159058490.00011659850.00011659850.11155994120.0063347660.006334766
0.00158937110.00010974680.00010974680.11077910590.00669510250.0066951025
0.00158623230.00011110480.00011110480.11046136920.00629453630.0062945363
0.00158769690.00011172360.00011172360.10951868510.00587700220.0058770022
No Recovery
Smart Recovery
Time (minutes)
Percentage of Nodes
Average % of nodes within 6 hops
1.950.1037092210.1037092212.30.08121132680.0812113268
1.952325840.01577391680.01577391682.301531310.0130040910.013004091
1.953678870.01496655880.01496655882.301357390.0151458140.015145814
1.953590520.01548581340.01548581342.299936020.01439586730.0143958673
1.953659860.01554898810.01554898812.301190710.01471179830.0147117983
1.95328670.01584233240.01584233242.30206940.0129134980.012913498
1.953829570.0150692160.0150692162.300477490.0133495080.013349508
1.954788830.01495036340.01495036342.301931530.01507990210.0150799021
1.954610480.01533573290.01533573292.301422760.01228129710.0122812971
1.955093470.0153484970.0153484972.301902860.01212360020.0121236002
1.955146470.01500929550.01500929552.302704810.01264109870.0126410987
1.95624110.01527774920.01527774922.30515580.01327696820.0132769682
1.955672610.01536275910.01536275912.299374460.01334313260.0133431326
1.949407030.0163621560.0163621562.385655710.01208466920.0120846692
1.924790560.01623475630.01623475632.434574660.01399855730.0139985573
1.899458830.0146119190.0146119192.434213970.00972090840.0097209084
1.879404410.01464699150.01464699152.751365420.01192319760.0119231976
1.861478410.01414329210.01414329212.895688740.01404199670.0140419967
1.845404570.01427567850.01427567852.771901820.01558512940.0155851294
1.830077590.01388990820.01388990822.744917120.02043762790.0204376279
1.815186670.01354669880.01354669882.723360530.01826282540.0182628254
1.801629210.01295176480.01295176482.709334920.0154022520.015402252
1.787863530.01221522910.01221522912.704945960.01850340250.0185034025
1.775780710.01222362170.01222362172.690584370.0133624750.013362475
1.763506470.01191443460.01191443462.673471640.01276703280.0127670328
1.751881410.01156059570.01156059572.670401190.01355871690.0135587169
1.740899590.01217064010.01217064012.669586360.01587006370.0158700637
1.729868460.01152238990.01152238992.659622250.01293701650.0129370165
1.718395040.01119737910.01119737912.645290560.01328720740.0132872074
1.708831410.01086792990.01086792992.643449090.01192074630.0119207463
1.698740910.01044465320.01044465322.638378990.01394955690.0139495569
1.688730150.01039113220.01039113222.630514430.0179193070.017919307
1.679823840.00992315180.00992315182.626762040.015752020.01575202
1.670274860.00919599520.00919599522.623787740.01556958850.0155695885
1.660993660.00983735950.00983735952.615220930.01277432180.0127743218
1.652730590.0091033310.0091033312.608704750.013884860.01388486
1.644599590.00895068180.00895068182.599120710.01427321530.0142732153
1.63518380.00827392140.00827392142.595478540.01388250310.0138825031
1.627237120.00796672440.00796672442.591830480.00745244130.0074524413
1.61929370.00766958260.00766958262.590371930.01252318210.0125231821
1.610430760.00715308960.00715308962.59129970.01373700580.0137370058
1.602827430.00660019760.00660019762.581863850.0097470320.009747032
1.595842430.00623951140.00623951142.575454150.01527021490.0152702149
1.591012370.00622176530.00622176532.555467830.01274074670.0127407467
1.588599810.00613759670.00613759672.504121510.01103129350.0110312935
1.589525510.0062860220.0062860222.493408130.0110184530.011018453
1.591006360.00614508790.00614508792.41715380.01048041810.0104804181
1.592711880.00652243280.00652243282.280763280.0068162440.006816244
1.594062610.00611043860.00611043862.277970850.00746328670.0074632867
1.595470740.00588707870.00588707872.277886130.00853262940.0085326294
1.596853390.00610127940.00610127942.277024950.00827989730.0082798973
1.598685110.00620038810.00620038812.276530060.00957547590.0095754759
1.599986880.0062153160.0062153162.270571720.00612057240.0061205724
1.601840290.00576958720.00576958722.271857760.00815321520.0081532152
1.60256870.00653324890.00653324892.268769550.00934328810.0093432881
1.604181340.00629765550.00629765552.269248850.00704313060.0070431306
1.605882370.00626224890.00626224892.267515610.00844547220.0084454722
1.607175170.00590808680.00590808682.266604270.00677518430.0067751843
1.608501670.00593929190.00593929192.267836780.00873346690.0087334669
1.610523120.00607246050.00607246052.266808740.00679198090.0067919809
1.611604280.00614966230.00614966232.264537690.0058815260.005881526
No Recovery
Smart Recovery
Time (minutes)
Pings
Average Number of Pings
-
Failure Detection Results
Chart1
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
0.00131666710.0600372580.0005423320.0005423320.00038132750.0003813275
0.0028870670.1040909940.0007575850.0007575850.00089601210.0008960121
0.00503910940.1411671540.0012169570.0012169570.00118738080.0011873808
0.00448099740.1182532110.0015168390.0015168390.00073391580.0007339158
0.00498171860.1070576650.0013093460.0013093460.00099260720.0009926072
0.00514949010.1011128320.0012694170.0012694170.00176009260.0017600926
0.00496743380.0965244510.0013185590.0013185590.00152504040.0015250404
0.00480805850.0941231460.0015413970.0015413970.00172832450.0017283245
0.00526148760.0914465030.0016576230.0016576230.00177157220.0017715722
0.00579270470.0885591880.0016935770.0016935770.00088540850.0008854085
0.00509324380.0861684160.001479130.001479130.00145816420.0014581642
0.00512661410.0850345860.0016607890.0016607890.00156919370.0015691937
0.00545373770.0842780990.0015188520.0015188520.002176010.00217601
0.00650877880.0823011890.0013519810.0013519810.00070479620.0007047962
0.00569852570.0806435410.0011964770.0011964770.00109792840.0010979284
0.0064804670.0797249910.0012825430.0012825430.00090137450.0009013745
0.00559904230.0787842420.0018507420.0018507420.00128599430.0012859943
0.00543097610.0785099550.0017091330.0017091330.00150700820.0015070082
0.00557424830.0769625720.0014754990.0014754990.00177728120.0017772812
0.00599003690.0761246780.0016141980.0016141980.00180048570.0018004857
0.0059356390.0761871210.0021566290.0021566290.00133462080.0013346208
0.00530911070.0750163920.0023886690.0023886690.00084396230.0008439623
0.00524305650.0742018020.0020820190.0020820190.00135880670.0013588067
0.00566260430.0742137380.0011609130.0011609130.00267140810.0026714081
0.00555614880.0742111460.0015506690.0015506690.00170878920.0017087892
0.0056596310.0734114520.0016095320.0016095320.00125181650.0012518165
0.00403507160.0727923710.0017350440.0017350440.00084356620.0008435662
0.00476985630.0721603960.0017554250.0017554250.00087119360.0008711936
0.00405265150.0715980310.0016211380.0016211380.00180316280.0018031628
0.00424520730.0712104260.0013517440.0013517440.0019868520.001986852
0.00356325980.0567623850.0011964030.0011964030.00198522640.0019852264
0.00234859560.0332197650.0005661720.0005661720.00120865630.0012086563
0.0009965380.0090888030.0002765660.0002765660.00072484830.0007248483
000000
000000
000000
000000
00.00000523070.00001025190.000010251900
00.0000052290.00001024870.000010248700
000000
000000
00.00000526730.00001032370.000010323700
000000
000000
000000
000000
000000
000000
Random
Malicious
Time (minutes)
Percent
Percentage of Nodes Detecting Attack
rand1
This is percentage of nodes detecting a faiulre
for 1000 nodes removed at random over 5 minute period
Can you make the confidence levels for this and plot against percentage of nodes that detect failure using smart with malicious attack
Time(sec)RandomMaliciousConfidence
000000000:00
1000000000:10
2000000000:20
3000000000:30
4000000000:40
5000000000:50
6000000001:00
7000000001:10
8000000001:20
9000000001:30
10000000001:40
11000000001:50
1200000000Start
1300.00171172530.00154953510.00115566270.00084974510.00131666710.00038132750.0600372580.0005423322:10
1400.00398205550.00315267980.00181132080.00260221190.0028870670.00089601210.1040909940.0007575852:20
1500.00666094770.00485996290.00372570740.00490981960.00503910940.00118738080.1411671540.0012169572:30
1600.00530624620.00351282180.00438817710.00471674440.00448099740.00073391580.1182532110.0015168392:40
1700.00496076940.00376770820.00495074510.00624765160.00498171860.00099260720.1070576650.0013093462:50
1800.00294072910.00447686120.00627784530.00690252490.00514949010.00176009260.1011128320.0012694173:00
1900.00385806390.00478734130.00400425770.00722007260.00496743380.00152504040.0965244510.0013185593:10
2000.00508336720.00550366070.00228542410.0063597820.00480805850.00172832450.0941231460.0015413973:20
2100.00626591950.00460107190.00305234780.00712661110.00526148760.00177157220.0914465030.0016576233:30
2200.00627454980.00531968790.0047900530.00678652820.00579270470.00088540850.0885591880.0016935773:40
2300.00572567860.00299522790.00520700390.00644506470.00509324380.00145816420.0861684160.001479133:50
2400.00573594180.00289766660.00521499050.00665785730.00512661410.00156919370.0850345860.0016607894:00
2500.00605656210.0031071720.00440190410.00824931260.00545373770.002176010.0842780990.0015188524:10
2600.00642508350.0061199510.00594445010.00754563070.00650877880.00070479620.0823011890.0013519814:20
2700.00602068650.00699693560.00431255780.00546392280.00569852570.00109792840.0806435410.0011964774:30
2800.00680552690.00762538380.00560209690.00588886050.0064804670.00090137450.0797249910.0012825434:40
2900.0063918570.00558573330.00375437150.00666420740.00559904230.00128599430.0787842420.0018507424:50
3000.00741756420.00420901340.0042233210.00587400560.00543097610.00150700820.0785099550.0017091335:00
3100.00789064690.00349344980.00572489560.00518800080.00557424830.00177728120.0769625720.0014754995:10
3200.00757594510.00339453790.00692220270.00606746190.00599003690.00180048570.0761246780.0016141985:20
3300.00624869820.00396580140.00709073030.00643732620.0059356390.00133462080.0761871210.0021566295:30
3400.00448711260.00603808640.00606752060.00464372320.00530911070.00084396230.0750163920.0023886695:40
3500.00466541240.00677177570.00591746690.00361757110.00524305650.00135880670.0742018020.0020820195:50
3600.00320381030.0077643770.00826661120.00341561870.00566260430.00267140810.0742137380.0011609136:00
3700.00404799830.00700280110.00712836260.00404543330.00555614880.00170878920.0742111460.0015506696:10
3800.0051522310.00514660010.0075579880.00478170480.0056596310.00125181650.0734114520.0016095326:20
3900.00404939570.00291560370.00501122310.00416406410.00403507160.00084356620.0727923710.0017350446:30
4000.00379123660.005893090.00496316810.00443193080.00476985630.00087119360.0721603960.0017554256:40
4100.00258711720.00588800080.00235577430.00537971380.00405265150.00180316280.0715980310.0016211386:50
4200.00322580650.00605987330.00188758390.00580756550.00424520730.0019868520.0712104260.001351744End
4300.00285487710.0045445130.00110201510.0057516340.00356325980.00198522640.0567623850.0011964037:10
4400.00248480040.00298382450.00057655010.00334920720.00234859560.00120865630.0332197650.0005661727:20
4500.00079285370.00172783920.00005236420.00141309470.0009965380.00072484830.0090888030.0002765667:30
46000000007:40
47000000007:50
48000000008:00
49000000008:10
5000000005.23E-061.03E-058:20
5100000005.23E-061.02E-058:30
52000000008:40
53000000008:50
5400000005.27E-061.03E-059:00
55000000009:10
56000000009:20
57000000009:30
58000000009:40
59000000009:50
600000000010:00
rand1
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000.0005423320.0005423320.00038132750.0003813275
000.0007575850.0007575850.00089601210.0008960121
000.0012169570.0012169570.00118738080.0011873808
000.0015168390.0015168390.00073391580.0007339158
000.0013093460.0013093460.00099260720.0009926072
000.0012694170.0012694170.00176009260.0017600926
000.0013185590.0013185590.00152504040.0015250404
000.0015413970.0015413970.00172832450.0017283245
000.0016576230.0016576230.00177157220.0017715722
000.0016935770.0016935770.00088540850.0008854085
000.001479130.001479130.00145816420.0014581642
000.0016607890.0016607890.00156919370.0015691937
000.0015188520.0015188520.002176010.00217601
000.0013519810.0013519810.00070479620.0007047962
000.0011964770.0011964770.00109792840.0010979284
000.0012825430.0012825430.00090137450.0009013745
000.0018507420.0018507420.00128599430.0012859943
000.0017091330.0017091330.00150700820.0015070082
000.0014754990.0014754990.00177728120.0017772812
000.0016141980.0016141980.00180048570.0018004857
000.0021566290.0021566290.00133462080.0013346208
000.0023886690.0023886690.00084396230.0008439623
000.0020820190.0020820190.00135880670.0013588067
000.0011609130.0011609130.00267140810.0026714081
000.0015506690.0015506690.00170878920.0017087892
000.0016095320.0016095320.00125181650.0012518165
000.0017350440.0017350440.00084356620.0008435662
000.0017554250.0017554250.00087119360.0008711936
000.0016211380.0016211380.00180316280.0018031628
000.0013517440.0013517440.0019868520.001986852
000.0011964030.0011964030.00198522640.0019852264
000.0005661720.0005661720.00120865630.0012086563
000.0002765660.0002765660.00072484830.0007248483
000000
000000
000000
000000
000.00001025190.000010251900
000.00001024870.000010248700
000000
000000
000.00001032370.000010323700
000000
000000
000000
000000
000000
000000
Random
Malicious
Time (minutes)
Percent
Percentage of Nodes Detecting Attack
-
Random Node Distribution
Chart1
0.04978333440.06411744490.00022217250.0002221725
0.14935747090.15834381010.00041407250.0004140725
0.22404367460.21864879370.00042025680.0004202568
0.22404740890.21242240430.00063243020.0006324302
0.16803555670.14945113830.0006695930.000669593
0.10081965360.098474190.00051456290.0005145629
0.05040814640.05390112020.00040362690.0004036269
0.02160241110.02547436520.0002646610.000264661
0.00810036410.01162080740.0001784320.000178432
0.00269989630.00505912020.00010708660.0001070866
0.00080988790.00192042240.00005849260.0000584926
0.00022085270.00056638330.00007352970.0000735297
Binomial
RDP
Frequency
Percent of Nodes
Distribution of Random Nodes Found
Sheet1
Can you plot these 4 distributions (confidence levels) against the binomial distribution for me?
BinomialOur distributionsRDPCONF
00.04978333440.0645287830.06342349420.06481160570.06370589690.06411744490.0002221725
10.14935747090.15940963030.159000540.15834034760.15662472240.15834381010.0004140725
20.22404367460.21741688730.21830052530.21849779670.22037996550.21864879370.0004202568
30.22404740890.20976757870.21265524520.2141407140.21312607940.21242240430.0006324302
40.16803555670.1507306070.15144077360.14715056690.14848260550.14945113830.000669593
50.10081965360.09998038640.0977369790.09669752930.09948186530.098474190.0005145629
60.05040814640.05398646660.05218202350.05471109570.05472489510.05390112020.0004036269
70.02160241110.02451701480.02528103680.02639005790.02570935110.02547436520.000264661
80.00810036410.01176816710.01217416920.01163539140.01090550210.01162080740.000178432
90.00269989630.00549181130.00505620740.00495123040.00473723170.00505912020.0001070866
100.00080988790.00205942920.00191448630.00203000450.00167776960.00192042240.0000584926
110.00022085270.00034323820.00083451970.00064365990.00044411550.00056638330.0000735297
Sheet1
000.00022217250.0002221725
000.00041407250.0004140725
000.00042025680.0004202568
000.00063243020.0006324302
000.0006695930.000669593
000.00051456290.0005145629
000.00040362690.0004036269
000.0002646610.000264661
000.0001784320.000178432
000.00010708660.0001070866
000.00005849260.0000584926
000.00007352970.0000735297
Binomial
RDP
Frequency
Percent of Nodes
Distribution of Random Nodes Found
Sheet2
Sheet3
-
Messages Per Node Results
-
ConclusionsBy planning for and detecting failures our recovery method can drastically increase the likelihood that the network will not become partitionedIt lessens the impact of malicious attacks on the querying capability of the network
-
Further WorkInvestigating other techniques for random node discoveryRestoring network to a scale free topology immediately following failuresHow the Gnutella network has changed over time
-
ThanksStefan Saroiu and Steven Gribble for letting us use their data and giving us adviceArmando Fox, George Candea, Dave Patterson, Aaron BrownBling-Bling Industries, 2001
40 sec
The basis for our distributed recovery method is that each node will help build and maintain a virtual exponential network. What I mean by virtual is that connections between the nodes in the network will not be actually made, and no traffic will be sent through the network.An exponential network will be build through random node discovery, each node maintaining a list of randomly chosen nodes as its neighbors on the virtual network. The random selection of neighbors makes this network exponential, and makes it very robust to malicious attacks.
Our recovery method also requires nodes to detect malicious attacks on the active network.
When attacks are detected, nodes will begin switching over to the exponential network.
40 minutesRandom node discovery would be easy if there was a centralized name authority which could provide a truly randomly selected node in the network. Because Gnutella is decentralized, we need another way to find a random node.
Our solution is built around the idea of taking random walks through a graph and selecting the node you end up at as a random node.
To do these random walks, we propose a message called a random discovery ping. A random discovery ping is originated by a node trying to discover a random neighbor, and it is forwarded through the network for a certain number of hops, after which point the node that ended up with the ping responds to the originator.
Each node receiving the RDP forwards it to only one of its neighbors, selected at random. Our RDPs use a hop count of 20, which is approximately equal to the diameter of Gnutella.
30 secMaintenance of the virtual exponential network is quite simple. Each node discovers N random nodes, where N is the minimum number of connections the node wants to maintain. These will be the nodes neighbors on the exponential network
The node periodically pings these neighbors to see if they are alive
If a neighbor is found to be dead, discover a new random node to replace it.40 secWe believe that malicious failures are far more likely to result in the loss of a nodes second degree neighbors than its first degree neighbors. If a node with 50 neighbors is removed, then all its neighbors will lose only 1 1st degree neighbor but 50 2nd degree neighbors. This unbalanced loss should tell a node that something malicious has happened
In order to detect failures in this way, nodes keep a history of 1st and 2nd degree neighbor loss over 30 seconds.
If this loss exceeds 50% of their 2nd degree neighbors and it exceeds the percentage of 1st degree neighbors lost, the failure is marked as malicious.
50 secondsReacting to failures is quite simple. When a failure has been detected, replace each 1st degree neighbor lost with a neighbor from the exponential network.
This has the advantage that only nodes local to the attack will switch, thus preserving the rest of the network if the attack is small scale.
The only other rule is that nodes should not attempt to discover new random nodes during an attack, in order to cut down the traffic on an already stressed network.
When the attack is over, return to normal operations.
30 secondsTo run our experiments we build a generalized P2P network simulator.
This simulator handles time management, routing messages between hosts.
It also has support for connecting new hosts and disconnecting current hosts from the network, as well as support for injecting failures into the network, which in our case means killing hosts.
We used this to simulate Gnutella by building a simple Gnutella client that would interface with the simulator, as well as an enhanced client with the recovery mechanism built into it.
We also wrote logging features and metric calculation algorithms. This was written in about 5000 lines of java.
40 secondsThis graph shows the percentage of nodes that detect a malicious failure when 1000 nodes are removed from the system over five minutes. The red line shows the results when we remove nodes maliciously, and the blue line shows the results when we remove nodes randomly.
As you can see, less than 1 percent of the nodes detect a malicious attack when we remove nodes randomly, but somewhere around 20% of the nodes detect a malicious attack when we remove nodes maliciously. Also, notice that no attack is detected outside of the failure range, even though nodes are entering and leaving the system.
20 secondsThis graph shows the distribution of nodes selected using the random ping discovery technique, plotted against the binomial distribution showing perfectly random results. As you can see, there is a little starvation and a little favoritism, but the distribution is very close to random.
This graph shows the average number of messages per node per second during a malicious attack.
The top line is with our recovery method in place, and the bottom line is without it. This only counts pings and pongs and does not count query messages.
This shows that our method only increases the number of messages sent to maintain the network by about 20%. This increase is negligible compared to query traffic.
There is an increase in messages during the beginning of the attack and this lasts throughout the attack
The first increase is due to nodes connecting to new neighbors and detecting failures, while the second increase is due to nodes searching for new random neighbors.