Maximization of lifetime in wireless sensor network using optimal routing

1. Maximization of lifetime in wireless sensor network using optimal routing YongJin Kwon yjkwon@comis.kaist.ac.kr KyungSub Shin ksshin@comis.kaist.ac.kr

2. 01 Introduction • 02 System Model • 03 Problem formulation • 04 Algorithm or analysis and results • 05 Big Picture • 06 Criticism and conclusion

3. Introduction (1/2) • Wireless Sensor Network. • Information obtained by the monitoring nodes needs to be routed to a set of designated gateway nodes • Every node is capable of sensing, data processing, and communication, and operates on its limited amount of battery energy • Power consumption • communication related • transmission, reception, and idle mode • non-communication related • Processing and sensing • Focus in power savings during transmission and reception.

4. Introduction (2/2) • Maximizing the network lifetime • Until the first node runs out of battery power • the time until a fraction of sensors run out of battery • the average sensor lifetime • the time until the first loss of some desired coverage • Nodes are not mobile and the topology of the network is static • Results are applicable to networks are either static • Topology changes slowly enough • Enough time for optimally balancing the traffic

5. System Model(1/4) • Basic System Model [1] • Routing model • Graph G(N,A) • N is the set of all nodes • A is the set of all directed links • Energy consumption model • Each node i has the initial battery energy Ei • transmission energy consumed at node i to transmit a data unit to its neighboring node j : • transmission rate of commodity • total amount of energy spent by a given sensor i

6. System Model(2/4) • Lifetime model • Sum total cost of the transmitted data • Sum the total cost of the received data • System lifetime orthe network lifetime • Conservation of flow condition • Total transmitted load equals the sum of sensor’s initial load and the total load received from other sensors

7. System Model(3/4) • Another conventional routing model [2] • Different assumptions • All links are assumed to bi-directional • Transmission rate on each link is fixed • Each node considers the energy consumption only from transmission • Data aggregation model [3] • Data collected by the neighboring senor nodes may carry redundant information • Aggregate the data at the intermediate nodes • The aggregated transit traffic • The transit traffic passed from the upstream nodes • Raw data originated from the upstream nodes

8. System Model(4/4) • Mobile sink model [4] • Distinct sink node s, moving between different locations • Traffic rate and transmission power • The sink is allowed to move between two locations, leading to double a network lifetime. • Schedule model with routing [6] • Schedule is periodic with N time slots • During each slot, set of powers and rates over each link N

9. Problem formulation(1/3) • Find the flow that maximizes the system lifetime • Linear programming problem • Conservation of linear programming problem

10. Problem formulation(2/3) • Ordinary optimization formulation[2] • Maximizes the network lifetime solve the following problem in a distributed manner. • Optimization formulation with mobile sink [4] • One more sigma notation from the mobile sink and its location is added

11. Problem formulation(3/3) • nth conditional lifetime maximization problem [5] • Want to find • Time slot formulation for scheduling [6] • Non-convex problem

12. Algorithm or analysis and results (1/16) • Chang and Tassiulas, August 2004. [1] • Flow augmentation (FA) algorithm • To find the minimum cost path. • Design the link cost function • some parameters to consider in calculating the link cost • energy expenditure for unit data transmission • initial energy, residual energy • Proposed link cost function

13. Algorithm or analysis and results (2/16) • Chang and Tassiulas, August 2004. [1] • Simulation result

14. Algorithm or analysis and results (3/16) • Madan and Lall, August 2006. [2] • Subgradient algorithm • Completely distributed algorithm

15. Algorithm or analysis and results (4/16) • Madan and Lall, August 2006. [2] • Partially distributed algorithm • Completely distributed algorithm

16. Algorithm or analysis and results (5/16) • Hua and Yum, August 2008. [3] • Smoothing Function • max function can be approximated by the following smoothing function • Minimizing the first term will enforce data aggregation at the intermediate nodes • Minimizing the second term of U(w,c) will cause the power consumption of the set of bottleneck nodes to be equalized • effect of maximizing the network lifetime

17. Algorithm or analysis and results (6/16) • Hua and Yum, August 2008. [3] • Optimality Conditions • Necessary Condition • Sufficient Condition

18. Algorithm or analysis and results (7/16) • Hua and Yum, August 2008. [3] • Distributed Algorithm and Protocol

19. Algorithm or analysis and results (8/16) • Gatzianas and Georgiadis, August 2006. [4] • Dual problem formulation • Subgradient projection algorithm

20. Algorithm or analysis and results (9/16) • Gatzianas and Georgiadis, August 2006. [4] • Proposed distributed Algorithm

21. Algorithm or analysis and results (10/16) • Gatzianas and Georgiadis, August 2006. [4] • Simulation results

22. Algorithm or analysis and results (11/16) • Dagher, Marcellin, and Neifeld, February 2007. [5] • Optimal algorithm via iteration

23. Algorithm or analysis and results (12/16) • Dagher, Marcellin, and Neifeld, February 2007. [5] • Energy sink node • Each sensor can independently waste an arbitrary amount of its energy by communicating with this energy sink • Properties

24. Algorithm or analysis and results (13/16) • Dagher, Marcellin, and Neifeld, February 2007. [5] • Theory

25. Algorithm or analysis and results (14/16) • Madan, Cui, Lall and Goldsmith, November 2006. [6] • Optimization problem : Routing, Power Control for a fixed scheduling • For a fixed link schedule, the convex optimization problem • Link Scheduling • To find the best link schedule, we need to solve above problem for all possible link schedules • Use suboptimal approach to iterate between scheduling and computation of rates and powers

26. Algorithm or analysis and results (15/16) • Madan, Cui, Lall and Goldsmith, November 2006. [6] • Suboptimal Algorithm

27. Algorithm or analysis and results (16/16) • Madan, Cui, Lall and Goldsmith, November 2006. [6] • Simulation results

28. Big Picture (1/2) • Common goal of papers • Maximization of lifetime in wireless sensor networks • Different approaches such as routing and scheduling • Different mathematical analyzing tools

29. Big Picture (2/2)

30. Criticism and conclusion • Lifetime maximization in sensor network • Survey six papers • Similar problems • But having special features • Using different mathematical approaches • Problems • Only choose papers related to routing • Want to narrow the scope • Show more relationships • Importance of routing in sensor network

31. References • [1] Jae-Hwan Chang and Leandros Tassiulas, "Maximum Lifetime Routing in Wireless Sensor Networks", IEEE Trans. Networking, Vol.12, No.4, pp. 609-619, August 2004. • [2] Ritesh Madan and Sanjay Lall, "Distributed Algorithms for Maximum Lifetime Routing in Wireless Sensor Netwokrs", IEEE Trans. Wireless Communications, Vol.5, No.8, pp. 2185-2193, August 2006. • [3] Cunqing Hua and Tak-Shing Peter Yum, "Optimal Routing and Data Aggregation for Maximizing Lifetime of Wireless Sensor Networks", IEEE Trans. Networking, Vol.16, No.4, pp. 892-903, August 2008. • [4] Marios Gatzianas and Leonidas Georgiadis, "A Distributed Algorithm for Maximum Lifetime Routing in Sensor Networks wih Mobile Sink", IEEE Trans. Wireless Communications, Vol.7, No.3, pp. 984-994, March 2008. • [5] Joseph C. Dagher, Michael W. Marcellin and Mark A. Neifeld, "A theory for Maximizing the Lifetime of Sensor Networks", IEEE Trans. Communication, Vol.55, No.2, pp. 323-332, February 2007. • [6] Ritesh Madan, Shuguang Cui, Sanjay Lall and Andrea Goldsmith, "Cross-Layer Design for Lifetime Maximization in Interference-Limited Wireless Sensor Networks", IEEE Trans. Wireless Communications, Vol.5, No.11, pp.1-11, November 2006.