Methods for modelling and generating probabilistic components in digital computer simulation when the standard distributions are not adequate

Schmeiser, Bruce W.

doi:10.1145/1102786.1102791

Cited by 11 publications

(5 citation statements)

References 31 publications

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“…The Gamma distribution is also known as the Pearson type III distribution, and is one of a family of distributions used to model the empirical distribution functions of certain data [31]. Based on the first four moments, the data can be associated with a preferred distribution.…”

Section: Mathematical Preliminariesmentioning

confidence: 99%

Modeling Heterogeneous Network Interference Using Poisson Point Processes

Heath

Kountouris

Bai

2013

IEEE Trans. Signal Process.

382

313

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Cellular systems are becoming more heterogeneous with the introduction of low power nodes including femtocells, relays, and distributed antennas. Unfortunately, the resulting interference environment is also becoming more complicated, making evaluation of different communication strategies challenging in both analysis and simulation. Leveraging recent applications of stochastic geometry to analyze cellular systems, this paper proposes to analyze downlink performance in a fixedsize cell, which is inscribed within a weighted Voronoi cell in a Poisson field of interferers. A nearest out-of-cell interferer, out-ofcell interferers outside a guard region, and cross-tier interference are included in the interference calculations. Bounding the interference power as a function of distance from the cell center, the total interference is characterized through its Laplace transform. An equivalent marked process is proposed for the out-of-cell interference under additional assumptions. To facilitate simplified calculations, the interference distribution is approximated using the Gamma distribution with second order moment matching. The Gamma approximation simplifies calculation of the success probability and average rate, incorporates small-scale and largescale fading, and works with co-tier and cross-tier interference. Simulations show that the proposed model provides a flexible way to characterize outage probability and rate as a function of the distance to the cell edge.

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Section: Mathematical Preliminariesmentioning

confidence: 99%

Modeling Heterogeneous Network Interference Using Poisson Point Processes

Heath

Kountouris

Bai

2013

IEEE Trans. Signal Process.

382

313

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“…Another commonly used approach is Gaussian-Chebyshev based approximation [24], which can provide a good approximation, but results in a long series and thus is too complicated for further analysis. In contrast, [25] shows that the Pearson distributions (a family of continuous probability functions) can provide accurate approximations to certain empirical distribution functions. Motivated by this, we adopt the Pearson type III distribution, i.e., the Gamma distribution [26], to approximate the distribution of X int , where the parameters of the Gamma distribution can be obtained by matching X int 's first and second moments, also known as moment matching.…”

Section: A Decoding Probability Of Swarm Headmentioning

confidence: 99%

Towards Reliable UAV Swarm Communication in D2D-Enhanced Cellular Network

Han

Liu

Duan

et al. 2020

Preprint

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In the existing cellular networks, it remains a challenging problem to communicate with and control an unmanned aerial vehicle (UAV) swarm with both high reliability and low latency. Due to the UAV swarm's high working altitude and strong ground-to-air channels, it is generally exposed to multiple ground base stations (GBSs), while the GBSs that are serving ground users (occupied GBSs) can generate strong interference to the UAV swarm. To tackle this issue, we propose a novel two-phase transmission protocol by exploiting cellular plus device-to-device (D2D) communication for the UAV swarm. In Phase I, one swarm head is chosen for ground-to-air channel estimation, and all the GBSs that are not serving ground users (available GBSs) transmit a common control message to the UAV swarm simultaneously, using the same cellular frequency band. Both the swarm head and other swarm members can utilize the high power gain from multiple available GBSs' transmission, to combat the strong interference from occupied GBSs, while some UAVs may fail to decode the message due to uncorrelated ground-to-air channels. In Phase II, all the UAVs that have decoded the common control message in Phase I further relay it to the other UAVs in the swarm via D2D communication, by exploiting the less interfered D2D frequency band and the proximity among UAVs. In this paper, we aim to characterize the reliability performance of the above two-phase protocol, i.e., the expected percentage of UAVs in the swarm that can decode the common control message, which is a non-trivial problem due to the complex system setup and the intricate coupling between the two transmission phases. Nevertheless, we manage to obtain an approximated expression of the reliability performance of interest, under reasonable assumptions and with the aid of the Pearson distributions. Numerical results validate the accuracy of our analytical results and show the effectiveness of our protocol over other benchmark protocols. We also study the effect of key system parameters on the reliability performance, to reveal useful insights on the practical design of cellular-connected UAV swarm communication.

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“…But what to do when the classical distributions are not adequate? Schmeiser (1977), in an input-modeling tutorial before commercial input-modeling software, emphasized classical four-parameter families of distributions such as the Pearson and Johnson, both elegant in that they provide one and only one distribution for any first four moments and inelegant in that they use more than one functional form. Also discussed were two relatively new four-parameter family designed explicitly for use in simulation experiments (Ramberg andSchmeiser 1974, Schmeiser andDeutsch 1977), elegant in that they used only one functional form and are relatively easy to fit, but inelegant in that the one-to-one relationship with moments is lost.…”

Section: Univariate Distributionsmentioning

confidence: 99%