Universal adaptive self-stabilizing traversal scheme: Random walk and reloading wave

Abstract

In this paper, we investigate random walk based token circulation in dynamic environments subject to faults. We describe hypotheses on the dynamic environment that allow random walks to meet the important property that the token visits any node infinitely often. The randomness of this scheme allows it to work on any topology, and requires no adaptation after a topological change, which is a desirable property for applications to dynamic systems. For random walks to be a traversal scheme and to solve the concurrency problem, one needs to guarantee that exactly one token circulates in the system. In the presence of transient faults, configurations with multiple tokens or with no token can occur. The meeting property of random walks solves the cases with multiple tokens. The reloading wave mechanism we propose, together with timeouts, allows us to detect and solve cases with no token. This traversal scheme is self-stabilizing, and universal, meaning that it needs no assumption on the system topology. We describe conditions on the dynamicity (with a local detection criterion) under which the algorithm is tolerant to dynamic reconfigurations. We conclude with a study on the time between two visits of the token to a node, which we use to tune the parameters of the reloading wave mechanism according to some system characteristics.