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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 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 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 Outline • • • • • 1. Introduction 2. Model Description 3. Mathematical Analysis 4. Numerical Results and Discussions 5. Conclusion 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 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. 2.Model Description • Continuous time Markov chain (CTMC) is used for analysis (Example: a two-state model is depicted as follows) State 0 State 1 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 t X (s)ds lim t 0 t E[ X ] Conti.(Cluster organization) • Two clusters: cluster 1 and 2 contain five groups and three groups respectively Cluster 1 Cluster 2 Conti. • Therefore, in general, each group in cluster i contains i nodes Node 1 Node i Conti. • The system includes finite number of clusters, where each group located in the same cluster owning the same number of nodes. 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. 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. Conti.(migration rule) 1 M gM 1 M Cluster M Cluster 1 1 N 1 N gN Cluster N 3. Mathematical analysis • The following notations are adopted for parameters Let N indicate the total number of nodes. Let g i indicate the total number of groups in cluster i then N ig i 1 i N Conti. • Let AU indicate the probability intensity that cluster 1 associates its U individuals to generate a group of cluster U • Let DU indicate the probability intensity that a group in cluster U disassociate into U individuals Conti.(state transition diagram) • Let G ( g1 , g 2 ,..., g k ) indicate the countable state space, and be the state, then the CTMC is as follows DU ( gU 1) g1 AU U ( g1 U , g 2 ,..., gU 1,..., g k ) ( g1 , g 2 ,..., gU ,..., g k ) Conti. • Where g1 g1! U U !(U g1 )! • Define the disassociate and associate operators as follows OU1 (G ) ( g1 U , g 2 ,..., gU 1,..., g k ) O1U (G ) ( g1 U , g 2 ,..., gU 1,..., g k ) Conti. • Then the transition rates between states are g1 T (G, O (G)) AU U 1 U and T (G, O (G )) DU ( gU ) U 1 Conti. • We have the following theorem Theorem: if there exist a positive numbers k1 , k 2 ,..., k N denoted by satisfying the following relation U !kU DU (k1 )U AU then the solution for the N nodes system has the closed form. Conti.(closed form solution) • I.e., N gi i k (G ) C N i 1 g i ! Where C N is the unique collection of positive numbers summing to unity, I.e., (G ) 1 • Proof > the proof is completed by conjunction of the above Equations and the balanced equation (G )T (G, OU1 (G )) (OU1 (G )T (OU1 (G ), G ) Conti. • Since the group number g i is a stochastic process with state space {1,2,…,k} that restart itself , then we can think the process is a regenerated counting process. Conti. • Using the strong law,The A/D ratio is X (t )dt i Ai P( X i x) 1 E ( X i ) Di P(Yi y ) 1 E (Yi ) lim 0 t t Y (t )dt i lim t 0 t 4. Results and discussions Type of A/D ratio increasing Estimated bandwidth 33 Original Reduced bandwidth percent 45 26% decreasing 36 45 20% normal 25 45 44% uniform 33 45 26% 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. General case considerations State(2,2,1,0,…,0) State (5,2,0,…,0)) Only allow one association or disassociation occurring In an infinite small time unit 5. Conclusions • <1> A/D ration has an critical influence to the system topology dominating • <2> the clustering method is wide spread applicable to other systems for the topology validation. • <3> our contribution is focused on provide simple estimation for topology construction Conti. • <4> future challenge (1): concentrating on searching more generic topology to achieve optimal performance. • <5>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). Thanks so much for you