Switch-and-Navigate: Controlling Data Ferry Mobility for Delay-Bounded Messages

1. Switch-and-Navigate:Controlling Data Ferry Mobility forDelay-Bounded Messages Liang Ma*, Ting He+, Ananthram Swami§, Kang-won Lee+ and Kin K. Leung* *Imperial College London, UK +IBM T.J. Watson Research Center, USA §Army Research Laboratory, USA

2. 2 3 4 5 6 1 Agenda Introduction Problem Formulation Local Control: Navigate Global Control: Switch Comparison and Simulation Results Conclusion

3. Problem DescriptionGoalMethodContributions Introduction Problem Description

4. Problem DescriptionGoalMethodContributions Introduction Permanently partitioned networks

5. Problem descriptionGoalMethodContributions Introduction Finite Lifetime Goal: Deliver delay-constrained messages among disconnected domains

6. Problem descriptionGoalMethodContributions Introduction Method: Relay messages by a designated communication node (data ferry)

7. Single data ferry mobility control 1 2 Finite message lifetime General inter-domain distances Problem descriptionGoalMethodContributions Introduction Features

8. 3 4 5 6 2 1 2 Agenda Introduction Problem Formulation Local Control: Navigate Global Control: Switch Comparison and Simulation Results Conclusion

9. Assumptions and Partial ObservationSAN StructureControl Objective Problem Formulation Assumptions & Partial Observation gateway

10. Assumptions and Partial ObservationSAN StructureControl Objective Problem Formulation • Partition each domain into cells • Gateway~Markovian mobility, transition P • Data ferry: inter-domain distance dij (in #slots), intra-domain distance 1 (slot) • Constant #messages generated at gateways each slot, with finite lifetime lmax Control data ferry among domains with partial observations The exact gateway location is unknown at slot t

11. Assumptions and Partial ObservationSAN StructureControl Objective Problem Formulation Switch-and-Navigate Structure (POMDP) Global control Local control

12. Assumptions and Partial ObservationSAN StructureControl Objective Problem Formulation Control Objective Discounted effective throughput (1) Control policy =1 No. of messages delivered within lifetime at t Discount factor

13. 2 4 5 6 1 3 Agenda Introduction Problem Formulation Local Control: Navigate Global Control: Switch Comparison and Simulation Results Conclusion

14. Bellman EquationMyopic Local Control Local Control Optimal policy The optimal policy of the navigation controller is the solution to the value iteration (T is the control duration): T-1 T 0 1 2 3 time Value iteration: (2)

15. Bellman EquationMyopic Local Control Local Control Myopic Local Policy (T=1) Suppose the data ferry knows the transition matrix Pq in each domain Distribution of gateway location (belief b) is updated every slot Until the gateway is finally found (3)

16. 2 3 5 6 1 4 Agenda Introduction Problem Formulation Local Control: Navigate Global Control: Switch Comparison and Simulation Results Conclusion

17. Buffer States UpdateMyopic Global PolicyTwo-step Global PolicyApproximations Global Control Global Control: Selecting the next domain to serve duration between 2 consecutive contacts is a round Gateway buffer state G Ferry buffer state F Before observation

18. Buffer States UpdateMyopic Global PolicyTwo-step Global PolicyApproximations Global Control After observation (4) where Rj is the identity matrix except row j is 0. (5)

19. Buffer States UpdateMyopic Global PolicyTwo-step Global PolicyApproximations Global Control Value Iteration for Global Control (7) where denotes the no. of delivered messages when a contact occurs, is the First Contact Time in domain j, is the total no. of rounds in the global control, Myopic Global Policy Future rounds =1 (8)

20. Buffer States UpdateMyopic Global PolicyTwo-step Global PolicyApproximations Global Control Two-step Global Policy predict the next round =2 Future rounds (9)

21. Buffer States UpdateMyopic Global PolicyTwo-step Global PolicyApproximations Global Control Approximations of Global Policies • For computational efficiency, • Approximate the belief by the steady-state distribution • Approximate the First Contact Time (FCT) by the average FCT • Original policies: • MY: Myopic policy • TS: Two-step policy • Steady-state-based approximations: • S-MY: Steady-state based myopic • S-TS: Steady-state based two-step policy • Further approximations: • S-TSA2: Average FCT is used in the 2nd step • S-TSA1,2: Average FCT is used in both steps

22. 2 3 4 6 5 1 5 Agenda Introduction Problem Formulation Local Control: Navigate Global Control: Switch Comparison and Simulation Results Conclusion

23. Choose some way-points and waits at each of them for a fixed no. of slots Connect the way-points to form the shortest closed path through TSP algorithms OPWPSimulation Results Comparison & Simulation Results SAN vis-à-vis Predetermined Control: OPWP

24. OPWPSimulations Comparison & Simulation Results Simulation settings Suppose the gateways follow 2-D localized random walk model. Homogeneous domain settings: Heterogeneous domain settings:

25. Discounted effective throughput OPWPSimulations Comparison & Simulation Results Simulation Results Homogeneous Heterogeneous

26. Message loss ratio OPWPSimulations Comparison & Simulation Results Simulation Results Homogeneous Heterogeneous

27. 2 3 4 5 6 1 6 Agenda Introduction Problem Formulation Local Control: Navigate Global Control: Switch Comparison and Simulation Results Conclusion

28. Conclusions Consider more practical constraints (constrained message delays, general inter-domain distances) Propose a hierarchical framework for controlling data ferry in highly partitioned networks The two-step policies and the approximations outperform the state of the art (optimized predetermined policy)

29. Thank you! Q & A

30. Choose some way-points and waits at each of them for a fixed no. of slots Connect the way-points to form the shortest closed path through TSP algorithms OPWPSimulation Results Comparison & Simulation Results SAN vis-à-vis Predetermined Control: OPWP