[ppt]a dynamic mobility histogram construction method …dbgroup/public_papers/2006... · web viewa...
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A Dynamic Mobility Histogram Construction Method Based on Markov Chains
Yoshiharu Ishikawa (Nagoya University)
Yoji Machida (University of Tsukuba)
Hiroyuki Kitagawa (University of Tsukuba)
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Outline
Background and ObjectivesModeling Movement PatternsMobility Histogram: Logical StructureMobility Histogram: Physical StructureExperimental ResultsConclusions
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Background
Advance of GPS and communication technology enabled tracking of moving objectsExample: A taxi company in Tokyo monitor >200 taxi cabs continuallyMovement data is delivered as a data stream
Data Stream
Movement Data
Moving ObjectDatabase
Moving Objects
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Objectives
Construction and maintenance of a mobility histogramCompact summary of movement data for a specific time periodUsed for mobility analysis and estimationProblemsConcrete definition of a mobility histogramHow to model movement patternsCompact representationTradeoff with accuracyEfficient construction and maintenanceIncremental processing for streamed data
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Basic Idea
Movement
Data (as a
Data Stream)
Mobilityhistogram
Histogram Maintenance
Module
Incremental
updates
Mobility Analysis /estimation
Module
Query for
estimation
Request for
analysis /
estimation
Results
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Outline
Background and ObjectivesModeling Movement PatternsMobility Histogram: Logical StructureMobility Histogram: Physical StructureExperimental ResultsConclusions
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Approach
2-D movement areaUniform cell decompositionsBut allow multiple spatial granularities (e.g., 4 x 4, 16 x 16)Movement pattern is represented as a sequence of cell numbersBased on the Markov chain modelTreats a movement pattern as a Markov chain sequenceWell-known model in traffic modeling
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Movement Patterns: Example (1)
Movement pattern of A
Movement pattern of B
Movement pattern of C
2 2 0 0
3 3 1 1
0 2 2 3
0
1
2
3
3
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Movement Patterns: Example (2)
Cell partitioning with different granularities
Movement pattern of A
11 9 3 1
0
2
8
10
1
3
9
11
4
6
12
14
5
7
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15
3
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Cell Numbering Scheme (1)
Based on Z-ordering methodSimple encoding methodAssign similar values to neighboring cellsTranslation to different granularities is easy
0
2
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10
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Cell Numbering Scheme (2)
0(2)0000
1(2)0001
2(2)0010
3(2)0011
Level-1 (21x21) decomposition
Level-2 (22x22) decomposition
12
1002
20123
20123210
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Markov Chain Model (example: order = 2)
Step 0
Step 1
Step 2
2(1) 3(1) 1(1)
9(2) 12(2) 6(2)
4
021321
16
0911226
2
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Outline
Background and ObjectivesModeling Movement PatternsMobility Histogram: Logical StructureMobility Histogram: Physical StructureExperimental ResultsConclusions
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Mobility Histogram as a Data Cube
Representing order-n Markov chain statistics as a (n +1)-d data cube
Example: 1(1) 1(1) 0(1)
nn+1
4011120
1101
Sum
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Histogram Maintenance
Periodical reconstructionTo cope with non-stationary movement patternsEase of maintenanceOld histograms are written to disk
Movement
Data
Mobilityhistogram
Histogram Maintenance
Module
Incremental
updates
Mobility Analysis /
EstimationModule
Query for
analysis
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Outline
Background and ObjectivesModeling Movement PatternsMobility Histogram: Logical StructureMobility Histogram: Physical StructureExperimental ResultsConclusions
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Mobility Histogram: Physical Structure
Problems in logical structure: huge space2GB (!) for a typical parameter settingNeeds multiple cubes for multiple spatial granularitiesData cubes are sparse: most of mobility patterns are hard to occurSolution: tree-based representationUnification of quad-tree, k-d tree, and trieIntegration of cubes in multiple granularitiesSelective allocation of nodesSaves memory space
1
323221012
2GB
04
510241024102410
22GB
quad treek-d-tree
quadtree x, y 1
k-d-tree
xyxy
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Insertion of 3(2) 6(2) 12(2): BASE method
10
root
x
: counter
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10
01
level 1
level 2
Binary representation
Step 0:
Step 1:
Step 2:
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00
(=3)
(=6)
(=12)
: visited edge : non-visited edge
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+1
+1
+1
+1
+1
+1
step 0 step 1 step 2
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23612
000111011021100
2000101211
1013
0111102002
1
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Approximated Histogram (APR)
Problem of the BASE methodMemory size requirement is still highApproximated method (APR)Compact histogram construction by adaptive tree expansionAllocate a buffer for each leaf nodeIf skew is observed, the leaf node is expanded2 statistics is used to check the non-uniformityInherited the idea from decision tree construction from streamed data (e.g., VFDT)
2
42
2
k-1k-2k-3
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Node Expansion
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trans_seq[0]
trans_seq[1]
buffer
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buffer
buffer
buffer
buffer
expansion
skew isdetected
root
root
internal node
leaf node
internal orleaf node
00
01
10
11
Quit expansion when no. of nodeshas reached a given constant
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Non-uniformity Check
Use of 2 test for goodness of fit
Null hypothesis: distribution is uniformIf 2 value > 7.815, the distribution is non-uniform at the significance level 5%
Example: 100 sequences in the buffer
22
23
27
28
10
20
50
20
Uniform
Non-uniform
x00
x01
x10
x11
Distribution ofnext steps
100
1
44
4
1
2
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Problems in Statistical Test
Problems: 2 value is not reliablewhen the total number is small
when some value(s) is close to 0
Solution: use non-parametric statistics while 2 value is not reliableDetail is shown in the paper
Total number = 1 + 2 + 1 + 4 = 8
These situations arecommon in our case
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Use of Bitmap Cube (APR-BM)
Minor improvement to the APR methodUse a small bitmap cube in addition to a tree-structured histogramRepresent correct summary in some coarse levelImprovement of precision
Tree-based
histogram
(APR method)
+
Small bitmap
cube in a coarse
level
Example:
When partition level = 3,
Markov order = 2,
bitmap size = 32KB
Accurateestimation for
some queries
3
32KB
4256256256/1024/1024/82MB
5128MB
221MB4
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Outline
Background and ObjectivesModeling Movement PatternsMobility Histogram: Logical StructureMobility Histogram: Physical StructureExperimental ResultsConclusions
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Dataset and Environments
Experimental dataUsed moving objects simulator by Brinkoff10241024 in finest granularities1,000 moving objects are on the map at every time instanceEnvironmentsCPUPentium4 3.2GHzMemory1GB RAMOSCygwin
Brinkhoff10
10241024
1000
Pentium4 3.2GHzCPU1GBWindows XPOSPC
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Histogram Size
SettingsData Size: 1K, 10K, 50KOrder-2 Markov transitionResultsBASE method requires huge storage
Data Size
Histogram Size (MB)
BASEAPRAPR-BM1K0.350.010.0410K2.70.100.1350K9.40.520.55
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Construction Time
Comparison of BASE and APRM: maximal partitioning level (granularity of input sequences)ResultsBASE has small construction costAPR has nearly O(n2) cost due to non-uniformity check, but still has small processing cost (less than 0.15 ms per input sequence)
Construction Time Construction Time per Sequence
Graph3
0.00930.00540.01430.0107
0.0080.005460.011780.03302
0.006790.0296120.0094420.156186
5()
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Data Size
Construction Time (ms)
1K10
10001 100010002 100010003 1000
1011
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11111.10.01118460112.60.01126
0.1290893555
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6768
7374
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706973
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69869.80.69869169.10.691717.10.071
10007 1 10008 1 10009 1
677872
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687569
727273
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697171
737074
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70370.30.70371671.60.71671171.10.711
100010 1
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68468.40.684638.76.387
10001 1 10002 1 10003 1
1513
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3114
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20320.30.20319819.80.19815215.20.152
10004 1 10005 1 10001 1
271716
351415
381414
371414
401416
151416
131417
131536
131433
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24424.40.24414414.40.14420920.90.209
10002 1 10003 1 10004 1
171717
171516
161415
141415
141714
142814
143614
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373414
172814
17417.40.17424224.20.24214714.70.147
10005 1
15
38
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14 1
21521.50.21577.80.778
DBWS1000 19619.60.0196
1 1475147.50.01475
10
1000 1000 1 10000
5 50000 10 100000 1323241
779922324622260133041
78123104046333136114043
781244288464410896105043
78205787646551904410612042
780161504846263407210722843
779172078046574404010835645
781882456846485079610940845
7836928872466958644101072445
78031033884466106854810 41
7801 463 10710.70.010742942.90.00429
780937809.30.15618646404640.00464
11 1000012 100001K10K50K100K
382232120232260
38430010403136
38040140428810896
38150416787619044
387612016481504834072
382722828562078044040
387835641922456850796
378940853642887258644
669276483811072466923388468548
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3302330.20.033023821382.10.03821
13 1000014 10000
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3703925531440
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3709370.90.0370939103910.03915511452
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15 100005 51 1465
3605050.00551651.60.00516146481464.80.029296
363
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358 368041834.40.036688
3602360.20.03602
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13 1000014 10000
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7170
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14 1 15 1 1
6967350.93.509
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74711 4.96322489394.9632248939
7069
7169
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71971.90.71969969.90.699
11 1 12 1 13 1
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1735
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20320.30.203210210.2121921.90.219
14 1 15 1 1
15171100.22
3432
35301 5.41871921181.0837438424
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25425.40.25421421.40.214
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1K10K50K100K1K10K50K
26.342.9223.8464
35.334.9275.91374.7
45.339.4825.44250.8
55.454.61480.67346.6551.61464.8
68.4111.92970.413547.1
78174.44299.518999.9
88.9223.9526922879
99.3270.86330.927022.6
1010.7330.27809.332393.3103137644.4
1000100005000010000010001000050000
1K10K50K100K1K10K50K
20.00630.004290.0044760.00464000
30.00530.003490.0055180.013747000
40.00530.003940.0165080.042508000
50.00540.005460.0296120.0734660.0050.005160.029296
60.00840.011190.0594080.135471000
70.0080.017440.085990.189999000
80.00890.022390.105380.22879000
90.00930.027080.1266180.270226000
100.01070.033020.1561860.3239330.010.03130.152888
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1K
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ms
1K0.350.011K0.350.010.77
10K2.70.110K2.70.10.87
50K9.40.5250K9.40.521.28
0.350.01
2.70.1
9.40.52
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27
18.0769230769
0.5222222222
5K0.5233844
1K50.5636804
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(ms)
12345678910
1000 432000120228356408724
428-320012010812852316
10000 4120014041616482856419253646692
4116-12014027612321208133611721328
50000 42321040428878761504820780245682887233884
42288083248358871725732378843045012
8553763440642202009614092861449019431321657724360458243694359069327362.36438980436951E161.51320947479649E18
8554613494402236416014313062409160359936058626303590403752083429785602.40133339506278E161.53685337284018E18
12345678910
1K8518484731764910498131591508816781183141917936628072411584
85176328832918284926611929169315338650.34931182860.0110473633
10K85497729966573788318810401111766012914913992314625027984606692107072
8548922498927412258102082313649114891077463272.66881942750.1021118164
50K85545986362199613300426372281417967456402490454510717980908033884542144
8553748090311325110081371855456863843534052202639.35466766360.5170288086
1(ms)
K
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0.697
0.203
0.707
0.264
0.703
0.192
2
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6.3
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54.6
223.9
330.2
223.8
1480.6
5269
7809.3
2
5
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ms
1K
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0.0063
0.0054
0.0089
0.0107
0.00429
0.00546
0.02239
0.03302
0.004476
0.029612
0.10538
0.156186
1K
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42.9
223.8
5.3
34.9
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39.4
825.4
5.4
54.6
1480.6
8.4
111.9
2970.4
8
174.4
4299.5
8.9
223.9
5269
9.3
270.8
6330.9
10.7
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7809.3
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0.0054
0.00546
0.029612
0.0084
0.01119
0.059408
0.008
0.01744
0.08599
0.0089
0.02239
0.10538
0.0093
0.02708
0.126618
0.0107
0.03302
0.156186
(KB)
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0.35
0.01
2.7
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0.52
5() 5() 8() 8() 10() 10()
1K9.35.488.914.310.7
10K8054.6107.1223.9117.8330.2
50K339.51480.6437.25269472.17809.3
5() 5() 10() 10()
1K9.35.414.310.7
10K8054.6117.8330.2
50K339.51480.6472.17809.3
5() 5() 10() 10()
1K0.00930.00540.01430.0107
10K0.0080.005460.011780.03302
50K0.006790.0296120.0094420.156186
5() 5() 5() 10() 10() 10()
1K9.35.4514.310.710
10K8054.651.6117.8330.2313
50K339.51480.61464.8472.17809.37644.4
5() 5() 5() 10() 10() 10()
1K0.00930.00540.0050.01430.01070.01
10K0.0080.005460.005160.011780.033020.0313
50K0.006790.0296120.02920.0094420.1561860.1529
5 7809.30.15619
15 1834.40.03669
1 330.20.03302
100010 112.60.01126
0000
0000
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&A
Page &P
5()
5()
10()
10()
(ms)
1K61.569.713.520.3
10K5970.713.826.4
50K58.770.313.819.2
1K0.6150.6970.1350.203
10K0.590.7070.1380.264
50K0.5870.7030.1380.192
5 70.319.2
15 350.9110
15 0.70.192
1(15) 3.5091.1
1
100010
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DBWS 100 1
1000 60.40.604
10000 61.70.617
1000 44.40.444
10000 41.90.419
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717468
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726870
686872
677370
727068
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69769.70.69770770.70.70770370.30.703
10 1
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70 69.770.770.3
69 20.326.419.2
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68K10K50K
72 0.6970.7070.703
73 0.2030.2640.192
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71571.50.000715
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142516
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20320.30.20326426.40.26419219.20.192
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1K10K
query:821689(10)->819832(10)->644146(10)0query:821689(10)->819832(10)->644146(10)0
query:445292(10)->445828(10)->447013(10)0query:445292(10)->445828(10)->447013(10)0
query:853121(10)->853053(10)->853071(10)0query:853121(10)->853053(10)->853071(10)0
query:251441(10)->229003(10)->227630(10)0query:251441(10)->229003(10)->227630(10)0
query:932312(10)->932878(10)->930770(10)0query:932312(10)->932878(10)->930770(10)0
query:467944(10)->467884(10)->467706(10)0query:467944(10)->467884(10)->467706(10)0
query:958480(10)->952993(10)->778110(10)0query:958480(10)->952993(10)->778110(10)0
query:260750(10)->260105(10)->255815(10)0query:260750(10)->260105(10)->255815(10)0
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2(2)->2(2)->2(2)422(2)->2(2)->2(2)200
7(2)->2(2)->7(2)07(2)->2(2)->7(2)0
6(3)->0(3)->1(3)06(3)->0(3)->1(3)0
2(1)->2(1)->2(1)1652(1)->2(1)->2(1)2179
2(2)->2(2)->3(2)32(2)->2(2)->3(2)19
2(2)->2(2)->2(2)422(2)->2(2)->2(2)200
7(2)->2(2)->7(2)07(2)->2(2)->7(2)0
6(3)->0(3)->1(3)06(3)->0(3)->1(3)0
2(1)->2(1)->2(1)1652(1)->2(1)->2(1)2179
2(2)->2(2)->3(2)32(2)->2(2)->3(2)19
2(2)->2(2)->2(2)422(2)->2(2)->2(2)200
7(2)->2(2)->7(2)07(2)->2(2)->7(2)0
6(3)->0(3)->1(3)06(3)->0(3)->1(3)0
2(1)->2(1)->2(1)1652(1)->2(1)->2(1)2179
2(2)->2(2)->3(2)32(2)->2(2)->3(2)19
2(2)->2(2)->2(2)422(2)->2(2)->2(2)200
7(2)->2(2)->7(2)07(2)->2(2)->7(2)0
6(3)->0(3)->1(3)06(3)->0(3)->1(3)0
2(1)->2(1)->2(1)1652(1)->2(1)->2(1)2179
2(2)->2(2)->3(2)32(2)->2(2)->3(2)19
2(2)->2(2)->2(2)422(2)->2(2)->2(2)200
7(2)->2(2)->7(2)07(2)->2(2)->7(2)0
6(3)->0(3)->1(3)06(3)->0(3)->1(3)0
2(1)->2(1)->2(1)1652(1)->2(1)->2(1)2179
2(2)->2(2)->3(2)32(2)->2(2)->3(2)19
2(2)->2(2)->2(2)422(2)->2(2)->2(2)200
7(2)->2(2)->7(2)07(2)->2(2)->7(2)0
6(3)->0(3)->1(3)06(3)->0(3)->1(3)0
2(1)->2(1)->2(1)1652(1)->2(1)->2(1)2179
2(2)->2(2)->3(2)32(2)->2(2)->3(2)19
2(2)->2(2)->2(2)422(2)->2(2)->2(2)200
7(2)->2(2)->7(2)07(2)->2(2)->7(2)0
6(3)->0(3)->1(3)06(3)->0(3)->1(3)0
2(1)->2(1)->2(1)1652(1)->2(1)->2(1)2179
2(2)->2(2)->3(2)32(2)->2(2)->3(2)19
2(2)->2(2)->2(2)422(2)->2(2)->2(2)200
7(2)->2(2)->7(2)07(2)->2(2)->7(2)0
6(3)->0(3)->1(3)06(3)->0(3)->1(3)0
277531544
1 1
27.75315.44
50K200K
0(1)->1(1)->1(1)449
2(1)->2(1)->2(1)11599
2(2)->2(2)->3(2)64
2(2)->2(2)->2(2)860
7(2)->2(2)->7(2)0
6(3)->0(3)->1(3)0
9(4)->6(4)->25(4)0
43(4)->82(4)->30(4)0.000015
64(3)->1(3)->0(3)0
3(3)->8(3)->15(3)0
22(5)->33(5)->26(5)0
470(8)->730(8)->315(8)0
0(1)->1(1)->1(1)449
2(1)->2(1)->2(1)11599
2(2)->2(2)->3(2)64
2(2)->2(2)->2(2)860
7(2)->2(2)->7(2)0
6(3)->0(3)->1(3)0
9(4)->6(4)->25(4)0
43(4)->82(4)->30(4)0.000015
64(3)->1(3)->0(3)0
3(3)->8(3)->15(3)0
22(5)->33(5)->26(5)0
470(8)->730(8)->315(8)0
0(1)->1(1)->1(1)449
2(1)->2(1)->2(1)11599
2(2)->2(2)->3(2)64
2(2)->2(2)->2(2)860
7(2)->2(2)->7(2)0
6(3)->0(3)->1(3)0
9(4)->6(4)->25(4)0
43(4)->82(4)->30(4)0.000015
64(3)->1(3)->0(3)0
3(3)->8(3)->15(3)0
22(5)->33(5)->26(5)0
470(8)->730(8)->315(8)0
0(1)->1(1)->1(1)449
2(1)->2(1)->2(1)11599
2(2)->2(2)->3(2)64
2(2)->2(2)->2(2)860
7(2)->2(2)->7(2)0
6(3)->0(3)->1(3)0
9(4)->6(4)->25(4)0
43(4)->82(4)->30(4)0.000015
64(3)->1(3)->0(3)0
3(3)->8(3)->15(3)0
22(5)->33(5)->26(5)0
470(8)->730(8)->315(8)0
0(1)->1(1)->1(1)449
2(1)->2(1)->2(1)11599
2(2)->2(2)->3(2)64
2(2)->2(2)->2(2)860
7(2)->2(2)->7(2)0
6(3)->0(3)->1(3)0
9(4)->6(4)->25(4)0
43(4)->82(4)->30(4)0.000015
64(3)->1(3)->0(3)0
3(3)->8(3)->15(3)0
22(5)->33(5)->26(5)0
470(8)->730(8)->315(8)0
2(1)->2(1)->2(1)11599
2(2)->2(2)->3(2)64
2(2)->2(2)->2(2)860
7(2)->2(2)->7(2)0
6(3)->0(3)->1(3)0
2(1)->2(1)->2(1)11599
2(2)->2(2)->3(2)64
2(2)->2(2)->2(2)860
7(2)->2(2)->7(2)0
6(3)->0(3)->1(3)0
2(1)->2(1)->2(1)11599
2(2)->2(2)->3(2)64
2(2)->2(2)->2(2)860
7(2)->2(2)->7(2)0
6(3)->0(3)->1(3)0
2(1)->2(1)->2(1)11599
2(2)->2(2)->3(2)64
2(2)->2(2)->2(2)860
7(2)->2(2)->7(2)0
6(3)->0(3)->1(3)0
2(1)->2(1)->2(1)11599
2(2)->2(2)->3(2)64
2(2)->2(2)->2(2)860
7(2)->2(2)->7(2)0
6(3)->0(3)->1(3)0
2(1)->2(1)->2(1)11599
2(2)->2(2)->3(2)64
2(2)->2(2)->2(2)860
7(2)->2(2)->7(2)0
6(3)->0(3)->1(3)0
2(1)->2(1)->2(1)11599
2(2)->2(2)->3(2)64
2(2)->2(2)->2(2)860
7(2)->2(2)->7(2)0
6(3)->0(3)->1(3)0
2(1)->2(1)->2(1)11599
2(2)->2(2)->3(2)64
2(2)->2(2)->2(2)860
7(2)->2(2)->7(2)0
6(3)->0(3)->1(3)0
165044.000075
1
1650.44000075
1
0
()
vs vs
()
0.00630.00540.00890.0107
0.004290.005460.022390.03302
0.0044760.0296120.105380.156186
0.004640.0734660.228790.323933
2
5
8
10
(ms)
2
5
8
10
(ms)
1K
1K
1K
1K
10K
10K
10K
10K
50K
50K
50K
50K
100K
100K
100K
100K
6.3
5.4
8.9
10.7
42.9
54.6
223.9
330.2
223.8
1480.6
5269
7809.3
464
7346.6
22879
32393.3
1K
10K
50K
100K
(ms)
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
6
6
6
6
7
7
7
7
8
8
8
8
9
9
9
9
10
10
10
10
0.0063
0.00429
0.004476
0.00464
0.0053
0.00349
0.005518
0.013747
0.0053
0.00394
0.016508
0.042508
0.0054
0.00546
0.029612
0.073466
0.0084
0.01119
0.059408
0.135471
0.008
0.01744
0.08599
0.189999
0.0089
0.02239
0.10538
0.22879
0.0093
0.02708
0.126618
0.270226
0.0107
0.03302
0.156186
0.323933
1K
10K
50K
100K
(ms)
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
6
6
6
6
7
7
7
7
8
8
8
8
9
9
9
9
10
10
10
10
6.3
42.9
223.8
464
5.3
34.9
275.9
1374.7
5.3
39.4
825.4
4250.8
5.4
54.6
1480.6
7346.6
8.4
111.9
2970.4
13547.1
8
174.4
4299.5
18999.9
8.9
223.9
5269
22879
9.3
270.8
6330.9
27022.6
10.7
330.2
7809.3
32393.3
(ms)
K
K
10K
10K
50K
50K
69.7
20.3
70.7
26.4
70.3
19.2
1(ms)
K
K
10K
10K
50K
50K
0.697
0.203
0.707
0.264
0.703
0.192
Graph5
9.35.414.310.7
8054.6117.8330.2
339.51480.6472.17809.3
5()
5()
10()
10()
Data Size
Construction Time (ms)
1K10
10001 100010002 100010003 1000
1011
1011
1011
1111
1111
1110
1410
1110
7247721080011
13 14
10710.70.010711111.10.0111110110.011
10004 100010005 100010006 1000
111111
11912
11912
11912
12912
14912
141215
11913
940115729110014
11 15
11711.70.0117868.60.008612812.80.0128
10007 100010008 100010009 1000
141014
141211
121311
121011
121113
121111
121111
121111
1000127281184811
12 11 17
12412.40.012411111.10.011112112.10.0121
100010 1000
12
11
11
11
11
11
11
11
97611
11
11111.10.01118460112.60.01126
0.1290893555
10
10001 1 10002 1 10003 1
6768
7374
6971
7071
7274
6969
7664
6875
7273
7566
69769.70.69771171.10.71170570.50.705
10004 1 10005 1 10006 1
706973
656877
726869
736769
727065
676967
746767
706773
677368
687368
69869.80.69869169.10.691717.10.071
10007 1 10008 1 10009 1
677872
727870
687569
727273
686672
697171
737074
726868
686671
747271
70370.30.70371671.60.71671171.10.711
100010 1
66
65
74
68
65
70
69
71
69
67 1
68468.40.684638.76.387
10001 1 10002 1 10003 1
1513
3314
3114
3313
1314
1413
1414
1413
1715
1429
20320.30.20319819.80.19815215.20.152
10004 1 10005 1 10001 1
271716
351415
381414
371414
401416
151416
131417
131536
131433
131432
24424.40.24414414.40.14420920.90.209
10002 1 10003 1 10004 1
171717
171516
161415
141415
141714
142814
143614
143914
373414
172814
17417.40.17424224.20.24214714.70.147
10005 1
15
38
34
42
15
14
14
16
13
14 1
21521.50.21577.80.778
DBWS1000 19619.60.0196
1 1475147.50.01475
10
1000 1000 1 10000
5 50000 10 100000 1323241
779922324622260133041
78123104046333136114043
781244288464410896105043
78205787646551904410612042
780161504846263407210722843
779172078046574404010835645
781882456846485079610940845
7836928872466958644101072445
78031033884466106854810 41
7801 463 10710.70.010742942.90.00429
780937809.30.15618646404640.00464
11 1000012 100001K10K50K100K
382232120232260
38430010403136
38040140428810896
38150416787619044
387612016481504834072
382722828562078044040
387835641922456850796
378940853642887258644
669276483811072466923388468548
379
3302330.20.033023821382.10.03821
13 1000014 10000
374389
374388
3723901000 10001 100005 50000
3703925531440
3663955521464
3773945521467
3713975521445
3663895511557
741636978523915511449
370 385 5511446
3709370.90.0370939103910.03915511452
5521463
15 100005 51 1465
3605050.00551651.60.00516146481464.80.029296
363
360
362
361
358
363
355
7196362
358 368041834.40.036688
3602360.20.03602
16
0.5615844727
5
11 1000012 10000
63
62
61
68
64
64
64
65
41669267
63
54654.60.0054664164.10.00641
13 1000014 10000
6867
6564
6769
6864
7066
7266
6566
6866
6527065263
65 64
67867.80.0067865565.50.00655
15 10000
55
57
58
56
54
56
54
57
52854
57 2940307.80.03078
55855.80.00558
16
0.0448608398
10
11 1 12 1 13 1
7170
7066
6871
6973
6575
6667
6962
7267
7070
7172
70770.70.70769169.10.69169369.30.693
14 1 15 1 1
6967350.93.509
6869
74711 4.96322489394.9632248939
7069
7169
6966
6970
7972
7574
7572
71971.90.71969969.90.699
11 1 12 1 13 1
1415
1735
1515
2935
1716
3215
1418
2828
1515
2927
20320.30.203210210.2121921.90.219
14 1 15 1 1
15171100.22
3432
35301 5.41871921181.0837438424
1515
3616
1638
1515
3516
1618
3717
25425.40.25421421.40.214
0000
0000
0000
0000
0000
0000
0000
0000
0000
1K
10K
50K
100K
1K10K50K100K1K10K50K
26.342.9223.8464
35.334.9275.91374.7
45.339.4825.44250.8
55.454.61480.67346.6551.61464.8
68.4111.92970.413547.1
78174.44299.518999.9
88.9223.9526922879
99.3270.86330.927022.6
1010.7330.27809.332393.3103137644.4
1000100005000010000010001000050000
1K10K50K100K1K10K50K
20.00630.004290.0044760.00464000
30.00530.003490.0055180.013747000
40.00530.003940.0165080.042508000
50.00540.005460.0296120.0734660.0050.005160.029296
60.00840.011190.0594080.135471000
70.0080.017440.085990.189999000
80.00890.022390.105380.22879000
90.00930.027080.1266180.270226000
100.01070.033020.1561860.3239330.010.03130.152888
000
000
000
000
000
000
000
000
000
1K
10K
50K
ms
1K0.350.011K0.350.010.77
10K2.70.110K2.70.10.87
50K9.40.5250K9.40.521.28
0.350.01
2.70.1
9.40.52
35
27
18.0769230769
0.5222222222
5K0.5233844
1K50.5636804
1K
10K
50K
ms
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
8
10
ms
0
0
0
0
0
0
0
0
0
0
0
0
2
5
8
10
ms
0
0
0
0
0
0
0
0
0
0
0
0
0.350.01
2.70.1
9.40.52
(MB)
vs vs
(MB)
5K
1K5
0.52
0.56
MB
1K
1K
1K
10K
10K
10K
50K
50K
50K
0.35
0.01
0.77
2.7
0.1
0.87
9.4
0.52
1.28
69.720.3
70.726.4
70.319.2
(ms)
12345678910
1000 432000120228356408724
428-320012010812852316
10000 4120014041616482856419253646692
4116-12014027612321208133611721328
50000 42321040428878761504820780245682887233884
42288083248358871725732378843045012
8553763440642202009614092861449019431321657724360458243694359069327362.36438980436951E161.51320947479649E18
8554613494402236416014313062409160359936058626303590403752083429785602.40133339506278E161.53685337284018E18
12345678910
1K8518484731764910498131591508816781183141917936628072411584
85176328832918284926611929169315338650.34931182860.0110473633
10K85497729966573788318810401111766012914913992314625027984606692107072
8548922498927412258102082313649114891077463272.66881942750.1021118164
50K85545986362199613300426372281417967456402490454510717980908033884542144
8553748090311325110081371855456863843534052202639.35466766360.5170288086
1(ms)
K
K
10K
10K
50K
50K
0.697
0.203
0.707
0.264
0.703
0.192
2
5
8
10
ms
1K
1K
1K
1K
10K
10K
10K
10K
50K
50K
50K
50K
6.3
5.4
8.9
10.7
42.9
54.6
223.9
330.2
223.8
1480.6
5269
7809.3
2
5
8
10
ms
1K
1K
1K
1K
10K
10K
10K
10K
50K
50K
50K
50K
0.0063
0.0054
0.0089
0.0107
0.00429
0.00546
0.02239
0.03302
0.004476
0.029612
0.10538
0.156186
1K
10K
50K
ms
2
2
2
3
3
3
4
4
4
5
5
5
6
6
6
7
7
7
8
8
8
9
9
9
10
10
10
6.3
42.9
223.8
5.3
34.9
275.9
5.3
39.4
825.4
5.4
54.6
1480.6
8.4
111.9
2970.4
8
174.4
4299.5
8.9
223.9
5269
9.3
270.8
6330.9
10.7
330.2
7809.3
1K
10K
50K
ms
2
2
2
3
3
3
4
4
4
5
5
5
6
6
6
7
7
7
8
8
8
9
9
9
10
10
10
0.0063
0.00429
0.004476
0.0053
0.00349
0.005518
0.0053
0.00394
0.016508
0.0054
0.00546
0.029612
0.0084
0.01119
0.059408
0.008
0.01744
0.08599
0.0089
0.02239
0.10538
0.0093
0.02708
0.126618
0.0107
0.03302
0.156186
(KB)
1K
1K
10K
10K
50K
50K
0.35
0.01
2.7
0.1
9.4
0.52
5() 5() 8() 8() 10() 10()
1K9.35.488.914.310.7
10K8054.6107.1223.9117.8330.2
50K339.51480.6437.25269472.17809.3
5() 5() 10() 10()
1K9.35.414.310.7
10K8054.6117.8330.2
50K339.51480.6472.17809.3
5() 5() 10() 10()
1K0.00930.00540.01430.0107
10K0.0080.005460.011780.03302
50K0.006790.0296120.0094420.156186
5() 5() 5() 10() 10() 10()
1K9.35.4514.310.710
10K8054.651.6117.8330.2313
50K339.51480.61464.8472.17809.37644.4
5() 5() 5() 10() 10() 10()
1K0.00930.00540.0050.01430.01070.01
10K0.0080.005460.005160.011780.033020.0313
50K0.006790.0296120.02920.0094420.1561860.1529
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ms
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