A Control Theory Approach to Self-stabilization in Large Distributed Systems
نویسندگان
چکیده
The stability of large distributed systems plays an important role in fault tolerance. However, it is generally difficult to evaluate the distributed stability in practice. This paper proposes to divide the stability into node stability and global stability. The node stability depicts the correct routing information acquired by a node due to network change, for example: node failure or leave. The stability of the system called global stability is derived by each node’s stability. We show that this approach reflects the real stability of the overall system. To study the stability, we model a large distributed system as a dynamic system consisting of two parameters p and q, which impacts the stability in contrary way. For example: p and q can in practice model the query rate and flush-stale-node rate, respectively. From the properties induced by asymptotic analysis, a self-stabilizing algorithm is proposed based on (p, q) feedback system. This algorithm shows that each node can asynchronously achieve the predefined stability in finite time. And global stability can be obtained by setting a global threshold.
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