Using Redundancy to Cope with Failures in a Delay Tolerant Network

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.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. Bernoulli Path Failure, are identical and independent • Family of allocation strategies is used for kth strategy • Probability of success of kth strategy

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

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

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 • Di 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