A Control Theory Approach to Self-Stabilizing in Large .ppt

1、sma5510-research methodology,1,A Control Theory Approach to Self-Stabilizing in Large Distributed System,Student: Fang Hui Supervisor: Teo Yong Meng,2,sma5510-research methodology,Outline,Objective Measurement model Dynamical analysis Algorithm based on parameters Conclusion,3,sma5510-research metho

2、dology,Objective,Find a way to describe the distributed system stability, and how to measure stabilityAnalyze the stability bound and finite convergence.,4,sma5510-research methodology,Stability of Distributed System,The conception of self-stabilizing distributed computation was first proposed and e

3、xplored by Dijkstra in 1974. A distributed system is self-stabilizing if, when started from an arbitrary initial state, it is guaranteed to reach a legitimate state. Once in a legal state, the system does not switch to an illegal state in the absence of failures.,5,sma5510-research methodology,Assum

4、ptions,Node can only communicate with neighbors whose pointer contained in its routing table The links and node both may fail and recover during normal operation The recovery should be without global intervention, but system will consider the stability in global state sense Each node will keep some

5、extent stability,6,sma5510-research methodology,Measurement,Global stability is accumulated by each nodes stability. The node stability is derived from its connectivity knowledge.,7,sma5510-research methodology,Measurement (contd),Divides the system stability into two types: vertex stability (consid

6、ering node failure/leave) , edge stability (considering routing information)G= (V, E), where | V | = n is network size Stability distribution matrix: (D : link, w :node),8,sma5510-research methodology,Node & Global Stability,The value of node-i stability,Global stability,9,sma5510-research methodolo

7、gy,Stability examples,10,sma5510-research methodology,Model of Dynamical System,Consider routing inconsistency An incoming message updates or adds new routing entries (new pointer to other node). This can also be caused by nodes periodically maintanence messages besides query messages. The extra mes

8、sage will consume bandwidth to some extent. The node flushes the outdated entries in its routing table, in terms of out-going message timeout or other possible way.,11,sma5510-research methodology,Two parameters (p,q),p: model the factor contributing to improving stability. q: model the factor contr

9、ibuting to decreasing stability.,12,sma5510-research methodology,Profile of node stability tendency,Max: p/(p+q),Node stability,13,sma5510-research methodology,When (p,q) vary,Now we consider the p and q the functions of abstract time t.,where p(t), q(t) in 0,1,14,sma5510-research methodology,Proved

10、 Property 2,15,sma5510-research methodology,(p,q)-feedback,Based on above, design a feed-back system and algorithm by dynamically adjusting factor p(t) and q(t) in each step. Node stability can be maintained in certain level efficiently.,16,sma5510-research methodology,Algorithm 1: achieve node stab

11、ility x* in finite time,17,sma5510-research methodology,Algorithm 2: achieve global stability in finite time,18,sma5510-research methodology,The advantage of algorithm,No explicit node coordination after global stability requirement sent out.Termination-detection unnecessary due to finite time.,19,s

12、ma5510-research methodology,Conclusion,Analyze the node behavior of distributed system and give a practical evaluation on the global stability, local stability and expected convergence time.Sort out the parameters which impact the stability dynamically, by disseminating the global stability requirem

13、ent and each node reach/maintain local stability in finite time.,20,sma5510-research methodology,Open issues,Introduce more advanced parameters to describe the global stability of system in control theory perspective.A predefined threshold value of stability may not enough. More accuracy on the global stability also depends on the network topology, or stability distribution (specified in previous section).,