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Clustering Poisson Process and 1/f Noise
Japanese Journal of Applied Physics, 1986A physical interpretation has been given to the clustering Poisson process which results in a 1/f spectrum; this model is compared with a model in which the 1/f spectrum is derived from a superposition of the Lorentzian spectra. For a point process, an expression has also been derived for the higher-frequency limit to 1/f fluctuations burried in ...
Ferdinand Grüneis, Toshimitsu Musha
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Simulating a Poisson cluster process for Internet traffic packet arrivals
Computer Communications, 2010An efficient algorithm to generate a large amount of data from a Poisson cluster process is developed. This algorithm is then used to do comparisons between simulated data and real-life Internet traffic data. The simulated data is also used to check the validity of the procedures used for estimating the parameters in the model, which are evaluated in ...
Bárbara González-Arévalo, Julie Roy
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A note on the non-homogeneous poisson cluster process
Journal of Applied Probability, 1977It is proved that, in a non-homogeneous Poisson cluster process whose cluster centre rate is λ(t), the long-term behaviour of several associated quantities is equivalent to their behaviour in a homogeneous process with centre rate Λ and the same cluster structure if λ(t)→ λ as t→∞.
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On interpoint distances for planar Poisson cluster processes
Journal of Applied Probability, 1983For stationary Poisson or Poisson cluster processes ξ on R2 we study the distribution of the interpoint distances using the interpoint distance function and the nearest-neighbor indicator function . Here Sr (x) is the interior of a circle of radius r having center x, I(t) is that subset of D which has x ∊ D and St
Kryscio, Richard J., Saunders, Roy
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Modeling and analysis of HetNet interference using Poisson Cluster Processes
2014 IEEE 25th Annual International Symposium on Personal, Indoor, and Mobile Radio Communication (PIMRC), 2014Future mobile networks are converging towards being heterogeneous, owing to the co-existence of multi-tier networks within the same geographical area, including macro, pico- and femto-cells. The deployment of such networks is generally based on user demand, which is irregular and random, implying that the deployment of base stations (BSs) is random as ...
Young Jin Chun +2 more
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Prediction in a Poisson cluster model with multiple cluster processes
Scandinavian Actuarial Journal, 2013AbstractWe consider a simple but flexible extension of the Poisson cluster model studied in Matsui & Mikosch (2010). In the former, model only a single cluster process starts at each jump point of the Poisson process, whereas we start a randomly given number of cluster processes at each jump.
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The Poisson Processes in Cluster Analysis
2010This paper aims to review some use of the point processes in cluster analysis. The homogeneous Poisson process is, in many ways, the simplest point process, and it plays a role in point process theory in most respects analogous to the normal distribution in the study of random variables.
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Count distributions, orderliness and invariance of Poisson cluster processes
Journal of Applied Probability, 1979The probability generating functional (p.g.fl.) of a non-homogeneous Poisson cluster process is characterized in Ammann and Thall (1977) via a decomposition of the KLM measure of the process. This p.g.fl. representation is utilized in the present article to show that the family 𝒟 of Poisson cluster processes with a.s. finite clusters is invariant under
Ammann, Larry P., Thall, Peter F.
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Nonlinear estimation problems of poisson cluster processes
2006Doubly stochastic Poisson processes whose unobservable intensity is a shot-noise process with random amplitude arise when each event of a primary Poisson process generates a random number of subsidiary events. We derive a stochastic partial differential equation for the unnormalized conditional moment generating function.
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A Fine-grained Analysis of Wireless Powered Communication with Poisson Cluster Process
2019 11th International Conference on Wireless Communications and Signal Processing (WCSP), 2019Wireless powered communication (WPC)can provide the wireless devices (WDs)practically infinite energy for information transmission, by deploying multiple power beacons (PBs)as dedicated energy transmitter. To enable efficient transmission in WPC, this paper proposes a PB deployment strategy where the distribution of PBs is subject to a truncated ...
Siyuan Zhou +3 more
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