Probability with Martingales

Williams, David

doi:10.1017/cbo9780511813658

Cited by 1,469 publications

(1,003 citation statements)

References 3 publications

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“…Since the stopping time has finite expectation and there is a global bound on the difference between successive variables, the Optional Stopping Theorem (see, for example, [11], p. 100) applies and so E(X T ) = X 0 . Consequently…”

Section: End Of Casesmentioning

confidence: 99%

Bounds on Herman's algorithm

Haslegrave¹

2014

Theoretical Computer Science

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Herman's self-stabilisation algorithm allows a ring of N processors having any odd number of tokens to reach a stable state where exactly one token remains. McIver and Morgan conjecture that the expected time taken for stabilisation is maximised when there are three equally-spaced tokens. We prove exact results on a related cost function, and obtain a bound on expected time which is very close to the conjectured bound.

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Section: End Of Casesmentioning

confidence: 99%

Bounds on Herman's algorithm

Haslegrave¹

2014

Theoretical Computer Science

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“…In this paper we employ basic results and tools of martingale theory (see, e.g., [36,40]) to analyze the distribution and tail bounds for certain random variables.…”

Section: Basic Notions Of Probability Theorymentioning

confidence: 99%

Analyzing probabilistic pushdown automata

Brázdil

Esparza²,

Kiefer

et al. 2012

Form Methods Syst Des

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“…Any book on standard reliability theory will provide greater detail on the above relations, we used [47].…”

Section: Distribution-independent Formulationmentioning

confidence: 99%

A Model-Based Case for Redundant Computation

Stearley

Robinson

Ferreira

et al. 2011

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Despite its seemingly nonsensical cost, we show through modeling and simulation that redundant computation merits full consideration as a resilience strategy for next-generation systems. Without revolutionary breakthroughs in failure rates, part counts, or stable-storage bandwidths, it has been shown that the utility of Exascale systems will be crushed by the overheads of traditional checkpoint/restart mechanisms. Alternate resilience strategies must be considered, and redundancy is a proven unrivaled approach in many domains. We develop a distribution-independent model for job interrupts on systems of arbitrary redundancy, adapt Daly's model for total application runtime, and find that his estimate for optimal checkpoint interval remains valid for redundant systems. We then identify conditions where redundancy is more cost effective than non-redundancy. These are done in the context of the number one supercomputers of the last decade, showing that thorough consideration of redundant computation is timely -if not overdue.

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Probability with Martingales

Cited by 1,469 publications

References 3 publications

Bounds on Herman's algorithm

Bounds on Herman's algorithm

Analyzing probabilistic pushdown automata

A Model-Based Case for Redundant Computation

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