Switch-and-Navigate: Controlling Data Ferry Mobility for Delay-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 Introduction Problem Formulation Local Control: Navigate Agenda 2345 Global Control: Switch 1 Comparison and Simulation Results 6 Conclusion

3 Introduction Problem Description Goal Method Contributions Problem Description

4 Permanently partitioned networks Introduction Problem Description Goal Method Contributions

5 Goal: Deliver delay- constrained messages among disconnected domains Introduction Problem description Goal Method Contributions

6 Method: Relay messages by a designated communication node ( data ferry ) Introduction Problem description Goal Method Contributions

7 2 General inter- domain distances Single data ferry mobility control Features Introduction Problem description Goal Method Contributions 1 Finite message lifetime

8 Introduction Problem Formulation Local Control: Navigate Agenda 345 Global Control: Switch Comparison and Simulation Results 6 Conclusion 221

9 Problem Formulation Assumptions and Partial Observation SAN Structure Control Objective gateway Assumptions & Partial Observation

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

11 Global control Local control Problem Formulation Assumptions and Partial Observation SAN Structure Control Objective Switch-and-Navigate Structure (POMDP)

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

13 Introduction Problem Formulation Local Control: Navigate Agenda 245 Global Control: Switch Comparison and Simulation Results 6 Conclusion 31

14 Local Control Bellman Equation Myopic Local Control The optimal policy of the navigation controller is the solution to the value iteration (T is the control duration): 0123 T-1T time Value iteration: (2) Optimal policy

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

16 Introduction Problem Formulation Local Control: Navigate Agenda 235 Global Control: Switch Comparison and Simulation Results 6 Conclusion 41

17 Global Control Buffer States Update Myopic Global Policy Two-step Global Policy Approximations Gateway buffer state G Ferry buffer state F G 11 G 12 G 13 … G 1(L-1) G 1L G 21 G 22 G 23 … G 2(L-1) G 2L G 31 G 32 G 33 … G 3(L-1) G 3L G 41 G 42 G 43 … G 4(L-1) G 4L F 11 F 12 F 13 … F 1(L-1) F 1L F 21 F 22 F 23 … F 2(L-1) F 2L F 31 F 32 F 33 … F 3(L-1) G 3L F 41 F 42 F 43 … F 4(L-1) G 4L duration between 2 consecutive contacts is a round Before observation Global Control: Selecting the next domain to serve

18 Global Control Buffer States Update Myopic Global Policy Two-step Global Policy Approximations where R j is the identity matrix except row j is 0. (4) (5) After observation

19 Global Control Buffer States Update Myopic Global Policy Two-step Global Policy Approximations Value Iteration for Global Control 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, Future rounds (8) Myopic Global Policy (7) =1

20 Global Control Buffer States Update Myopic Global Policy Two-step Global Policy Approximations Future rounds predict the next round (9) Two-step Global Policy =2

21 Global Control Buffer States Update Myopic Global Policy Two-step Global Policy Approximations 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-TSA 2 : Average FCT is used in the 2 nd step S-TSA 1,2 : Average FCT is used in both steps Approximations of Global Policies

22 Introduction Problem Formulation Local Control: Navigate Agenda 234 Global Control: Switch Comparison and Simulation Results 6 Conclusion 551

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 Comparison & Simulation Results OPWP Simulation Results SAN vis-à-vis Predetermined Control: OPWP

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

25  Discounted effective throughput Comparison & Simulation Results OPWP Simulations Homogeneous Heterogeneous Simulation Results

26  Message loss ratio Comparison & Simulation Results OPWP Simulations Homogeneous Heterogeneous Simulation Results

27 Introduction Problem Formulation Local Control: Navigate Agenda 2345 Global Control: Switch Comparison and Simulation Results Conclusion 661

28 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) Conclusions

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 Comparison & Simulation Results OPWP Simulation Results SAN vis-à-vis Predetermined Control: OPWP