Rigorous Performance Evaluation of Self-Stabilization Using Probabilistic Model Checking

Abstract

We propose a new metric for effectively and accurately evaluating the performance of self-stabilizing algorithms. Self-stabilization is a versatile category of fault-tolerance that guarantees system recovery to normal behavior within a finite number of steps, when the state of the system is perturbed by transient faults (or equally, the initial state of the system can be some arbitrary state). The performance of self-stabilizing algorithms is conventionally characterized in the literature by asymptotic computation complexity. We argue that such characterization of performance is too abstract and does not reflect accurately the realities of deploying a distributed algorithm in practice. Our new metric for characterizing the performance of self-stabilizing algorithms is the expected mean value of recovery time. Our metric has several crucial features. Firstly, it encodes accurate average case speed of recovery. Secondly, we show that our evaluation method can effectively incorporate several other parameters that are of importance in practice and have no place in asymptotic computation complexity. Examples include the type of distributed scheduler, likelihood of occurrence of faults, the impact of faults on speed of recovery, and network topology. We utilize a deep analysis technique, namely, probabilistic model checking to rigorously compute our proposed metric. All our claims are backed by detailed case studies and experiments.

Cloud Application Predictability through Integrated Load-Balancing and Service Time Control

“…Bounding latencies is of utmost importance, but this is quite difficult in the presence of changes [5,6,14,24,25,42]. Changes are unpredictable, they can be dramatic, and they can include malfunctioning [23], slow down [12], failures [18], and much more. Graceful degradation [31] is then introduced into the runtime system, to handle these changes and guarantee performance in the presence of uncertainty.…”

Synthesizing optimal bias in randomized self-stabilization

“…A more challenging avenue of research is to not only parameterize the probability function, but also make the computational model parametric in terms of the number of processes. Finally, we can use our techniques to automatically generate state encoding [14,15] schemes to orthogonally improve the recovery time.…”

“…This paper addresses the aforementioned problem in the context of randomized self-stabilizing systems. Following the results in [14,15], our choice of performance metric is average recovery time. In particular, we propose a fully automated technique that takes as input a randomized selfstabilizing algorithm, where processes execute their actions with some probability, and generates as output the probability value based on which, the self-stabilizing algorithm exhibits the minimum average recovery time.…”

“…Finally, in [15], the authors studied the role of different parameters on the convergence time of self-stabilizing systems using probabilistic model checking. In particular, they showed that the asymptotic worst-case complexity is not necessarily the best metric to characterize the performance of self-stabilizing systems.…”

Improving Cloud Service Resilience Using Brownout-Aware Load-Balancing

“…In the context of self-stabilization, a new metric has been proposed to measure the recovery performance of an algorithm, the expected number of recovery steps [34]. An equivalent metric, the number of control decisions to recovery, could be used by a service operator for tuning the service to the expected capacity drop and the request servicing time of the replicas.…”