Xinyan Pan 11/22/2004

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 = {sa = s1, …, sn=sq}. • Source node (sa)sends informationVato destination node (sq). • Information routed through optimally chosen set S’ S of intermediate nodes • Each node can fail with probability 1-pi  (0,1). • Link costs cij >0 • Each node forms one link.

6. RQR Game • Sensor si’s strategy is a binary vector • li= (li1, …, li,i-1, li,i+1, …, lin) Where li1 = 1/0, sensor si sending/not sending a data packet to sensor sj • 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 = (li, l-i) resulting in a tree T rooted at sq, 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 sq • The routing protocol includes data aggregation • Benefit to any sensor si, denoted as Xi, is a function of the path reliability from si onwards and a function of the expected value of information that can reach si.

8. Benefit function • the path reliability from si onwards to sq, denoted as Ri • the expected value of information that can reach si where

9. Benefit function • Benefit function for si: • 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 li is said to be a best response of player i to l-i if • Let BRi(l-i) denote the set of player i’s best response to l-i. A strategy profile l = (l1, …, ln) 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 Di = {si1,si2,…,sil} be the set of downstream next-hop neighbors of si. • For each sij in Di, let expected values of incoming information be divided into Nij 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 si 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 si along with the reliability and next hop neighbor on the optimal path from si to sq 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