1. Using Redundancy to Cope with Failures in a Delay Tolerant Network Sushant Jain, Michael Demmer, Rabin Patra, Kevin Fall Source: www.cs.utexas.edu/~lili/ classes/F05/slides/dtn-yogita.pptwww.cs.utexas.edu/~lili/ classes/F05/slides/dtn-yogita.ppt

2. Outline of Discussion Introduction Erasure Coding Formal Problem Statement Path Failure Models Evaluation Related Work Conclusion Future Development

3. Introduction Routing in Delay Tolerant Network (DTN) in presence of path failures is difficult Retransmissions cannot be used for reliable delivery  Timely feedback may not be possible How to achieve reliability in DTN?  Replication, Erasure coding

4. Erasure Coding N block message is encoded into large (>N) number of code blocks. Message can be decoded when fraction 1/r or more blocks are received. Replication factor = r Allocation of code blocks over different links not simple.

7. Family of allocation strategies is used for k th strategy Probability of success of k th strategy Bernoulli Path Failure, are identical and independent

8. Bernoulli Path Failure, are identical and independent contd.

9. Bernoulli Path Failure, are different Objective Function: Formulation of Mixed Integer Program (MIP)

10. Partial Path Failures Objective: Maximize Sharpe Ratio

11. Markowitz algorithm

12. Evaluation Three scenarios used for evaluation:  DTN routing over data MULEs Path independent, data loss Bernoulli  DTN routing over set of city buses Paths dependent, data loss Bernoulli  DTN routing large sensor network Partial path failures

13. Data MULE Scenario Simulation Setup: 1km x 1km planar area, source and destination at opposite corners. Message size 10KB, Contact bandwidth 100Kbps, Storage capacity of MULE 1MB Velocity of MULE 10m/s. Probability of success of ith path is D i is the delay in distribution by ith MULE, T is the message expiration time pi = Prob(Di ≤ T),

14. MULE Density

15. Forced Splitting

16. Different Success Probabilities

17. Tolerance to Probability Estimation Errors

18. Bus Network Scenario Simulation Setup  Radio bandwidth 400kbps, radio range 100m  20 messages of size 10kb, sent randomly every hour for 12 hours  bus storage 1Mb  Message expiration time 6 hours  Paths are multi-hop

19. Bus Network Scenario contd.

20. Sensor Network Scenario Simulation Setup  Nodes placed in 40x16 foot grid, grid size 8ft

21. Benefits of Erasure coding

22. Related Work Portfolio Theory  Theory used to optimize the Sharpe-ratio Waterfilling in Gaussian channels  Formulation uses convex optimization techniques FEC, Erasure Coding, Internet Routing  Choice of erasure code Combinatorial Optimization  Computes Prob(Y>c) for a given configuration

23. Summary Problem of reliable transmission in DTN Replication and erasure code for increasing reliability Formulate the optimal allocation problem Study of this problem for Bernoulli and partial path failures Evaluation of the analysis in three different scenarios

24. Strengths:  Use of erasure coding and replication in DTN  Performed extensive analysis of the optimal allocation problem  The idea presented in generic and can be applied in other fields too Weakness:  Computations involved are complex and may not feasible  The study is applicable for probabilities which remain constant over time  In partial path failure analysis, it is assumed that the path probabilities have comparable mean and variance. This might not be always true

25. Future Development Apply this analysis to other fields such as replication of objects in distributed system Develop an efficient method for allocation in Bernoulli path failures Theoretical analysis for choosing replication factor