Automated Analysis of Impact of Scheduling on Performance of Self-stabilizing Protocols

Aflaki, Saba; Bonakdarpour, Borzoo; Tixeuil, Sébastien

doi:10.1007/978-3-319-21741-3_11

Cited by 3 publications

(13 citation statements)

References 12 publications

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“…One can clearly see that the new algorithm significantly improves upon the original one. Comparing Old Sparse (1) and Sparse(1) which only differ in the used algorithm one can clearly see that the improved algorithm is more than two times faster. Using a symbolic representation improves the runtime further.…”

Section: Timings Of the Parameter Synthesis Algorithmmentioning

confidence: 97%

“…We also note that our techniques are completely independent of the probabilistic scheduling policy in the underlying PMC. In case the type of scheduler is of importance, one can combine the techniques introduced in this paper with the composition method in [1].…”

Section: Our Contribution-synthesizing Optimal Biasmentioning

confidence: 99%

“…We evaluate six different configurations of our parameter synthesis algorithm and display the total time in a logarithmic scale. Configuration Old Sparse (1) is the original algorithm used in previous work [2]. This configuration uses a sparse matrix representation of the PMC and is single-threaded.…”

Section: Timings Of the Parameter Synthesis Algorithmmentioning

confidence: 99%

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Synthesizing optimal bias in randomized self-stabilization

et al. 2021

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Randomization is a key concept in distributed computing to tackle impossibility results. This also holds for self-stabilization in anonymous networks where coin flips are often used to break symmetry. Although the use of randomization in self-stabilizing algorithms is rather common, it is unclear what the optimal coin bias is so as to minimize the expected convergence time. This paper proposes a technique to automatically synthesize this optimal coin bias. Our algorithm is based on a parameter synthesis approach from the field of probabilistic model checking. It over- and under-approximates a given parameter region and iteratively refines the regions with minimal convergence time up to the desired accuracy. We describe the technique in detail and present a simple parallelization that gives an almost linear speed-up. We show the applicability of our technique to determine the optimal bias for the well-known Herman’s self-stabilizing token ring algorithm. Our synthesis obtains that for small rings, a fair coin is optimal, whereas for larger rings a biased coin is optimal where the bias grows with the ring size. We also analyze a variant of Herman’s algorithm that coincides with the original algorithm but deviates for biased coins. Finally, we show how using speed reducers in Herman’s protocol improve the expected convergence time.

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Section: Timings Of the Parameter Synthesis Algorithmmentioning

confidence: 97%

Section: Our Contribution-synthesizing Optimal Biasmentioning

confidence: 99%

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Synthesizing optimal bias in randomized self-stabilization

et al. 2021

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“…This approach often proves to be the most effective solution when there is a lack of global information about the topology of a network. This applies to a range of possible networks, ad‐hoc, wireless sensor, and so on, so the approach has attracted a significant amount of attention …”

Section: Introductionmentioning

confidence: 99%

“…This applies to a range of possible networks, ad-hoc, wireless sensor, and so on, so the approach has attracted a significant amount of attention. [2][3][4][5][6][7][8] The advantage of self-stabilization algorithms lies in their elegance and simplicity. However, this comes at a cost.…”

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confidence: 99%

Performance analysis of Israeli‐Jalfon's algorithm using probabilistic model checking

2018

Concurrency and Computation

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Summary Israeli‐Jalfon's self‐stabilization algorithm provides a solution to the problem of fault tolerance in distributed systems. To quantitatively evaluate the algorithm and discover the factors contributing to its performance, we used a probabilistic model checking technique to study the algorithm across different configurations. The mainstream probabilistic model checker PRISM assisted with our final assessment. We focus here on three aspects of the algorithm's performance: convergence, time complexity, and maximum execution time. Our experimental results show that time complexity is O (N^2) when N is less than 23, and we examine the factors contributing to this performance. These prove to be: the number of tokens, the number of processes, the probability of token transmission, and how tokens are spaced. Performance degrades as the number of tokens grows. For a certain number of processes, better performance can be obtained when the probability of token transmission is 0.5. Three tokens spaced evenly, meanwhile, yields the worst performance. The main contribution of this paper is its exhaustive quantitative performance analysis of Israeli‐Jalfon's algorithm and the presentation of accurate rather than approximate numerical results. Moreover, our assessment was undertaken in a reducible fashion, with stable states being set against a proper subset of the set of possible configurations rather than allowing two sets to coincide.

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Exploring Worst Cases of Self-stabilizing Algorithms Using Simulations

Jahier,

Altisen,

Devismes

2023

Lecture Notes in Computer Science

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Self-stabilization qualifies the ability of a distributed system to recover after transient failures. SASA is a simulator of self-stabilizing algorithms written in the atomic-state model, the most commonly used model in the selfstabilizing area. A simulator is, in particular, useful to study the time complexity of algorithms. For example, one can experimentally check whether existing theoretical bounds are correct or tight. Simulations are also useful to get insights when no bound is known.In this paper, we use SASA to investigate the worst cases of various well-known self-stabilization algorithms. We apply classical optimization methods (such as local search, branch and bound, Tabu list) on the two sources of non-determinism: the choice of initial configuration and the scheduling of process activations (daemon). We propose a methodology based on heuristics and an open-source tool to find tighter worst-case lower bounds.

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Automated Analysis of Impact of Scheduling on Performance of Self-stabilizing Protocols

Cited by 3 publications

References 12 publications

Synthesizing optimal bias in randomized self-stabilization

Synthesizing optimal bias in randomized self-stabilization

Performance analysis of Israeli‐Jalfon's algorithm using probabilistic model checking

Exploring Worst Cases of Self-stabilizing Algorithms Using Simulations

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