Topological Adaptability for the Distributed Token Circulation Paradigm in Faulty Environment

Abstract

In this paper, we combine random walks and self-stabilization to design a single token circulation algorithm. Random walks have proved their efficiency in dynamic networks and are perfectly adapted to frequent network topological changes. Self-stabilization is the most general technique to design an algorithm that tolerates transient failures. Taking account that the token circulates continually according to a random walk scheme, designing a self-stabilizing algorithm implies to solve two situations (1) no token in the system and (2) several tokens in the system. The former is generally solved by a time-out mechanism, upon timeout a new token is created. In this paper, we focus on this problem. Just state that one may choose a sufficiently long time-out period is not possible in our case: the system could never stabilize. Indeed, a random walk based token eventually cover the network but only the expected time to cover the network can be captured. Therefore, we introduce a mechanism “the reloaded wave propagation” to prevent unnecessary token creation and preserve self-stabilization properties.