Distributed computation of transient state distributions and passage time quantiles in large semi-Markov models

Bradley, Jeremy T.; Dingle, Nicholas J.; Harrison, Peter G.; Knottenbelt, William J.

doi:10.1016/j.future.2006.02.011

Cited by 14 publications

(11 citation statements)

References 14 publications

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“…Furthermore, as α becomes smaller, the difference between E[R j ] and E[Z j ] increases as expected. 3 The above results also show that the process of switching to new users can significantly reduce the lifetime of a link and that deterministic DHT systems with Pareto L can exhibit…”

Section: Putting the Pieces Togethermentioning

confidence: 63%

“…This arises from the fact that zone size Y 1 is different from Y 2 , while Y j for j ≥ 3 are all distributed as Y 2 . Since Y 1 is stochastically smaller than Y 2 (see Lemma 3), it follows that R 1 is stochastically larger 3. Recall that smaller α leads to stochastically larger Z j and thus increases reliability of never-switching systems [13].…”

Section: Putting the Pieces Togethermentioning

confidence: 97%

“…Although it is known that the Laplace transform of the first-hitting time of a semi-Markov chain can be computed using spectral properties of kernel Q(t) [3], this approach hides the effect of system parameters on the resulting distribution. Due to the simplicity of state transitions of chain {A y δ }, we next deriveR(s, y) without involving matrix operations on Q(t).…”

Section: Conditional Link Lifetimesmentioning

confidence: 99%

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Analysis of Link Lifetimes and Neighbor Selection in Switching DHTs

Yao

Loguinov

2011

IEEE Trans. Parallel Distrib. Syst.

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Abstract-Several models of user churn, resilience, and link lifetime have recently appeared in the literature [13], [14], [36], [37]; however, these results do not directly apply to classical Distributed Hash Tables (DHTs) in which neighbor replacement occurs not only when current users die, but also when new users arrive into the system, and where replacement choices are often restricted to the successor of the failed zone in the DHT space. To understand neighbor churn in such networks, which we call switching DHTs, this paper proposes a simple, yet accurate, model for capturing link dynamics in structured P2P systems and obtains the distribution of link lifetimes for fairly generic DHTs. Similar to [9], our results show that deterministic networks (e.g., Chord [30], CAN [25]) unfortunately do not extract much benefit from heavy-tailed user lifetimes since link durations are dominated by small remaining lifetimes of newly arriving users that replace the more reliable existing neighbors. We also examine link lifetimes in randomized DHTs equipped with multiple choices for each link and show that selecting the best neighbor in these scenarios is rather complicated as it depends on the desired load-balancing, link resilience, and overhead. We offer insight into the various selection algorithms, their performance, and possibilities for improvement.

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Section: Putting the Pieces Togethermentioning

confidence: 63%

Section: Putting the Pieces Togethermentioning

confidence: 97%

Section: Conditional Link Lifetimesmentioning

confidence: 99%

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Analysis of Link Lifetimes and Neighbor Selection in Switching DHTs

Yao

Loguinov

2011

IEEE Trans. Parallel Distrib. Syst.

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“…The chain therefore can be studied as a renewal stream, with a renewal at each transition; we only need its holding time distribution as the life distribution of the stream (Jalali-Naini 1997; Minh 2001). See previous studies of Kulkarni (1995), Cotea and Stein (2006), Bradley et al (2006), Bradley and Wilson (2005), and Jenamani et al (2003) for some general references about semi-Markov models.…”

Section: Semi-markov Modelmentioning

confidence: 99%

Forecasting time and place of earthquakes using a Semi-Markov model (with case study in Tehran province)

Sadeghian

2012

J Ind Eng Int

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The paper examines the application of semi-Markov models to the phenomenon of earthquakes in Tehran province. Generally, earthquakes are not independent of each other, and time and place of earthquakes are related to previous earthquakes; moreover, the time between earthquakes affects the pattern of their occurrence; thus, this occurrence can be likened to semi-Markov models. In our work, we divided the province of Tehran into six regions and grouped the earthquakes regarding their magnitude into three classes. Using a semi-Markov model, it proceeds to predict the likelihood of the time and place of occurrence of earthquakes in the province.

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“…Semi-Markov stochastic Petri nets (SM-SPNs) [Ciardo94,Bradley03b] are extensions of GSPNs that support arbitrary marking-dependent holding-time distributions, and that generate an underlying semi-Markov process rather than a Markov process.…”

Section: Semi-markov Stochastic Petri Netsmentioning

confidence: 99%

Performance Trees: A Query Specification Formalism for Quantitative Performance Analysis

Knottenbelt¹,

Dingle²,

Suto³

Computational Science, Engineering &Amp; Technology Series

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Real-life systems are often plagued by unanticipated performance problems caused by subtle bugs and bottlenecks. It is thus essential for system designers and engineers to have an understanding of their fundamental performance characteristics, both before and after implementation. Stochastic modelling and analysis respectively provide the means to abstract systems as mathematical descriptions and to derive quantifiable measures of interest from them.A major, and so far largely unaddressed, challenge is the specification of complex performance queries on models in an accessible manner that does not sacrifice expressiveness. This thesis attempts to address this challenge by introducing Performance Trees, a new formalism for the graphical specification of complex performance queries on stochastic models. Performance Trees are designed to be accessible by providing a more intuitive approach to query specification, expressive by being able to reason about a far broader range of concepts than current alternatives, extensible by supporting additional user-defined concepts, and versatile through their applicability to multiple modelling formalisms. Performance Trees are presented in the context of a rigorous formal framework that defines the syntax, typing and quantitative semantics of operators.Prototype tool support is implemented in the form of a module of the PIPE2 Petri net tool, which provides graphical user interfacing and Performance Tree query design capabilities.

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Distributed computation of transient state distributions and passage time quantiles in large semi-Markov models

Cited by 14 publications

References 14 publications

Analysis of Link Lifetimes and Neighbor Selection in Switching DHTs

Analysis of Link Lifetimes and Neighbor Selection in Switching DHTs

Forecasting time and place of earthquakes using a Semi-Markov model (with case study in Tehran province)

Performance Trees: A Query Specification Formalism for Quantitative Performance Analysis

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