DTN-Meteo: Forecasting DTN Performance under Heterogeneous Mobility

Transcription

1 : Forecasting DTN Performance under Heterogeneous Mobility Andreea Picu Dr. Thrasyvoulos Spyropoulos Computer Engineering and Networks Laboratory (TIK) Communication Systems Group (CSG) June 21, 2012

2 1 Motivation & Goals 2 Markov Chain 3 Calculating In Practice 4 Assumptions Derivation In Practice 5 A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 2 of 29

3 Delay Tolerant Networks a.k.a. Opportunistic Networks always disconnected data exchange through node mobility nodes come within communication range contact connectivity graph = highly dynamic, disconnected A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 3 of 29

4 Greed Is Not a Sin in DTNs Sporadic, partial connectivity Highly dynamic graph Greedy algorithms for everything This present contact Potential future contacts *Proverb: A bird in hand is worth two in the bush. A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 4 of 29

5 Current DTN Analytical s A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 5 of 29

6 Current DTN Analytical s A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 5 of 29

7 Studies of Real Mobility A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 6 of 29

8 Using Real Mobility New Algorithms/Protocols (still greedy) E. Daly and M. Haahr Social network analysis for routing in disconnected delay-tolerant MANETs MobiHoc 2007 P. Hui, J. Crowcroft and E. Yoneki BubbleRap: Social-based Forwarding in Delay Tolerant Networks MobiHoc 2008 s (still very problem-specific) T. Spyropoulos, T. Turletti and K. Obraczka Routing in Delay-Tolerant Networks Comprising Heterogeneous Node Populations TMC 2009 A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 7 of 29

9 Unified for Optimization in DTNs Markov Chain Decouple mobility (contact probability matrix P c ij ) algorithms (most of the time greedy) to obtain correctness conditions on mobility scenario [Globecom 11] convergence probability and convergence delay [now] Illustrative examples: talk: Content Placement with limited replication paper: + Routing with limited replication (SimBet, BubbleRap) [WoWMoM 12]: Forced replication (i.e., epidemic protocols) A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 8 of 29

10 Content/service placement Markov Chain x = (1, 0, 1, 1, 1, 0,..., 0)( N L ) A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 9 of 29

11 Content/service placement Markov Chain x = (1, 0, 1, 1, 1, 0,..., 0)( N L ) A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 9 of 29

12 Example problem description Markov Chain Node state space S = {0, 1} Network state space A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 10 of 29

13 Example problem description Markov Chain Node state space S = {0, 1} Network state space Ω = {x x = (x 1, x 2,..., x N )}, x i S A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 10 of 29

14 Example problem description Markov Chain Node state space S = {0, 1} Network state space Ω = {x x = (x 1, x 2,..., x N )}, x i S A set of constraints N i=1 x i L A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 10 of 29

15 Example problem description Markov Chain Node state space S = {0, 1} Network state space Ω = {x x = (x 1, x 2,..., x N )}, x i S A set of constraints N i=1 x i L A utility function U x = N i=1 x i d i or U x = N i=1 x i U SimBet i or U x = N i=1 x i U BubbleRap i A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 10 of 29

16 Content/service placement Markov Chain x = (x 1, x 2,..., x N ) = (1, 0, 1, 1, 1, 0,..., 0)( N L ) A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 11 of 29

17 Content/service placement Markov Chain x = (x 1, x 2,..., x N ) = (1, 0, 1, 1, 1, 0,..., 0)( N L ) A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 11 of 29

18 Exploring the Solution Space Markov Chain δ(x, y) = 1{x i y i } 1 i N A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 12 of 29

19 Exploring the Solution Space Markov Chain δ(x, y) = 1{x i y i } 1 i N A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 12 of 29

20 Exploring the Solution Space Markov Chain δ(x, y) = 1{xi yi } 1 i N A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 12 of 29

21 Heterogeneous mobility Markov Chain Contact probability matrix: 0 p c 12 p c 1N P c p = c 21 0 p c 2N p c N1 0 p c ij estimated from pairwise intercontacts of (i, j) A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 13 of 29

22 Local Optimization Algorithms Markov Chain Transition probability p xy : 1 contact probability 2 acceptance probability A xy = 1{U x < U y } A xy = f(u x, U y ) p c ij A xy = 0 (greedy) (probabilistic) A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 14 of 29

23 Local Optimization Algorithms Markov Chain Transition probability p xy : 1 contact probability 2 acceptance probability A xy = 1{U x < U y } A xy = f(u x, U y ) p c ij A xy = 0 (greedy) (probabilistic) A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 14 of 29

24 Local Optimization Algorithms Markov Chain Transition probability p xy : 1 contact probability 2 acceptance probability A xy = 1{U x < U y } A xy = f(u x, U y ) p c ij A xy = 0 (greedy) (probabilistic) A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 14 of 29

25 Local Optimization Algorithms Markov Chain Transition probability p xy : 1 contact probability 2 acceptance probability A xy = 1{U x < U y } A xy = f(u x, U y ) p c ij A xy = 0 (greedy) (probabilistic) A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 14 of 29

26 Putting the pieces together Markov Chain Pieces of : 1 Mobility (heterogeneous) p c ij 2 Solution space (node & network) 3 Utilities 4 Algorithm A = A xy contact probability matrix P c = {p c ij } e.g. combinations of L nodes e.g., combinations e.g. node degree acceptance probability matrix A = {A xy } A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 15 of 29

27 The Markov Chain Markov Chain Complicated problem Transition matrix, P = {p xy } mobility algorithm P c A 0 p c 12 p c 1N 1 A x1x2 A x1xm p c 21 0 p c 2N A x2x1 1 A x2xm p c N1 0 A xm x 1 1 P = {p xy } = p c ij A xy A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 16 of 29

28 The Markov Chain Complicated problem Transition matrix, P = {p xy } Markov Chain P = p x1x1 p x1x2 p x1xm p x2x1 p x2x2 p x2xm p xm x 1 p xm x M P = {p xy } = p c ij A xy A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 16 of 29

29 Why Is This Useful? Markov Chain Correctness analysis [Globecom 11] Feasability of (mobility + algorithm) analysis [now] Achieve trade-off (e.g., delay vs. # copies) Tune parameters Assess performance A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 17 of 29

30 Recall Our Absorbing Markov Chain Complicated problem Transition matrix, P = {p xy } Calculating In Practice P = p x1x1 p x1x2 p x1xm p x2x1 p x2x2 p x2xm p xm x 1 p xm x M P = {p xy } = p c ij A xy A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 18 of 29

31 Transient Markov Chain Calculating In Practice P = TR LM Q R 1 R 2 0 I x TR LM x Fundamental matrix: N = (I Q) 1 A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 19 of 29

32 Probability Calculating In Practice L Optimum Best local max. pred. meas. pred. meas. ETH N/A N/A Infocom MIT TVCM TVCM Table: Absorption probabilities A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 20 of 29

33 Content Placement: Delays Calculating In Practice Expected delays pred. meas. Expected convergence delay eth info mit tvcm24 tvcm104 Traces Expected delays Expected convergence delay (local max.) pred. meas. eth info mit tvcm24 tvcm104 Traces Optimum states Local maxima A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 21 of 29

34 Routing: End-to-end Delays Calculating In Practice Expected delays Expected end to end delay pred. meas. eth info mit tvcm24 tvcm104 Traces Expected delays Expected end to end delay pred. meas. eth info mit tvcm24 tvcm104 Traces SimBet BubbleRap A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 22 of 29

35 The Limitation of Increased replication increased solution space Simplified model: Assumptions Derivation In Practice A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 23 of 29

36 Copies Are Indenpendent Assumptions Derivation In Practice L/N D ( 10 5 ) Table: Copy dependency vs. L to N ratio A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 24 of 29

37 Copies Are Indenpendent Assumptions Derivation In Practice L/N D ( 10 5 ) Table: Copy dependency vs. L to N ratio A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 24 of 29

38 Multi-copy Delay from Single-copy Results Routing: τ rt = E[T rt ] = E [min(t s1d,..., T sl d)]. (1) Assumptions Derivation In Practice Content Placement: τ cp = E[T cp ] = E [ L i=1 T(L i+1) i ]. (2) absorption times of finite MC s T si d and T (L i+1) i : phase-type distributions approximately exponential A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 25 of 29

39 Multi-copy Delay from Single-copy Results Routing: τ rt = E[T rt ] = E [min(t s1d,..., T sl d)]. (1) Assumptions Derivation In Practice Content Placement: τ cp = E[T cp ] = E [ L i=1 T(L i+1) i ]. (2) absorption times of finite MC s T si d and T (L i+1) i : phase-type distributions approximately exponential A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 25 of 29

40 Approximation Accuracy Assumptions Derivation In Practice Expected delays Expected convergence delay approx. pred. meas. Expected delays Expected end to end delay approx. pred. meas. 0 eth info mit tvcm24 tvcm104 Traces 0 eth info mit tvcm24 tvcm104 Traces Content Placement SimBet Routing A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 26 of 29

41 Conclusion New unified model for DTNs 1 st analytical predictions for utility-based algorithms and heterogeneous mobility is generic (see paper in WoWMoM 12) Practical value Local maxima small delivery ratio Tuning replication to achieve target performance Tuning utility function parameters A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 27 of 29

42 Mobility model Semi-Markov No exponential assumption More on generality... Implicitly limited replication Bounds on approximation errors A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 28 of 29

43 The End Thank you for your attention. Your questions, please. A. Picu, Dr. T. Spyropoulos Forecasting DTN Performance 29 of 29