1. Online Data Gathering for Maximizing Network Lifetime in Sensor Networks IEEE transactions on Mobile Computing Weifa Liang, YuZhen Liu

2. 2 Outline Introduction System model Generic Cost Model of Energy Consumption Problem Definition Algorithms For Online Data Gathering Performance Evaluation Conclusions

3. 3 Introduction The main constraint of sensor nodes is their low battery energies, which limit the networks lifetime. The network lifetime of a wireless sensor network is defined as the time of the first node failure in the network. Energy efficiency in the design of routing protocols for sensor network is of paramount importance.

4. 4 Introduction To prolong the network lifetime, there are many different energy optimization metrics have been proposed. – Minimize the total energy consumption – Maximize the lifetime of each node There are two typical forms of data gathering queries: – Periodic collection. – Event driven.

5. 5 Introduction Consider an online data gathering problem in sensor networks: – There is a sequence of data gathering queries, which arrive one by one. – To respond each query as it arrives, the system build a routing tree for it. – Within the tree, the volume of the data transmitted by each internal node depends on not only the volume of sensed data by the node itself, but also the volume of data received from it children.

6. 6 Introduction The objective is to maximize the network lifetime without any knowledge of future query arrivals and generation rates. The experimental results show that, among the proposed algorithms, one algorithm that takes into account both residual energy and the volume of data at each sensor outperform the others.

7. 7 System Model Consider a wireless sensor network consisting of : – N stationary sensor nodes and a base station S distributed over a region. – Location of each sensor and base station are fixed and known a priori. – Every sensor equipped with an omni-directional antenna. We take into account the transmission energy consumption only and assume that the other energy consumption such as reception are negligible.

8. 8 System Model The wireless sensor network can be modeled by a directed graph M = (N,A). – N is the set of nodes, A is the set of edges, – Edge in A if node v is within the transmission range of u. – For u, v with distance, the transmission energy at node u is modeled to be proportional to if a unit of message is transferred from u to v. – is a path-loss exponent parameter depending on the characteristics of communication medium.

9. 9 Generic Cost Model of Energy Consumption – Symbol Definition Given a data gathering query, we aim to build a routing tree T rooted at the sink node. For each node v: – p(v) be the parent of v in T. – be the length of the sensed message by v – A relay node v in T, assume the lengths of messages that v received from t children are – be the amount of energy consumption of receiving and sensing a unit of message by a sensor.

10. 10 Generic Cost Model of Energy Consumption v may or may not aggregate these messages and its own sensed message before transmitting them as a single message to its parent p(v). The length of message transmitted by v to its parent is a function f with parameters and

11. 11 Generic Cost Model of Energy Consumption The definition of f may vary, depending on application domains. There are two frequently used f below: – The length of message transmitted by a relay node is independent of message lengths of its children and itself. – The length of the message transmitted by a relay node depends on the message lengths of its children and itself.

12. 12 Generic Cost Model of Energy Consumption If v is a relay node with children the cost c(v) of v is thus – If v is a leaf node, f is a function of only the cost c(v) of v is thus –

13. 13 Generic Cost Model of Energy Consumption-Three well-known model Case1: Assume that – Total transmission energy consumption is considered: – Minimum residual energy among the nodes is considered:

14. 14 Generic Cost Model of Energy Consumption-Three well-known model Case2: Assume that – Total transmission energy consumption is considered: – Minimum residual energy among the nodes is considered: Case3 is the mixture of case1 and case2 that takes into account both optimization objectives simultaneously.

15. 15 Problem Definition The online data gathering problems is to maximize the network lifetime without knowledge of future query arrivals and the generation rate. As a query arrives, the response by the system to query is to build a routing tree rooted at the sink and spanning the other nodes for it. All in all, the problem is to maximize the number of queries answered until the first node in the network fails.

16. 16 Algorithms for Online Data Gathering -MNL The proposed algorithm is that, once a data gathering query arrives, a data gathering tree for the query is constructed using a greedy policy that maximize the minimum residual energy among the nodes. If node v is included into the tree if it leads to maximizing the minimum residual energy. The nodes are included into the tree one by one.

17. 17 Algorithms for Online Data Gathering -MNL Symbol Definition T and : the tree and the set of nodes included in T. Initially, the set of nodes in T contains the sink node only. Each time the algorithms picks up a node v from such that is maximized. The algorithm continues until all nodes are checked

18. 18 Algorithms for Online Data Gathering -MNL Let node be the considered node. 1. If there are l edges from v to the nodes in denoted by, where for all I, define 2. Otherwise( there is not any edge from v to the nodes in ), define

19. 19 Algorithms for Online Data Gathering -MNL

20. 20 Algorithms for Online Data Gathering -MNL

21. 21 Algorithms for Online Data Gathering -MMRE Maximization of the minimum residual energy (MMRE) among the nodes in the network. An inverted spanning tree instead of a broadcast tree is constructed. Let T be tree tree and be the set of nodes in T. The sink node s in included in T and initially. Each time it picks up a node if v satisfies The Algorithm continues until

22. 22 Algorithms for Online Data Gathering -SPT Minimization of the total transmission energy consumption of relaying the sensed message from a sensor to the sink node. An energy graph G(V,E) is derived from the sensor network. – V: the set of sensor nodes and sink node s – Directed edge in E from u to v if the residual energy at u is at least – The weight assigned to the edge is, which is the energy consumption of transmitting a init message between of two nodes A single-source shortest path tree rooted at the sink node is constructed. The minimum transmission energy consumption to send its k- units sensed message to the sink node is Thus, the total transmission energy consumption is

23. 23 Algorithms for Online Data Gathering -BT An undirected, energy graph for the sensor network is defined. – V: set of sensor nodes – E: set of undirected links We aim to prolong the network lifetime by dealing with two opposite optimization. – Minimize the total energy consumption of all nodes – Minimize the total energy consumption by each node However, constructing a spanning tree that meets these two optimization objective is NP-hard

24. Balancing Minimum Spanning and Shortest Path Trees, 1993 24 Algorithms for Online Data Gathering -BT An approximate algorithm that balances these two optimization objectives is available, and a solution delivered by the proposed algorithm is within times of the optimum [15]. Despite algorithm BT taking the total energy consumption for realizing a data gathering query into consideration, it doesn’t take into account the residual energy at each individual node. This results in the nodes near the tree root running out of their batteries quickly.

25. Efficient Algorithms for Finding minimum spanning Trees in Undirected and Directed Graphs 25 Algorithms for Online Data Gathering -MDST Is similar to the one of algorithm BT, but different weight function is used. The weight assigned to a link is Where Beta is the energy utilization ratio at node u, between its consumed energy and its initial capacity.

26. 26 Performance Evaluation

27. 27 Performance Evaluation

28. 28 Performance Evaluation

29. 29 Conclusions The experimental results showed that algorithm MNL significantly outperforms the others algorithms including MDST, MMRE, SPT, and BT. An Algorithm take the total energy consumption for realizing a data gathering query into consideration, it would result in the nodes near the tree root running out of their batteries quickly after a number of data gathering queries are realized, since those nodes always relay messages for the other nodes.