Checkpointing in Failure Recovery in Computing and Data Transmission

Asmussen, Søren; Lipsky, Lester; Thompson, Stephen A.

doi:10.1007/978-3-319-08219-6_18

Cited by 3 publications

(3 citation statements)

References 23 publications

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“…Recall that the distribution of L b has finite support on [0, b], given by (2). First, we prove the following general upper bound.…”

Section: Resultsmentioning

confidence: 98%

“…It was first recognized in [6] that this model results in power law distributions when the distributions of L ≡ L ∞ and A have a matrix exponential representation, and this result was rigorously proved and further generalized in [3], [11], and [16]. A related study when L = is a constant and failure/arrival rates are time-dependent Poisson distributions can be found in [2].…”

Section: Introductionmentioning

confidence: 95%

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Distribution of the Number of Retransmissions of Bounded Documents

Jelenković¹,

Skiani

2015

Advances in Applied Probability

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Retransmission-based failure recovery represents a primary approach in existing communication networks that guarantees data delivery in the presence of channel failures. Recent work has shown that, when data sizes have infinite support, retransmissions can cause long (-tailed) delays even if all traffic and network characteristics are light-tailed. In this paper we investigate the practically important case of bounded data units 0 ≤ L b ≤ b under the condition that the hazard functions of the distributions of data sizes and channel statistics are proportional. To this end, we provide an explicit and uniform characterization of the entire body of the retransmission distribution P[N b > n] in both n and b. Our main discovery is that this distribution can be represented as the product of a power law and Gamma distribution. This rigorous approximation clearly demonstrates the coupling of a power law distribution, dominating the main body, and the Gamma distribution, determining the exponential tail. Our results are validated via simulation experiments and can be useful for designing retransmission-based systems with the required performance characteristics. From a broader perspective, this study applies to any other system, e.g., computing, where restart mechanisms are employed after a job processing failure.

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“…Recall that the distribution of L b has finite support on [0, b], given by (2). First, we prove the following general upper bound.…”

Section: Resultsmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 95%

Distribution of the Number of Retransmissions of Bounded Documents

Jelenković¹,

Skiani

2015

Advances in Applied Probability

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“…The sybil attack resistant network centralities based on the hitting times of a random walk with restart have been proposed in [14,18]. Markov processes with restart are useful for the analysis of replace and restart types protocols in computer reliability, [2], [3], [17]. The restart policy is also used to speedup the Las Vegas type randomized algorithms [1], [19].…”

Section: Introductionmentioning

confidence: 99%

Hitting Times in Markov Chains with Restart and their Application to Network Centrality

Avrachenkov¹,

Piunovskiy

Zhang

2017

Methodol Comput Appl Probab

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Abstract:Motivated by applications in telecommunications, computer science and physics, we consider a discrete-time Markov process with restart. At each step the process either with a positive probability restarts from a given distribution, or with the complementary probability continues according to a Markov transition kernel. The main contribution of the present work is that we obtain an explicit expression for the expectation of the hitting time (to a given target set) of the process with restart. The formula is convenient when considering the problem of optimization of the expected hitting time with respect to the restart probability. We illustrate our results with two examples in uncountable and countable state spaces and with an application to network centrality. Key-words:Discrete Motivé par diverses applications provenant de télécommunications, informatique et de la physique, nous considerons un processus generale de Markov dans l'espace de Borel avec une possibilité de redémarrage. À chaque étape, avec une probabilité le processus redémarre a partir d'une distribution donnée et avec la probabilité complémentaire le processus continue l'évolution selon une noyau de Markov. Nous étudions l'espérance du temps de premier passage à l'ensemble donné. Nous obtenons une formule explicite pour l'espérance du temps de premier passage et démontrons que le processus avec redémarrage est Harris positif récurrent. Ensuite, nous établissons que les assertions suivantes sont équivalentes : (a) le fait d'être limité (par rapport à l'état initiale) de l'espérance du temps de premier passage; (b) la finitude de l'espérance du temps de premier passage pour presque tous les états initiaux par rapport à la probabilité invariante unique; et, (c) l'ensemble cible est de mesure positive par rapport à la probabilité invariante. Enfin, nous illustrons nos résultats théoriques avec deux exemples dans les espaces dénombrables et non dénombrables et avec l'application à la mesure de centralité de réseau.

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