Introducing speculation in self-stabilization

Abstract

Self-stabilization ensures that, after any transient fault, the system recovers in a finite time and eventually exhibits correct behavior. Speculation consists in guaranteeing that the system satisfies its requirements for any execution but exhibits significantly better performances for a subset of executions that are more probable. A speculative protocol is in this sense supposed to be both robust and efficient in practice.We introduce the notion of speculative stabilization which we illustrate through the mutual exclusion problem. We then present a novel speculatively stabilizing mutual exclusion protocol. Our protocol is self-stabilizing for any asynchronous execution. We prove that its stabilization time for synchronous executions is diam(g)/2 steps (where diam(g) denotes the diameter of the system).This complexity result is of independent interest. The celebrated mutual exclusion protocol of Dijkstra stabilizes in n steps (where n is the number of processes) in synchronous executions and the question whether the stabilization time could be strictly smaller than the diameter has been open since then (almost 40 years). We show that this is indeed possible for any underlying topology. We also provide a lower bound proof that shows that our new stabilization time of diam(g)/2 steps is optimal for synchronous executions, even if asynchronous stabilization is not required.

Exploiting Synchronicity for Immediate Feedback in Self-Stabilizing PIF Algorithms

“…In our approach, we need four states in the design of our PIF algorithm, because we need to have four different meaningful tokens. Considering the convergence time complexity, the work [20] presents a mutual exclusion algorithm for any connected graph G, whose convergence time in synchronous environments is less than the graph diameter. Although the convergence time is interesting, the e-time is relatively high if the number of active processes is low.…”

Self-stabilizing Systems in Spite of High Dynamics

“…the "quality" of the environment, i.e., the more favorable the environment is, the better the complexity of the algorithm should be. Interestingly, Dubois and Guerraoui [26] have investigated speculation in self-stabilizing, yet static, systems. They illustrate this property with a self-stabilizing mutual exclusion algorithm whose stabilization time is significantly better when the execution is synchronous.…”

On Implementing Stabilizing Leader Election with Weak Assumptions on Network Dynamics

“…Indeed, an algorithm is speculative whenever it satisfies its requirements for all executions, but also exhibits significantly better performances in a subset of more probable executions. Speculative self-stabilization has been initially investigated in static networks [19]. Yet, recently, speculative selfstabilizing solutions for dynamic networks have been proposed [2]: when convergence time cannot be bounded in a very general class, an important subclass where it can be is exhibited.…”