M&M: Multi-level Markov Model for Wireless Link Simulations

Transcription

1 M&M: Multi-level Markov Model for Wireless Link Simulations Miguel Á. Carreira-Perpiñán Alberto Cerpa School of Engineering University of California Merced Merced, CA, 95343, USA November 3, / 29

2 2 / 29

3 SimCity - The World of Simulation 1 Computation and communication models 2 Testing of novel ideas, CHEAPLY 3 Design decisions 4 Core Component: Wireless Communication 3 / 29

4 Why leave SimCity? Simulator Assumption [Kotz et al. MSWiM 04] 1 The world is flat. 2 A radios transmission area is circular 3 All radios have equal range 4 If I can hear you, you can hear me (symmetry) 5 If I can hear you at all, I can hear you perfectly 6 Signal strength is a simple function of distance 4 / 29

5 Why leave SimCity? Simulator Assumption [Kotz et al. MSWiM 04] 1 The world is flat. 2 A radios transmission area is circular 3 All radios have equal range 4 If I can hear you, you can hear me (symmetry) 5 If I can hear you at all, I can hear you perfectly 6 Signal strength is a simple function of distance 4 / 29

6 Why leave SimCity? Simulator Assumption [Kotz et al. MSWiM 04] 1 The world is flat. 2 A radios transmission area is circular 3 All radios have equal range 4 If I can hear you, you can hear me (symmetry) 5 If I can hear you at all, I can hear you perfectly 6 Signal strength is a simple function of distance Simulation does not mimic reality 4 / 29

7 Statement How can we model wireless links so that we can improve quality of simulation results? 5 / 29

8 Wireless Link Quality in Sensor Networks Good Link Bad Link 6 / 29

9 Wireless Link Quality in Sensor Networks Intermediate Links Difficult to Model 7 / 29

10 8 / 29

11 8 / 29

12 GOAL: Replicate multiscale structure present in wireless links. 8 / 29

13 Wireless ing 9 / 29

14 Gilbert Model 2 State model Bernoulli output distribution. 10 / 29

15 Our Modeling Approach Gilbert Model 11 / 29 - Hierarchical in nature

16 L1 HMM: models long term dynamics L2-MMB: models short term dynamics Trained using Expectation-Maximization (EM) algorithm for HMM with MMB output distribution (HMM-MMB). 12 / 29

17 Data Collection Packet reception traces One transmitter and all others nodes act as receivers byte packets per second for durations of 1/2, 1, 2, 6 and 12 hours. Record sequence number, received signal strength value (RSSI) and link quality indicator (LQI) value of each data packet. Collected noise traces. Parameters Values Channel 26 Num. Noise Samples 196,608 Noise Sampling Period 1ms Table: Data collection parameters. 13 / 29

18 Overview Model Size: Q: HMM States (=6) M: Number of Mixture Components (=20) W : Window Size (=128) Get initial values for parameters. HMM: Transition probability matrix MMB: Mixture Proportions (π i ) and Bernoulli parameters ( p i ) Refine estimates using the EM algorithm for HMM-MMB. 14 / 29

19 Initializing the 15 / 29

20 Initializing the 15 / 29

21 Initializing the 15 / 29

22 Initializing the 16 / 29

23 Initializing the 16 / 29

24 Initializing the 16 / 29

25 Trained HMM-MMB: Initialize HMM-MMB with: 1 L 1 HMM Transition Matrix 17 / 29

26 Trained HMM-MMB: Initialize HMM-MMB with: 1 L 1 HMM Transition Matrix 2 L 2 MMB Parameters 17 / 29

27 Trained HMM-MMB: Initialize HMM-MMB with: 1 L 1 HMM Transition Matrix 2 L 2 MMB Parameters Relatively fast convergence to local optima 17 / 29

28 Model 18 / 29

29 Things of Interest Packet Reception Rate (PRR) 19 / 29

30 Things of Interest Packet Reception Rate (PRR) Run Length (RL) Distribution 19 / 29

31 Things of Interest Packet Reception Rate (PRR) Run Length (RL) Distribution Conditional Packet Delivery Function (CPDF) [Srinivasan et al. SenSys 08] 19 / 29

32 Comparing RL and CPDF Distributions - L 1 norm Absence of rare cases of long runs does not affect the L 1 norm. 20 / 29

33 Comparing RL and CPDF Distributions - L 1 norm L 1 norm unfairly penalizes run length distributions. 20 / 29

34 Comparing RL and CPDF Distributions - Nearest Neighbor Distance D(P, Q) = P(1) Q(1) + P(2) Q(2) + P(3) Q(3) + P(4) Q(4) + P(5) Q(5) + P(6) Q(6) + P(7) Q(8) /1000 P(100) Q(8) / / 29

35 Comparing RL and CPDF Distributions - Nearest Neighbor Distance D(P, Q) = P(1) Q(1) + P(2) Q(2) + P(3) Q(3) + P(4) Q(4) + P(5) Q(5) + P(6) Q(6) + P(7) Q(8) /1000 P(100) Q(8) /1000 D(Q, P) = Q(1) P(1) + Q(2) P(2) + Q(3) P(3) + Q(4) P(4) + Q(5) P(5) + Q(6) P(6) + Q(8) P(7) / / 29

36 Comparing RL and CPDF Distributions - Nearest Neighbor Distance D(P, Q) = P(1) Q(1) + P(2) Q(2) + P(3) Q(3) + P(4) Q(4) + P(5) Q(5) + P(6) Q(6) + P(7) Q(8) /1000 P(100) Q(8) /1000 D(Q, P) = Q(1) P(1) + Q(2) P(2) + Q(3) P(3) + Q(4) P(4) + Q(5) P(5) + Q(6) P(6) + Q(8) P(7) /1000 Nearest Neighbor Distance NND PQ = D(P,Q)+D(Q,P) 2 21 / 29

37 M&M Simulator Simulate traces in TOSSIM. PRRs from 0% to 100%. TOSSIM code: 22 / 29

38 Comparison Methodology 1 Simulate traces for M&M as follows: For a given model size, generate a sequence using the model parameters. 2 Simulate traces for TOSSIM as follows: Use average RSSI of received packets as the gain value of the simulated trace. Model noise using the CPM algorithm (Lee et al. IPSN 07). 23 / 29

39 - Long Term Dynamics Original PRR 28% 24 / 29

40 - Long Term Dynamics Original PRR 28% 24 / 29 TOSSIM PRR=49%

41 - Long Term Dynamics Original PRR 28% 24 / 29 TOSSIM PRR=49% M&M PRR=27%

42 - Short Term Dynamics Run Length of 0s 25 / 29

43 - Short Term Dynamics Run Length of 0s 25 / 29

44 - Short Term Dynamics Run Length of 0s 25 / 29

45 - Short Term Dynamics Run Length of 1s 25 / 29

46 - Short Term Dynamics Run Length of 1s 25 / 29

47 - Short Term Dynamics Run Length of 1s 25 / 29

48 Sensitivity to Window Size W Original W=8 W NND Vectors per State (Trace Length = ) / 29

49 Future Directions Model Adaptation 27 / 29

50 Future Directions Model Adaptation Simulate different network conditions 27 / 29

51 Future Directions Model Adaptation Simulate different network conditions Minimal deployment and training data 27 / 29

52 Future Directions Model Adaptation Simulate different network conditions Minimal deployment and training data User Control 27 / 29

53 Future Directions Model Adaptation Simulate different network conditions Minimal deployment and training data User Control Length of burst of 1/0s 27 / 29

54 Future Directions Model Adaptation Simulate different network conditions Minimal deployment and training data User Control Length of burst of 1/0s Qualitative factors 27 / 29

55 Future Directions Model Adaptation Simulate different network conditions Minimal deployment and training data User Control Length of burst of 1/0s Qualitative factors Extend to RSSI 27 / 29

56 Future Directions Model Adaptation Simulate different network conditions Minimal deployment and training data User Control Length of burst of 1/0s Qualitative factors Extend to RSSI Better representation of link quality (Srinivasan and Levis EmNets 06) 27 / 29

57 Future Directions Model Adaptation Simulate different network conditions Minimal deployment and training data User Control Length of burst of 1/0s Qualitative factors Extend to RSSI Better representation of link quality (Srinivasan and Levis EmNets 06) Complement CPM 27 / 29

58 Conclusion GOAL: Replicate multiscale structure in wireless links. Long Term Dynamics 28 / 29 Short Term Dynamics THANK YOU.

59 Conclusion GOAL: Replicate multiscale structure in wireless links. 28 / 29 Long Term Dynamics Short Term Dynamics THANK YOU.

60 References for Slides David Kotz, Calvin Newport, Robert S. Gray, Jason Liu, Yougu Yuan, and Chip Elliott, Experimental evaluation of wireless simulation assumptions, in MSWiM 04. Kannan Srinivasan, Maria Kazandjieva, Saatvik Agarwal, and Philip Levis, The -factor: Measuring Wireless Link Burstiness, in SenSys 08. HyungJune Lee, Alberto Cerpa, and Philip Levis, Improving Wireless Simulation Through Noise Modeling, in IPSN / 29