The Factor: Inferring Protocol Performance Using Inter-link Reception Correlation

Transcription

1 The Factor: Inferring Protocol Performance Using Inter-link Reception Correlation Kannan Srinivasan, Mayank Jain, Jung Il Choi, Tahir Azim, Edward S Kim, Philip Levis and Bhaskar Krishnamachari MobiCom rd Sep 2010

2 Spatial Independence Assumption Losses on different links are independent after a link failure, routing protocols choose the next shortest path forwarder simulators explicitly generate channel states independently 2

3 Spatial Independence Assumption Losses on different links are independent after a link failure, routing protocols choose the next shortest path forwarder simulators explicitly generate channel states independently When is this assumption safe? Why does it matter? 3

4 Inter-link (Spatial) Correlation (a) Real Trace, Mirage 4

5 Inter-link (Spatial) Correlation (a) Real Trace, Mirage (b) Synthetic (Independent) Trace (Every link has the same packet reception ratio (PRR) as in real trace) 5

6 Inter-link (Spatial) Correlation (a) Real Trace, Mirage (b) Synthetic (Independent) Trace Losses are well aligned (correlated) 6

7 Traditional Routing n1 So what? S n2 n D Edge weights are PRRs S selects n5 as next-hop ETX: expected number of transmissions 0.2 n ETX = = n5 7

8 Opportunistic Routing n1 So what? S n2 n D S lists n1-n5 as next-hops S stops as soon as at least one of the next 0.2 n4 1.0 hop nodes receives n5 8

9 Opportunistic Routing n1 So what? S n2 n D Independent: ETX = 1 1 (1 0.2) = n4 1.0 n5 9

10 Opportunistic Routing n1 So what? S n2 n D Independent: ETX = 1 1 (1 0.2) = n Perfectly Correlated: ETX = 1 1 (1 0.2) + 1 = 6.0 n5 Same cost as traditional routing (without coordination cost)! Correlation has implications to protocol performance 10

11 So far Spatial correlation assumption does not always hold true a measured network: 70% of link pairs are highly correlated The degree of correlation has implications to protocol performance 11

12 Problem Statement Need a good way to measure spatial correlation to understand its implications to protocol performance existing metrics conflate correlation with link pair PRRs 12

13 Research Contributions Present a new metric: Show how well network coding protocols perform, based on Show s ability to predict opportunistic routing protocol performance (in paper) perfect prediction when a node has 2 potential forwarders more than 2 forwarders: perfect prediction for most of the nodes 13

14 Outline Desired Metric Properties The Metric s Usefulness Open Questions 14

15 Outline Desired Metric Properties The Metric s Usefulness Open Questions 15

16 Desired Metric Properties a) A scalar with a finite range: [-1,1] >0: positive correlation <0: negative correlation P x x t P y y 16

17 Desired Metric Properties a) A scalar with a finite range: [-1,1] b) Symmetric P x x t P y y Metric(x,y) = Metric(y,x) 17

18 Desired Metric Properties a) A scalar with a finite range: [-1,1] b) Symmetric c) Irrespective of PRRs: P x x t P y y 1 for perfectly positively correlated link pair -1 for perfectly negatively correlated link pair 18

19 Desired Metric Properties a) A scalar with a finite range: [-1,1] b) Symmetric c) Irrespective of PRRs: P x x t P y y 1 for perfectly positively correlated link pair -1 for perfectly negatively correlated link pair Not a made-up property! 19

20 Perfect Positive Correlation (Metric = 1) Same PRR Link Pair x t y Opportunistic routing should choose x or y, but not both 20

21 Perfect Positive Correlation (Metric = 1) Same PRR Link Pair t x y Different PRR Link Pair t x y Opportunistic routing should only choose x 21

22 Perfect Negative Correlation (Metric = -1) Sum of Link Pair PRRs = 1 x t y Every packet succeeds on only one link 22

23 Perfect Negative Correlation (Metric = -1) Sum of Link Pair PRRs = 1 x t y Sum of Link Pair PRRs > 1 t x y Every packet succeeds at one or both the links 23

24 Perfect Negative Correlation (Metric = -1) Sum of Link Pair PRRs < 1 x t y Opportunistic routing benefits most, given the two PRRs 24

25 Desired Metric Properties a) A scalar with a finite range: [-1,1] b) Symmetric c) Irrespective of PRRs: P x x t P y y 1 for perfectly positively correlated link pair -1 for perfectly negatively correlated link pair 25

26 An existing metric: A recent inter-link correlation metric [1,2,3]: = P(x=0 y=0) - P(x=0) =0 losses are independent t P x x P y y [1] A. Miu, G. Tan, H. Balakrishnan and J. Apostolopoulos, Divert: fine-grained path selection for wireless LANs, MobiSys [2] C. Reis, R. Mahajan, M. Rodrig, D. Wetherall and J. Zahorjan, Measurement-based models for delivery and interference in static wireless networks, SIGCOMM CCR [3] R. Laufer, H. D.-Ferriere and L. Kleinrock, "Multirate Anypath Routing in Wireless Mesh Networks, INFOCOM

27 is not the desired metric = P(x=0 y=0) - P(x=0) a) A scalar with a finite range of [-1,1] b) Symmetric c) Irrespective of PRRs: 1 for perfectly positively correlated link pair -1 for perfectly negatively correlated link pair 27

28 is not symmetric x t y = P(x=0 y=0) - P(x=0) x,y = 4/7-4/10 =

29 is not symmetric x t y = P(x=0 y=0) - P(x=0) x,y = 4/7-4/10 = 0.17 = P(y=0 x=0) - P(y=0) y,x = 1-7/10 = 0.3 x,y y,x 29

30 does not satisfy property (c) c) 1 for perfectly positively correlated link pair For the same PRR case (P(x=1) = P(y=1)): = P(x=0 y=0) - P(x=0) t x y P(x=0 y=0) = 1 = P(x=1) 1 looks independent for low PRR link pairs 30

31 does not satisfy property (c) c) 1 for perfectly positively correlated link pair For the same PRR case (P(x=1) = P(y=1)): = P(x=0 y=0) - P(x=0) t x y P(x=0 y=0) = 1 = P(x=1) 1 is not the desired metric 31

32 Cross-correlation Index: ρ ρ = { 0, P(x=1,y=1) - P(x=1).P(y=1) P(x=1)P(x=0)P(y=1)P(y=0) otherwise, P(x=a)P(y=a) 0 a {0,1} 32

33 Cross-correlation Index: ρ ρ = { 0, P(x=1,y=1) - P(x=1).P(y=1) P(x=1)P(x=0)P(y=1)P(y=0) otherwise, P(x=a)P(y=a) 0 a {0,1} a) A scalar with a finite range of [-1,1] b) Symmetric c) Irrespective of PRRs: 1 for perfectly positively correlated link pair -1 for perfectly negatively correlated link pair 33

34 ρ does not satisfy property (c) c) 1 for perfectly positively correlated link pair For the same PRR case (Px(1) = Py(1)): ρ = 2 Px,y(1,1) - Px(1) Px(1).Px(0) t x y Px,y(1,1) = Px(1) ρ = 1 Works when PRRs are same 34

35 ρ does not satisfy property (c) c) 1 for perfectly positively correlated link pair For the different PRR case (Px(1) Py(1)): Px,y(1,1) = min(px(1), Py(1)) t x ρ = y Px(0).Py(1) Px(1).Py(0) 1 Does NOT work when PRRs are different 35

36 ρ does not satisfy property (c) Similarly, for perfectly negatively correlated link pairs: is -1: only when PRRs sum to 1 does not work for other cases ρ is not the desired metric 36

37 Outline Desired Metric Properties The Metric s Usefulness Open Questions 37

38 New Metric: ρ almost satisfied all the desired properties Normalizing ρ satisfies all the properties: { ρ ρmax -ρ ρmin, if ρ>0, if ρ<0 0, otherwise 38

39 New Metric: { ρ ρmax -ρ ρmin, if ρ>0, if ρ<0 0, otherwise [-1.0, 1.0], Px, Py (0, 1) 0: independent pairs >0: positively correlated pairs 1: perfectly positively correlated pairs <0: negatively correlated pairs -1: perfectly negatively correlated pairs 39

40 on Mirage Ch 16 Ch 26 More correlated (Mirage) 40

41 WiFi (802.11) and Spectrum 41

42 WiFi (802.11) and Spectrum WiFi No WiFi 42

43 Outline Desired Metric Properties The Metric s Usefulness Open Questions 43

44 How useful is? Dissemination: Deliver large data to all nodes Eg. SPIN, RBP Deluge (standard protocol) Rateless Deluge (network coding) Compare the total time for dissemination 44

45 Dissemination Deluge: R1 P1 R2 P2 S P3 P4 original pkts R3 R4 Number of transmissions from S: 4 45

46 Dissemination Deluge: R1 P2 P3 P4 R2 P1 P3 P4 P1 P2 S P3 R3 P1 P2 P4 P4 original pkts R4 P1 P2 P3 Number of transmissions from S: 4 46

47 Dissemination Deluge: R1 P2 P3 P4 need P1 P1 need P2 R2 P1 P3 P4 P2 P3 S need P3 R3 P1 P2 P4 P4 original need P4 pkts R4 P1 P2 P3 Number of transmissions from S: 4 47

48 Dissemination Deluge: R1 P1 P2 P3 P4 R2 P1 P2 P3 P4 P1 P2 S P3 R3 P1 P2 P3 P4 P4 original pkts R4 P1 P2 P3 P4 Number of transmissions from S: 4+4 = 8 48

49 Dissemination with Network Coding Rateless Deluge: R1 P1 c1 R2 P2 c2 S P3 P4 original pkts c3 c4 coded pkts R3 R4 49

50 Dissemination with Network Coding Rateless Deluge: R1 c2 c3 c4 R2 c1 c3 c4 P1 c1 P2 c2 S P3 c3 R3 c1 c2 c4 P4 c4 original coded pkts pkts R4 c1 c2 c3 Number of transmissions from S: 4 50

51 Dissemination with Network Coding Rateless Deluge: need 1 R1 c2 c3 c4 P1 need 1 R2 c1 c3 c4 P2 P3 S need 1 R3 c1 c2 c4 P4 original need 1 pkts R4 c1 c2 c3 Number of transmissions from S: 4 51

52 Dissemination with Network Coding Rateless Deluge: R1 c5 c2 c3 c4 R2 c1 c5 c3 c4 P1 P2 c5 S P3 R3 c1 c2 c5 c4 P4 original coded pkts pkts R4 c1 c2 c3 c5 Number of transmissions from S:4+1=5 52

53 Deluge vs Rateless Deluge Correlation Type Rateless Deluge Deluge (# of pkts) (# of pkts) Perfect Negative 8 5 Rateless Deluge is great! 53

54 Deluge vs Rateless Deluge Correlation Type Rateless Deluge Deluge (# of pkts) (# of pkts) Perfect Negative 8 5 Perfect Positive

55 Total Dissemination Time Correlation Type Rateless Deluge Deluge (# of pkts) (# of pkts) Perfect Negative 8 5 Perfect Positive 5 5 Total dissemination time: Deluge = 5p Rateless = 5p + 5c p = time to send packets, c = time to code In this case, Deluge is better! 55

56 A Controlled Study 1 transmitter at highest tx power 7 single-hop receivers with perfect reception Independent Losses: Receivers randomly (with prob. Pr) drop packets Correlated Losses: Transmitter randomly (with prob. Pt) drops packets from tx queue Vary Pt and Pr to vary spatial correlation and PRR of links 56

57 A Controlled Study PRR = 0.8 Better When PRR is high, Deluge is better! 57

58 A Controlled Study PRR = 0.8 PRR = 0.4 When PRR is low, Rateless Deluge is almost always better! 58

59 Dissemination Time Performance Deluge is better Rateless Deluge is better Shows how much faster Rateless Deluge is over Deluge 59

60 Uncontrolled Experiment Measureκand then run the experiment 1 transmitter (injection point) and 8 receivers 3 setups Ch 16: high correlation Ch 26: medium correlation Movement: low correlation 60

61 Deluge vs Rateless Deluge Scenario Avg κ Avg PRR Ch16 (High) Ch % Time (sec) Ch16 Deluge Rateless Deluge (Network Coding) 61

62 Deluge vs Rateless Deluge Scenario Avg κ Avg PRR Ch16 (High) Ch26 (Medium) Ch26 Ch16 Time (sec) % -33% 0 Ch16 Ch26 Deluge Rateless Deluge (Network Coding) 62

63 Deluge vs Rateless Deluge Scenario Avg κ Avg PRR Ch16 (High) Ch26 (Medium) Movement (Low) % Ch26 Ch16 Time (sec) % -33% Movement 0 Ch16 Ch26 Movement Deluge Rateless Deluge (Network Coding) 63

64 Outline Desired Metric Properties The Metric s Usefulness Open Questions 64

65 Open Questions can change over time how to measure it online? useful for adaptive protocol design Is useful with adaptive protocols? adaptive rate adaptive packet size adaptive channel and bandwidth 65

66 Summary Presented a spatial correlation metric, does not conflate correlation with PRRs has great predictive qualities predicts network coding protocol performance shows how well opportunistic routing protocols perform 66

67 A Shameless Advertisement I m looking for a faculty/research position contact: srikank@stanford.edu Mayank and Jung Il are looking for industrial research positions contact for Mayank: mayjain@stanford.edu contact for Jung Il: jungilchoi@stanford.edu 67

68 Backup Slides 68

69 on networks Roofnet (Outdoor) SWAN (Indoor) 69

70 Anypath ETX Ratio Py A B C Px s: Anypath ETX Ratio = E[A] E[A]inde E[A] max E[A] inde, E[A] E[A] inde E[A] inde E[A] min, PBC E[A] E[A] inde otherwise. where, the max, independent and min anypath ETX s 70

71 Opportunistic Routing: and Roofnet 11Mbps 71

72 Causes WiFi No WiFi Movement 72