Gradual stabilization

doi:10.1016/j.jpdc.2018.09.002

2019-01-01

PRE

DOI：10.1016/j.jpdc.2018.09.002

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摘要

En 中文

We consider dynamic distributed systems, i.e., distributed systems that can suffer from topological changes over the time. Following the superstabilizing approach, we assume here that topological changes are transient events. In this context, we introduce the notion of gradual stabilization under (tau, rho)-dynamics (gradual stabilization, for short). A gradually stabilizing algorithm is a self-stabilizing algorithm with the following additional feature: after up to tau dynamic steps of a given type rho occur starting from a legitimate configuration, it first quickly recovers to a configuration from which a specification offering a minimum quality of service is satisfied. It then gradually converges to specifications offering stronger and stronger safety guarantees until reaching a configuration (1) from which its initial (strong) specification is satisfied again, and (2) where it is ready to achieve gradual convergence again in case of up to tau new dynamic steps of type rho. A gradually stabilizing algorithm being also self-stabilizing, it still recovers within finite time (yet more slowly) after any other finite number of transient faults, including for example more than tau arbitrary dynamic steps or other failure patterns such as memory corruptions. We illustrate this new property by considering three variants of a synchronization problem respectively called strong, weak, and partial unison. We propose a self-stabilizing unison algorithm which achieves gradual stabilization in the sense that after one dynamic step of a certain type BULCC (such a step may include several topological changes) occurs starting from a configuration which is legitimate for the strong unison, it maintains clocks almost synchronized during the convergence to strong unison: it satisfies partial unison immediately after the dynamic step, then converges in at most one round to weak unison, and finally re-stabilizes to strong unison. (C) 2018 Elsevier Inc. All rights reserved.

Keyword:

Self-stabilization

Synchronization problems

Unison

Gradual stabilization

Superstabilization

Safe-convergence