A Distributed Framework for Correlated Data Gathering in Sensor Networks

1. A Distributed Framework for Correlated Data Gathering in Sensor Networks Kevin Yuen, Ben Liang, Baochun Li IEEE Transactions on Vehicular Technology 2008

2. Outline • Introduction • Problem Formulation • Localized Slepian-Wolf Coding • Distributed Solution: A Price-Based Framework • Implementation Issues • Performance Evaluation

3. Introduction • Recent technological advances have enabled the production of low-cost sensors. • Usually sensors are densely deployed in sensor networks. (Overlapping sensing ranges) • Find a transmission structure to minimize total energy • This framework should be compatiblee.g. multi-sink, distributed solution, asynchronous network settings, sink mobility, duty schedules

4. Problem Formulation • Model the WSN as a directed graph G=(V,E) • V = • Assign every node i with rate • Transmission range and exists if • Each link(i,j) has a weight • represents the flow rate of link(i,j) • We can minimize the optimization objective by adjusting and

5. Problem Formulation • Use rate distortion theory to analyze the problem • Let S be a spatially correlated random Gaussian vector

6. Problem Formulation • Goal : Minimize transmission energy • Constraints • Flow Conservation • Channel Contention • Rate Admissibility

7. Problem Formulation • The constraints and the correlated data-gathering problem can be modeled as an exponential-constraint linear programming formulation

8. Localized Splepian-Wolf Coding • Disadvantages of the optimization formulations • Difficult to solve • Require global knowledge of the correlation structure • Use Slepian-Wolf coding to relax the rate admissibility constraints such that only local correlation information is required. • Each sensor node i should encode its data at a rate equal to the conditioned entropy • Consider the data correlation with one-hop neighbors in

9. Localized Splepian-Wolf Coding • Supports multiple sinks • :a subset of sensors within the neighborhood of sensor that are closer to sensor ’s sink

10. Distributed Solution:A Price-Based Framework

11. LagrangianDualization(1/2) • Goal: allocate the limited capacity of the wireless shared medium • Price-based resource allocation • Each wireless link is a basic resource unit • A price can reflect the relation between the traffic load of the link and its bandwidth capacity • Relax the channel contention constraints with Lagrangiandualization

12. LagrangianDualization(2/2) energycapacity cost The weight of each link is equal to the sum of its energy and capacity cost.

13. SubgradientAlgorithm • An efficient iterative algorithm to solve the Lagrangian dual problem. • Solve the Lagrangian sub problem by finding the shortest path from each sensor node to its nearest sink node with current Lagrangian multiplier during each iteration • Update the Lagrangianmultiplier

14. Distributed Algorithm(1/2)

15. Distributed Algorithm(2/2) • The algorithm requires 3 control packets • Flow rates of all links within the cluster • Prices for all clusters that are inherent to it • The identities of other sensor nodes in its neighborhood and their distance to destination sink node 90sensors, 10sinks, Transmission rage=30m

16. Asynchronous Network Model • Synchronous network model • Every node simultaneously execute at every time instance • It is expensive to synchronize local clocks across the entire network • Partial-asynchronous network model • The time between consecutive updates is bounded by B • At time t, instead of the most recent information, a node may receive a sequence of recent updates • Compute the average of the sequence of updates from time to

17. Implementation Issues • Primal Recovery • Guarantee to generate feasible primal solution • The network must remain static : step size : the weights of convex combination

18. Implementation Issues • Capacity Reservation • The rate allocation generated by subgradientalgorithm often violate the channel contention constraints • Generate feasible solutions by reserving a suitable amount of capacity (e.g. 10%) • Handling Network Dynamics • Nodes retrieve up-to-date topology in their neighborhood

19. Performance Evaluation

20. Simulation Environments • Implement with C++ • Experiments are performed on the random topology with 90 sensor nodes and 10 sink nodes • Transmission range & interference range are 30m • The capacity of wireless shared medium is 150 bits • Correlation parameter • Per node distortion

21. Converge Speed • Chose 10% as sink nodes • The algorithm is executed in synchronous environment with 500 iterations Primal Sub gradient

22. Impact of Asynchronous Network Settings Primal • Run 500 iterations with different time bounds B = 1,5,10,25 • The convergence speed is associated with the time bound B. Sub gradient

23. Effect of Data Correlation • Compare the effect of data correlation between synchronous and independent environment. • D = 0.001, 0.01 and 0.1 • W = 0.9 to 0.9999 Implementation I : local Implementation II: global

24. Adaptation to Sink Mobility

25. Adaptation to Duty Schedules • Model duty schedules as a 2-state Markov chain • and are state transition probabilities • Set the simulation environment for 300s