1. 慈濟大學醫學資訊系演講簡報 題目 運用叢集組合及分散法則於無線網路點遷移 拓樸之定型 (Cluster Association and Dissociation Method due to node migrations for Topology Dominating in Wireless Networks) Presented by Reu-Ching Chen 2009/10/26

2. 個人簡歷 學歷 : 逢甲大學資訊博士 (95 年畢業 ) 經歷 : 中華電信高級技術員 (70/1~95/3) 現職 : 南開科技大學助理教授 (95/8~ 迄今 ) 證照 : 高考及格 榮譽 : 中央研究院 JISE 2007 Annual best paper award

3. 可教授科目 1. 演算法, 計算機結構, 作業系統 2. 線性代數, 機率論, 隨機過程

4. Outline 1. Introduction 2. Model Description 3. Mathematical Analysis 4. Numerical Results and Discussions 5. Conclusion

5. 1.Introduction Traditional organization on real-time communications  Infrastructure-based ( which is fixed organization) Modern organization  Self-organized Peer-to-peer communication will be unrealistic when the total number of communicating node become large

6. Conti. Node partition method due to cluster association and dissociation will be useful for topology dominating. Closed migration system(total number of nodes in the system N is fixed) is considered here. Markov-chain(memory-less property) is adopted for the system topology dominating in our study.

7. 2.Model Description Continuous time Markov chain (CTMC) is used for analysis (Example: a two-state model is depicted as follows) State 0State 1

8. Conti. Where and are the transition probability for state 0 and 1, respectively The system is assumed ergodic, I.e., for the existence of the steady state condition,we have

9. Conti.(Cluster organization) Two clusters: cluster 1 and 2 contain five groups and three groups respectively Cluster 1Cluster 2

10. Conti. Therefore, in general, each group in cluster i contains i nodes Node 1 Node i

11. Conti. The system includes finite number of clusters, where each group located in the same cluster owning the same number of nodes.

12. Conti. Theoretically, since the system topology changes with time dynamically, then in a unit of time,any nodes of a group (belongs to a specific cluster) can dissociate and be combined with other nodes to constitute one group of a cluster.

13. Conti. For convenience, the system state transitions are carried by the following migration rules. Rule1: U individuals of cluster 1 can associate to constitute a group of cluster U. Rule 2:one group of cluster U can only dissociate to constitute a U individuals of cluster 1.

14. Conti.(migration rule) Cluster 1Cluster MCluster N 1 M 1N 1 M1N

15. 3. Mathematical analysis The following notations are adopted for parameters Let N indicate the total number of nodes. Let indicate the total number of groups in cluster i then

16. Conti. Let indicate the probability intensity that cluster 1 associates its U individuals to generate a group of cluster U Let indicate the probability intensity that a group in cluster U disassociate into U individuals

17. Conti.(state transition diagram) Let indicate the countable state space, and be the state, then the CTMC is as follows

18. Conti. Where Define the disassociate and associate operators as follows

19. Conti. Then the transition rates between states are and

20. Conti. We have the following theorem Theorem: if there exist a positive numbers denoted by satisfying the following relation then the solution for the N nodes system has the closed form.

21. Conti.(closed form solution) I.e., Proof > the proof is completed by conjunction of the above Equations and the balanced equation Where is the unique collection of positive numbers summing to unity, I.e.,

22. Conti. Since the group number is a stochastic process with state space {1,2,…,k} that restart itself, then we can think the process is a regenerated counting process.

23. Conti. Using the strong law,The A/D ratio is

24. 4. Results and discussions Type of A/D ratio Estimated bandwidth Original bandwidth Reduced percent increasing334526% decreasing364520% normal254544% uniform334526%

25. Conti. a more accurate estimation for system performance is obtained from the the dominating topology provided here. The proposed method cab be easily implemented in any topology dominating. Node association and disassociation can be generalized without constraint.

26. Only allow one association or disassociation occurring In an infinite small time unit General case considerations State(2,2,1,0,…,0)State (5,2,0,…,0))

27. 5. Conclusions A/D ration has an critical influence to the system topology dominating the clustering method is wide spread applicable to other systems for the topology validation. our contribution is focused on provide simple estimation for topology construction

28. Conti. future challenge (1): concentrating on searching more generic topology to achieve optimal performance. future challenge(2): extend the system of closed migration process to open migration process (allow node to enter or leave the as well as to move between clusters).

29. Thanks so much for you