Fluctuation Theory of Recurrent Events

Feller, William

doi:10.2307/1990420

Cited by 60 publications

(75 citation statements)

References 3 publications

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“…These properties, which are also well-known characteristics of certain stochastic systems, such as finite aperiodic Markov chains [22][23][24], have been rigourously established for deterministic dynamical systems exhibiting sufficiently strong mixing [25][26][27]. They have also been shown valid for a wider class of systems that remains, however, hyperbolic [28].…”

Section: Theorymentioning

confidence: 99%

Recurrence plots for the analysis of complex systems

et al. 2007

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Section: Theorymentioning

confidence: 99%

Recurrence plots for the analysis of complex systems

et al. 2007

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“…Theorem 2 ( [27]): Assume that . Then, we have where is a function of such that it goes to 0 as goes to .…”

Section: Short-term Fairnessmentioning

confidence: 99%

Design and Analysis of Medium Access Protocol: Throughput and Short-Term Fairness Perspective

Kim

Hwang

2015

IEEE/ACM Trans. Networking

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We consider a simple MAC protocol, called the renewal access protocol (RAP), that adopts all of the legacy 802.11 standard but the backoff stage feature. To meet two objectives in the design of the RAP-optimal throughput and high short-term fairness-we develop a mathematical model of the RAP and rigorously analyze the performance of the RAP. First, we show that the throughput performance of the RAP depends only on the expectation of the selection distribution where the backoff counter is selected, provided that the number of terminals is fixed, which is in accordance with a well-known result. Second, with the help of renewal and reliability theories, we analyze the short-term fairness of the RAP. We also show that if the RAP has a selection distribution of the New Better than Used in Expectation (NBUE) type, the RAP can guarantee high short-term fairness. Third, we construct a special binomial distribution that is obviously of the NBUE type that can achieve high short-term fairness as well as optimal throughput when used as the selection distribution of the RAP. Furthermore, by the Poisson approximation for binomial distributions, we propose to use in practice a Poisson distribution corresponding to the special binomial distribution. Numerical and simulation results are provided to validate our analysis.

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“…See Appendix, and also Blumenfeld and Mandelbrot (1997) who credit Feller (1949) as the original source.…”

Section: Mittag-leffler Distributionsmentioning

confidence: 99%