1. Game-Theoretic Models for Reliable Path- Length and Energy-Constrained Routing With Data Aggregation -Rajgopal Kannan and S. Sitharama Iyengar Xinyan Pan 11/22/2004

2. Main Issues in Sensor Network Energy-efficiency Reliability of a data transfer path Path Length (proportional to energy cost of transmission Most prevalent routing algorithms focusing on minimizing overall energy consumption. However such routing strategies may result in uneven energy depletion across sensor nodes and expedite network partition.

3. Sensor-centric information routing strategy Optimizes energy costs, path reliability and path length simultaneously. Energy costs are local Path reliability and path length are network-wide metrics Sensors can be modeled as players in a routing game with appropriate strategies and utility functions (payoffs) Reliable Query Reporting (RQR) Model

4. Game-Theoretic Framework Each sensor makes decision taking individual costs and benefits into account Decentralized decision-making Self-configuring and adaptive networks Identify equilibrium outcomes for reliable communication

5. RQR Model Setup Set of players: S = {s a = s 1, …, s n =s q }. Source node (s a ) sends information V a to destination node (s q ). Information routed through optimally chosen set S’  S of intermediate nodes Each node can fail with probability 1-p i  (0,1). Link costs c ij >0 Each node forms one link.

6. RQR Game Sensor s i ’s strategy is a binary vector  li = (l i1, …, l i,i-1, l i,i+1, …, l in ) Where l i1 = 1/0, sensor s i sending/not sending a data packet to sensor s j  Each sensor’s strategy is constrained to be nonempty  Strategies resulting in a node linking to its ancestors are not allowed A strategy profile defines the outcome of the RQR game. In a standard non-cooperative game each player cares only about individual payoffs – therefore behavior is selfish.

7. Benefit function For a strategy profile l = (l i, l -i ) resulting in a tree T rooted at s q, where l -i denotes the strategy chosen by all the other players except player i.  Network is unreliable and every sensor that receives data has an incentive in its reaching the query node s q  The routing protocol includes data aggregation  Benefit to any sensor s i, denoted as X i, is a function of the path reliability from s i onwards and a function of the expected value of information that can reach s i.

8. Benefit function the path reliability from s i onwards to s q, denoted as R i the expected value of information that can reach s i where

9. Benefit function Benefit function for s i : Exmaple *Data aggregation is assumed to be additive

10. Payoffs General Payoff Function where

11. RQR Model Properties Benefits depend on the total reliability of realized paths. Thus each sensor is induced to have a cooperative outlook in the game. Cost are individually borne and differ across sensors, thereby capturing the tradeoffs between global reliability and individual sensor costs

12. RQR Model Properties Definition: A strategy l i is said to be a best response of player i to l -i if Let BR i (l -i ) denote the set of player i’s best response to l -i. A strategy profile l = (l 1, …, l n ) is said to be an optimal RQR tree T if, i.e., sensors are playing a Nash equilibrium.

13. Optimal RQR Computation in Geographically Routed Sensor Networks Let D i = {s i 1,s i 2,…,s i l } be the set of downstream next-hop neighbors of s i. For each s i j in D i, let expected values of incoming information be divided into N i j disjoint consecutive intervals -- the left and right endpoints -- optimal path reliability from onwards for information of expected value in the given interval -- payoff to sensor s i on sending information of value to downstream neighbor

14. Optimal RQR Computation in Geographically Routed Sensor Networks Lemma:

15. Optimal RQR Computation in Geographically Routed Sensor Networks To compare two different intervals, we only need to evaluate their payoff at the smallest point. Algorithm of optimal-next-neighbor at each node enables computation of the optimal RQR path. Assume that upstream and downstream neighbors of each node are known a priori The output of the algorithm is the set of disjoint and contiguous information value intervals at s i along with the reliability and next hop neighbor on the optimal path from s i to s q for each interval

16. Algorithm of Optimal-next-neighbor

17. References R. Kannan, S.S. Iyengar, Game-theoretic models for reliable path-length and energy-constrained routing with data aggregation in wireless sensor networks, IEEE J. Selected Areas Comm., Vol. 22, No. 6, August 2004, 1141-1150 R. Kannan, S. Sarangi, S.S. Iyengar, Sensor-centric energy-constrained reliable query routing for wireless sensor networks, J. Parallel Distrib. Comput. 64 (2004), 839-852