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Journal articles on the topic 'Poisson superposition'

Author: Grafiati

Published: 25 May 2024

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1

Crane, Harry, and Peter Mccullagh. "Poisson superposition processes." Journal of Applied Probability 52, no. 4 (December 2015): 1013–27. http://dx.doi.org/10.1239/jap/1450802750.

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Superposition is a mapping on point configurations that sends the n-tuple into the n-point configuration , counted with multiplicity. It is an additive set operation such that the superposition of a k-point configuration in is a kn-point configuration in . A Poisson superposition process is the superposition in of a Poisson process in the space of finite-length -valued sequences. From properties of Poisson processes as well as some algebraic properties of formal power series, we obtain an explicit expression for the Janossy measure of Poisson superposition processes, and we study their law under domain restriction. Examples of well-known Poisson superposition processes include compound Poisson, negative binomial, and permanental (boson) processes.

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2

Crane, Harry, and Peter Mccullagh. "Poisson superposition processes." Journal of Applied Probability 52, no. 04 (December 2015): 1013–27. http://dx.doi.org/10.1017/s0021900200113051.

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Superposition is a mapping on point configurations that sends the n-tuple into the n-point configuration , counted with multiplicity. It is an additive set operation such that the superposition of a k-point configuration in is a kn-point configuration in . A Poisson superposition process is the superposition in of a Poisson process in the space of finite-length -valued sequences. From properties of Poisson processes as well as some algebraic properties of formal power series, we obtain an explicit expression for the Janossy measure of Poisson superposition processes, and we study their law under domain restriction. Examples of well-known Poisson superposition processes include compound Poisson, negative binomial, and permanental (boson) processes.

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3

Nagel, Werner, and Viola Weiss. "Limits of sequences of stationary planar tessellations." Advances in Applied Probability 35, no. 1 (March 2003): 123–38. http://dx.doi.org/10.1239/aap/1046366102.

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In order to increase the variety of feasible models for random stationary tessellations (mosaics), two operations acting on tessellations are studied: superposition and iteration (the latter is also referred to as nesting). The superposition of two planar tessellations is the superposition of the edges of the cells of both tessellations. The iteration of tessellations means that one tessellation is chosen as a ‘frame’ tessellation. The single cells of this ‘frame’ are simultaneously and independently subdivided by cut-outs of tessellations of an independent and identically distributed sequence of tessellations. In the present paper, we investigate the limits for sequences of tessellations that are generated by consecutive application of superposition or iteration respectively. Sequences of (renormalised) superpositions of stationary planar tessellations converge weakly to Poisson line tessellations. For consecutive iteration the notion of stability of distributions is adapted and necessary conditions are formulated for those tessellations which may occur as limits.

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4

Nagel, Werner, and Viola Weiss. "Limits of sequences of stationary planar tessellations." Advances in Applied Probability 35, no. 01 (March 2003): 123–38. http://dx.doi.org/10.1017/s0001867800012118.

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In order to increase the variety of feasible models for random stationary tessellations (mosaics), two operations acting on tessellations are studied: superposition and iteration (the latter is also referred to as nesting). The superposition of two planar tessellations is the superposition of the edges of the cells of both tessellations. The iteration of tessellations means that one tessellation is chosen as a ‘frame’ tessellation. The single cells of this ‘frame’ are simultaneously and independently subdivided by cut-outs of tessellations of an independent and identically distributed sequence of tessellations. In the present paper, we investigate the limits for sequences of tessellations that are generated by consecutive application of superposition or iteration respectively. Sequences of (renormalised) superpositions of stationary planar tessellations converge weakly to Poisson line tessellations. For consecutive iteration the notion of stability of distributions is adapted and necessary conditions are formulated for those tessellations which may occur as limits.

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5

Daribayev, Beimbet, Aksultan Mukhanbet, and Timur Imankulov. "Implementation of the HHL Algorithm for Solving the Poisson Equation on Quantum Simulators." Applied Sciences 13, no. 20 (October 20, 2023): 11491. http://dx.doi.org/10.3390/app132011491.

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The Poisson equation is a fundamental equation of mathematical physics that describes the potential distribution in static fields. Solving the Poisson equation on a grid is computationally intensive and can be challenging for large grids. In recent years, quantum computing has emerged as a potential approach to solving the Poisson equation more efficiently. This article uses quantum algorithms, particularly the Harrow–Hassidim–Lloyd (HHL) algorithm, to solve the 2D Poisson equation. This algorithm can solve systems of equations faster than classical algorithms when the matrix A is sparse. The main idea is to use a quantum algorithm to transform the state vector encoding the solution of a system of equations into a superposition of states corresponding to the significant components of this solution. This superposition is measured to obtain the solution of the system of equations. The article also presents the materials and methods used to solve the Poisson equation using the HHL algorithm and provides a quantum circuit diagram. The results demonstrate the low error rate of the quantum algorithm when solving the Poisson equation.

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6

Møller, Jesper, and Kasper K. Berthelsen. "Transforming Spatial Point Processes into Poisson Processes Using Random Superposition." Advances in Applied Probability 44, no. 1 (March 2012): 42–62. http://dx.doi.org/10.1239/aap/1331216644.

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Most finite spatial point process models specified by a density are locally stable, implying that the Papangelou intensity is bounded by some integrable function β defined on the space for the points of the process. It is possible to superpose a locally stable spatial point process X with a complementary spatial point process Y to obtain a Poisson process X ⋃ Y with intensity function β. Underlying this is a bivariate spatial birth-death process (Xt, Yt) which converges towards the distribution of (X, Y). We study the joint distribution of X and Y, and their marginal and conditional distributions. In particular, we introduce a fast and easy simulation procedure for Y conditional on X. This may be used for model checking: given a model for the Papangelou intensity of the original spatial point process, this model is used to generate the complementary process, and the resulting superposition is a Poisson process with intensity function β if and only if the true Papangelou intensity is used. Whether the superposition is actually such a Poisson process can easily be examined using well-known results and fast simulation procedures for Poisson processes. We illustrate this approach to model checking in the case of a Strauss process.

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7

Møller, Jesper, and Kasper K. Berthelsen. "Transforming Spatial Point Processes into Poisson Processes Using Random Superposition." Advances in Applied Probability 44, no. 01 (March 2012): 42–62. http://dx.doi.org/10.1017/s0001867800005449.

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Most finite spatial point process models specified by a density are locally stable, implying that the Papangelou intensity is bounded by some integrable function β defined on the space for the points of the process. It is possible to superpose a locally stable spatial point process X with a complementary spatial point process Y to obtain a Poisson process X ⋃ Y with intensity function β. Underlying this is a bivariate spatial birth-death process (X t , Y t ) which converges towards the distribution of (X, Y). We study the joint distribution of X and Y, and their marginal and conditional distributions. In particular, we introduce a fast and easy simulation procedure for Y conditional on X. This may be used for model checking: given a model for the Papangelou intensity of the original spatial point process, this model is used to generate the complementary process, and the resulting superposition is a Poisson process with intensity function β if and only if the true Papangelou intensity is used. Whether the superposition is actually such a Poisson process can easily be examined using well-known results and fast simulation procedures for Poisson processes. We illustrate this approach to model checking in the case of a Strauss process.

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8

Yang, Tae Young, and Lynn Kuo. "Bayesian computation for the superposition of nonhomogeneous poisson processes." Canadian Journal of Statistics 27, no. 3 (September 1999): 547–56. http://dx.doi.org/10.2307/3316110.

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9

Chen, Louis H. Y., and Aihua Xia. "Poisson process approximation for dependent superposition of point processes." Bernoulli 17, no. 2 (May 2011): 530–44. http://dx.doi.org/10.3150/10-bej290.

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10

Hegyi, S. "Scaling laws in hierarchical clustering models with Poisson superposition." Physics Letters B 327, no. 1-2 (May 1994): 171–78. http://dx.doi.org/10.1016/0370-2693(94)91546-6.

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11

Cowpertwait, P. S. P. "Mixed rectangular pulses models of rainfall." Hydrology and Earth System Sciences 8, no. 5 (October 31, 2004): 993–1000. http://dx.doi.org/10.5194/hess-8-993-2004.

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Abstract. A stochastic rainfall model, obtained as the superposition of independent Neyman-Scott Rectangular Pulses (NSRP), is proposed to provide a flexible parameterisation and general procedure for modelling rainfall. The methodology is illustrated using hourly data from Auckland, New Zealand, where the model is fitted to data collected for each calendar month over the period: 1966–1998. For data taken over the months April to August, two independent superposed NSRP processes are fitted, which may correspond to the existence of mixtures of convective and stratiform storm types for these months. The special case of the superposition of an independent NSRP process and a Poisson rectangular pulses process fits the data for January to March, whilst the original NSRP model (i.e. without superposition) fits the data for September to November. A simulation study verifies that the model performs well with respect to the distribution of annual totals, the proportion of dry periods, and extreme values. Keywords: stochastic processes; point processes; rainfall time series; Poisson cluster models

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12

yang, Y., PR Zhao, XB Wang, JL zhang, FM Yang, and ZW Min. "Extremely Weak Signal Detection Algorithm of Multi-Pixel Photon Detector." Journal of Physics: Conference Series 2476, no. 1 (April 1, 2023): 012026. http://dx.doi.org/10.1088/1742-6596/2476/1/012026.

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Abstract For the detection of extremely weak signals in underwater long distance wireless optical communication, the Geiger mode of the multi pixel photon detector has serious pulse superposition effect and Poisson noise, which leads to counting difficulties and affects the measurement accuracy. This paper proposes a deconvolution joint generalized Anscombe transform (DUGAT) detection algorithm. First, the deconvolution filtering technology is used to process the weak signal to reduce the superposition effect and converge the pulse width. Secondly, the noise signal of Poisson+Gaussian (P+G) distribution is converted into Gaussian variable by using generalized Anscombe transform (GAT), which is equivalent to additive Gaussian noise signal. Finally, the symbols are counted by hard decision algorithm. The experimental results show that the sensitivity of this algorithm is improved by 8.57dB and 9.95dB respectively compared with the traditional AR and ML detection algorithms.

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13

Chandramohan, J., and Lung-Kuang Liang. "Bernoulli, multinomial and Markov chain thinning of some point processes and some results about the superposition of dependent renewal processes." Journal of Applied Probability 22, no. 4 (December 1985): 828–35. http://dx.doi.org/10.2307/3213950.

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We show that Bernoulli thinning of arbitrarily delayed renewal processes produces uncorrelated thinned processes if and only if the renewal process is Poisson. Multinomial thinning of point processes is studied. We show that if an arbitrarily delayed renewal process or a doubly stochastic Poisson process is subjected to multinomial thinning, the existence of a single pair of uncorrelated thinned processes is sufficient to ensure that the renewal process is Poisson and the double stochastic Poisson process is at most a non-homogeneous Poisson process. We also show that a two-state Markov chain thinning of an arbitrarily delayed renewal process produces, under certain conditions, uncorrelated thinned processes if and only if the renewal process is Poisson and the Markov chain is a Bernoulli process. Finally, we identify conditions under which dependent point processes superpose to form a renewal process.

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Chandramohan, J., and Lung-Kuang Liang. "Bernoulli, multinomial and Markov chain thinning of some point processes and some results about the superposition of dependent renewal processes." Journal of Applied Probability 22, no. 04 (December 1985): 828–35. http://dx.doi.org/10.1017/s002190020010806x.

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We show that Bernoulli thinning of arbitrarily delayed renewal processes produces uncorrelated thinned processes if and only if the renewal process is Poisson. Multinomial thinning of point processes is studied. We show that if an arbitrarily delayed renewal process or a doubly stochastic Poisson process is subjected to multinomial thinning, the existence of a single pair of uncorrelated thinned processes is sufficient to ensure that the renewal process is Poisson and the double stochastic Poisson process is at most a non-homogeneous Poisson process. We also show that a two-state Markov chain thinning of an arbitrarily delayed renewal process produces, under certain conditions, uncorrelated thinned processes if and only if the renewal process is Poisson and the Markov chain is a Bernoulli process. Finally, we identify conditions under which dependent point processes superpose to form a renewal process.

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15

Kim, Hyeji, Benjamin Nachman, and Abbas El Gamal. "Superposition Coding Is Almost Always Optimal for the Poisson Broadcast Channel." IEEE Transactions on Information Theory 62, no. 4 (April 2016): 1782–94. http://dx.doi.org/10.1109/tit.2016.2527790.

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16

Rodrigues, Josemar, Juan E. R. Cid, and Jorge A. Achcar. "BAYESIAN ANALYSIS FOR THE SUPERPOSITION OF TWO DEPENDENT NONHOMOGENEOUS POISSON PROCESSES." Communications in Statistics - Theory and Methods 31, no. 9 (August 21, 2002): 1467–78. http://dx.doi.org/10.1081/sta-120013005.

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17

Perona, Paolo, Edoardo Daly, Benoît Crouzy, and Amilcare Porporato. "Stochastic dynamics of snow avalanche occurrence by superposition of Poisson processes." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2148 (October 3, 2012): 4193–208. http://dx.doi.org/10.1098/rspa.2012.0396.

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We study the dynamics of systems with deterministic trajectories randomly forced by instantaneous discontinuous jumps occurring according to two different compound Poisson processes. One process, with constant frequency, causes instantaneous positive random increments, whereas the second process has a state-dependent frequency and describes negative jumps that force the system to restart from zero (renewal jumps). We obtain the probability distributions of the state variable and the magnitude and intertimes of the jumps to zero. This modelling framework is used to describe snow-depth dynamics on mountain hillsides, where the positive jumps represent snowfall events, whereas the jumps to zero describe avalanches. The probability distributions of snow depth, together with the statistics of avalanche magnitude and occurrence, are used to explain the correlation between avalanche occurrence and snowfall as a function of hydrologic, terrain slope and aspect parameters. This information is synthesized into a ‘prediction entropy’ function that gives the level of confidence of avalanche occurrence prediction in relation to terrain properties.

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18

Wille, Clara. "Murena id est Lampreda: Quelques observations lexicologiques et culinaires." Reinardus / Yearbook of the International Reynard Society 20 (December 12, 2008): 170–87. http://dx.doi.org/10.1075/rein.20.11wil.

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Le nom latin murena, un poisson fort apprécié à la table médiévale, est unanimement rendu par les gloses, les glossaires et les encyclopédies médiévaux par le terme anglo-normand et ancien français lamproie et vice-versa. Or, selon les histoires naturelles modernes, la murena est un poisson rapace qui vit dans les mers tropicales et sous-tropicales et elle appartient à l’ordre des anguilliformes et à la famille des muraenidae. La lampreda, par contre, fait partie de la famille des petromyzonidae et vit alternativement dans les eaux douces et les eaux salées des régions du nord. La superposition des deux termes désignant les deux poissons à l’époque médiévale s’explique par leur ressemblance: la murène et la lamproie ont une allure serpentine assez caractéristique. Mais il y a un second point qui a dû faciliter la confusion: tout comme la murène était un mets recherché par les riches Romains, la lamproie faisait les délices des rois anglo-normands et français. La lamproie ne manque en effet jamais dans les recueils de recettes de l’époque. Cet essai se propose, à l’aide de textes historiques et culinaires et de documents iconographiques, d’éclaircir les rapports entre ces deux noms et les poissons qu’ils désignent.

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19

Cruise, R. J. R. "Poisson convergence, in large deviations, for the superposition of independent point processes." Annals of Operations Research 170, no. 1 (September 13, 2008): 79–94. http://dx.doi.org/10.1007/s10479-008-0435-x.

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20

Perry, David, and Wolfgang Stadje. "The busy cycle of the reflected superposition of Brownian motion and a compound Poisson process." Journal of Applied Probability 38, no. 1 (March 2001): 255–61. http://dx.doi.org/10.1239/jap/996986660.

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We consider a reflected superposition of a Brownian motion and a compound Poisson process as a model for the workload process of a queueing system with two types of customers under heavy traffic. The distributions of the duration of a busy cycle and the maximum workload during a cycle are determined in closed form.

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Perry, David, and Wolfgang Stadje. "The busy cycle of the reflected superposition of Brownian motion and a compound Poisson process." Journal of Applied Probability 38, no. 01 (March 2001): 255–61. http://dx.doi.org/10.1017/s0021900200018672.

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We consider a reflected superposition of a Brownian motion and a compound Poisson process as a model for the workload process of a queueing system with two types of customers under heavy traffic. The distributions of the duration of a busy cycle and the maximum workload during a cycle are determined in closed form.

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22

CARIÑENA, J. F., J. DE LUCAS, and C. SARDÓN. "LIE–HAMILTON SYSTEMS: THEORY AND APPLICATIONS." International Journal of Geometric Methods in Modern Physics 10, no. 09 (August 30, 2013): 1350047. http://dx.doi.org/10.1142/s0219887813500473.

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This work concerns the definition and analysis of a new class of Lie systems on Poisson manifolds enjoying rich geometric features: the Lie–Hamilton systems. We devise methods to study their superposition rules, time independent constants of motion and Lie symmetries, linearizability conditions, etc. Our results are illustrated by examples of physical and mathematical interest.

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23

Kella, Offer, David Perry, and Wolfgang Stadje. "A STOCHASTIC CLEARING MODEL WITH A BROWNIAN AND A COMPOUND POISSON COMPONENT." Probability in the Engineering and Informational Sciences 17, no. 1 (January 2003): 1–22. http://dx.doi.org/10.1017/s026996480317101x.

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We consider a stochastic input–output system with additional total clearings at certain random times determined by its own evolution (and specified by a controller). Between two clearings, the stock level process is a superposition of a Brownian motion with drift and a compound Poisson process with positive jumps, reflected at zero. We introduce meaningful cost functionals for this system and determine them explicitly under several (classical and new) clearing policies.

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24

Eraiah, B., Ramakrishnaiah, and R. V. Anavekar. "Elastic properties of zinc-phosphate glasses doped with erbium trioxide." Canadian Journal of Physics 88, no. 7 (July 2010): 513–16. http://dx.doi.org/10.1139/p10-031.

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New glasses of the system xEr2O3-(60-x)ZnO-40P2O5 (where x = 0.1 to 0.5 mol%) have been prepared by using a conventional meltquenching method. We have measured the densities of these glasses by using a displacement method, and corresponding molar volumes have also been calculated. We have measured both longitudinal and transverse ultrasonic sound velocities of these glasses using a pulse-echo superposition method. These ultrasonic velocities have been used to calculate the elastic moduli, Poisson ratio, and Debye temperatures. The variations of density, molar volume, ultrasonic sound velocities, elastic moduli, Poisson ratio, and Debye temperature have been discussed with respect to Er2O3 concentration.

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25

Neuts, Marcel F., and Charles E. M. Pearce. "The superposition of independent discrete Markovian packet streams." Journal of Applied Probability 28, no. 1 (March 1991): 84–95. http://dx.doi.org/10.2307/3214742.

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In a finite, aperiodic, irreducible Markov chain, a visit to some states generates a one; to some others, a zero, while the remaining states are considered silent, in that neither symbol is generated. States during which either a one or a zero is generated are called active states, and sojourns in the set of active states correspond to messages. The output process is called a Markovian packet stream. Informally, a stream is called thin, if the steady-state fraction of time spent in the active states is small and messages are separated by silent periods of long durations. A limit theorem for the superposition of a large number of independent, stochastically identical and appropriately thin Markovian packet streams is obtained. The class of limit processes consists of a family of stationary, integer-valued, discrete-parameter processes of dependent Poisson random variables. Some properties of the limit processes are established.

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26

Neuts, Marcel F., and Charles E. M. Pearce. "The superposition of independent discrete Markovian packet streams." Journal of Applied Probability 28, no. 01 (March 1991): 84–95. http://dx.doi.org/10.1017/s0021900200039449.

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In a finite, aperiodic, irreducible Markov chain, a visit to some states generates a one; to some others, a zero, while the remaining states are considered silent, in that neither symbol is generated. States during which either a one or a zero is generated are called active states, and sojourns in the set of active states correspond to messages. The output process is called a Markovian packet stream. Informally, a stream is called thin, if the steady-state fraction of time spent in the active states is small and messages are separated by silent periods of long durations. A limit theorem for the superposition of a large number of independent, stochastically identical and appropriately thin Markovian packet streams is obtained. The class of limit processes consists of a family of stationary, integer-valued, discrete-parameter processes of dependent Poisson random variables. Some properties of the limit processes are established.

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27

Perry, David, and Wolfgang Stadje. "EXACT DISTRIBUTIONS IN A JUMP-DIFFUSION STORAGE MODEL." Probability in the Engineering and Informational Sciences 16, no. 1 (January 2002): 19–27. http://dx.doi.org/10.1017/s026996480216102x.

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We consider a reflected independent superposition of a Brownian motion and a compound Poisson process with positive and negative jumps, which can be interpreted as a model for the content process of a storage system with different types of customers under heavy traffic. The distributions of the duration of a busy cycle and the maximum content during a cycle are determined in closed form.

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28

Hong, John Meng-Kai, and Reyna Marsya Quita. "Approximation of generalized Riemann solutions to compressible Euler-Poisson equations of isothermal flows in spherically symmetric space-times." Tamkang Journal of Mathematics 48, no. 1 (March 30, 2017): 73–94. http://dx.doi.org/10.5556/j.tkjm.48.2017.2274.

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In this paper, we consider the compressible Euler-Poisson system in spherically symmetric space-times. This system, which describes the conservation of mass and momentum of physical quantity with attracting gravitational potential, can be written as a $3\times 3$ mixed-system of partial differential systems or a $2\times 2$ hyperbolic system of balance laws with $global$ source. We show that, by the equation for the conservation of mass, Euler-Poisson equations can be transformed into a standard $3\times 3$ hyperbolic system of balance laws with $local$ source. The generalized approximate solutions to the Riemann problem of Euler-Poisson equations, which is the building block of generalized Glimm scheme for solving initial-boundary value problems, are provided as the superposition of Lax's type weak solutions of the associated homogeneous conservation laws and the perturbation terms solved by the linearized hyperbolic system with coefficients depending on such Lax solutions.

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29

Willie, Helmut. "A note on single server loss systems with a superposition of inputs." Journal of Applied Probability 34, no. 1 (March 1997): 213–22. http://dx.doi.org/10.2307/3215188.

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Explicit formulas for the time congestion and the call blocking probability are derived in a single server loss system whose total input consists of a finite superposition of independent general stationary traffic streams with exponentially distributed service times. The results are used for studying to what extent two arrival processes with coinciding customer-stationary state distributions are similar or even identical, and whether an arrival process with coinciding customer-stationary and time-stationary state distributions is of the Poisson type.

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Willie, Helmut. "A note on single server loss systems with a superposition of inputs." Journal of Applied Probability 34, no. 01 (March 1997): 213–22. http://dx.doi.org/10.1017/s002190020010083x.

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Explicit formulas for the time congestion and the call blocking probability are derived in a single server loss system whose total input consists of a finite superposition of independent general stationary traffic streams with exponentially distributed service times. The results are used for studying to what extent two arrival processes with coinciding customer-stationary state distributions are similar or even identical, and whether an arrival process with coinciding customer-stationary and time-stationary state distributions is of the Poisson type.

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31

Guillemin, Fabrice M., Ravi R. Mazumdar, Catherine P. Rosenberg, and Yu Ying. "A Stochastic Ordering Property for Leaky Bucket Regulated Flows in Packet Networks." Journal of Applied Probability 44, no. 2 (June 2007): 332–48. http://dx.doi.org/10.1239/jap/1183667405.

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We show in this paper that if a stationary traffic source is regulated by a leaky bucket with leak rate ρ and bucket size σ, then the amount of information generated in successive time intervals is dominated, in the increasing convex ordering sense, by that of a Poisson arrival process with rate ρ/σ, with each arrival bringing an amount of information equal to σ. By exploiting this property, we then show that the mean value in the stationary regime of the content of a buffer drained at constant rate and fed with the superposition of regulated flows is less than the mean value of the same buffer fed with an adequate Poisson process, whose characteristics depend upon the regulated input flows.

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32

Guillemin, Fabrice M., Ravi R. Mazumdar, Catherine P. Rosenberg, and Yu Ying. "A Stochastic Ordering Property for Leaky Bucket Regulated Flows in Packet Networks." Journal of Applied Probability 44, no. 02 (June 2007): 332–48. http://dx.doi.org/10.1017/s0021900200117863.

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We show in this paper that if a stationary traffic source is regulated by a leaky bucket with leak rate ρ and bucket size σ, then the amount of information generated in successive time intervals is dominated, in the increasing convex ordering sense, by that of a Poisson arrival process with rate ρ/σ, with each arrival bringing an amount of information equal to σ. By exploiting this property, we then show that the mean value in the stationary regime of the content of a buffer drained at constant rate and fed with the superposition of regulated flows is less than the mean value of the same buffer fed with an adequate Poisson process, whose characteristics depend upon the regulated input flows.

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33

Guillemin, Fabrice M., Ravi R. Mazumdar, Catherine P. Rosenberg, and Yu Ying. "A Stochastic Ordering Property for Leaky Bucket Regulated Flows in Packet Networks." Journal of Applied Probability 44, no. 02 (June 2007): 332–48. http://dx.doi.org/10.1017/s0021900200003004.

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We show in this paper that if a stationary traffic source is regulated by a leaky bucket with leak rate ρ and bucket size σ, then the amount of information generated in successive time intervals is dominated, in the increasing convex ordering sense, by that of a Poisson arrival process with rate ρ/σ, with each arrival bringing an amount of information equal to σ. By exploiting this property, we then show that the mean value in the stationary regime of the content of a buffer drained at constant rate and fed with the superposition of regulated flows is less than the mean value of the same buffer fed with an adequate Poisson process, whose characteristics depend upon the regulated input flows.

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34

Gilardoni, Gustavo L., and Enrico A. Colosimo. "On the superposition of overlapping Poisson processes and nonparametric estimation of their intensity function." Journal of Statistical Planning and Inference 141, no. 9 (September 2011): 3075–83. http://dx.doi.org/10.1016/j.jspi.2011.03.029.

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35

Lederhofer, R., J. Schnakenberg, and H. Stieve. "Stochastic Treatment of Bump Latency and Temporal Overlapping in Limulus Ventral Photoreceptors." Zeitschrift für Naturforschung C 46, no. 3-4 (April 1, 1991): 291–304. http://dx.doi.org/10.1515/znc-1991-3-421.

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We present quantum bumps obtained from flash experiments at the Limulus ventral nerve photoreceptor under voltage clamp conditions. The results are shown and discussed in form of histograms for the latency, amplitude and net charge transfer (current time integral) of the bump current responses. We argue that the experimental latency histogram s cannot be described satisfactorily by chemical models if one assumes that not more than one photon is captured per flash. Instead of, one has to take into account the Poisson statistics of the captures of 0,1,2 ,... photons released by a single flash. We show that the inclusion of Poisson statistics makes the effective latency histograms of flash responses typically asymmetric and skewed to wards short latencies as compared to that of model histograms for one-photon responses. Our conjecture also implies that under our experimental conditions a fraction of up to 20% of the bump responses evoked by a flash should be suspected to be superpositions of two ore more one-photon responses which cannot be separated by any kind of evaluation analysis. Consequently, the average values of amplitudes and net charge transfers of the light-evoked bump responses are expected to be overestimated as compared to that of true one-photon responses. This hypothesis is confirm ed by a numerical simulation of light-evoked bump responses using experimentally recorded spontaneous bumps (at times larger than 1 s after the flash) as the simulation material. We show that the superposition of one-photon events in the light-evoked bump responses due to Poisson statistics settles the question why their amplitudes and net charge transfers are found to be larger than that of the spontaneous bumps. We suggest that true one-photon responses evoked by a light flash and spontaneous bumps start from the same activated rhodopsin state and take the same biochemical pathway.

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36

Kulik, S. P., K. S. Kravtsov, and S. N. Molotkov. "Experimental resources needed to implement photon number splitting attack in quantum cryptography." Laser Physics Letters 19, no. 2 (January 13, 2022): 025203. http://dx.doi.org/10.1088/1612-202x/ac46cb.

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Abstract The analysis of the security of quantum key distribution systems with respect to an attack with nondemolishing measurement of the number of photons (photon number splitting—PNS attack) is carried out under the assumption that in the communication channel in each parcel there is a pure Fock state with a different number of photons, and the distribution of states by number of photons has Poisson statistics. In reality, in the communication channel in each parcel there are not individual Fock states, but a pure coherent state with a random phase—a superposition of Fock states with different numbers of photons. The paper analyzes the necessary experimental resources necessary to prepare individual Fock states with a certain number of photons from the superposition of Fock states for a PNS attack. Optical schemes for implementing such an attack are given, and estimates of experimental parameters at which a PNS attack is possible are made.

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Li, Chen, Junjun Zheng, Hiroyuki Okamura, and Tadashi Dohi. "Performance Evaluation of a Cloud Datacenter Using CPU Utilization Data." Mathematics 11, no. 3 (January 18, 2023): 513. http://dx.doi.org/10.3390/math11030513.

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Cloud computing and its associated virtualization have already been the most vital architectures in the current computer system design. Due to the popularity and progress of cloud computing in different organizations, performance evaluation of cloud computing is particularly significant, which helps computer designers make plans for the system’s capacity. This paper aims to evaluate the performance of a cloud datacenter Bitbrains, using a queueing model only from CPU utilization data. More precisely, a simple but non-trivial queueing model is used to represent the task processing of each virtual machine (VM) in the cloud, where the input stream is supposed to follow a non-homogeneous Poisson process (NHPP). Then, the parameters of arrival streams for each VM in the cloud are estimated. Furthermore, the superposition of estimated arrivals is applied to represent the CPU behavior of an integrated virtual platform. Finally, the performance of the integrated virtual platform is evaluated based on the superposition of the estimations.

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Le Gall, Quentin, Bartłomiej Błaszczyszyn, Élie Cali, and Taoufik En-Najjary. "Continuum line-of-sight percolation on Poisson–Voronoi tessellations." Advances in Applied Probability 53, no. 2 (June 2021): 510–36. http://dx.doi.org/10.1017/apr.2020.69.

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AbstractIn this work, we study a new model for continuum line-of-sight percolation in a random environment driven by the Poisson–Voronoi tessellation in the d-dimensional Euclidean space. The edges (one-dimensional facets, or simply 1-facets) of this tessellation are the support of a Cox point process, while the vertices (zero-dimensional facets or simply 0-facets) are the support of a Bernoulli point process. Taking the superposition Z of these two processes, two points of Z are linked by an edge if and only if they are sufficiently close and located on the same edge (1-facet) of the supporting tessellation. We study the percolation of the random graph arising from this construction and prove that a 0–1 law, a subcritical phase, and a supercritical phase exist under general assumptions. Our proofs are based on a coarse-graining argument with some notion of stabilization and asymptotic essential connectedness to investigate continuum percolation for Cox point processes. We also give numerical estimates of the critical parameters of the model in the planar case, where our model is intended to represent telecommunications networks in a random environment with obstructive conditions for signal propagation.

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Prabhakar, Balaji, Nicholas Bambos, and T. S. Mountford. "The synchronization of Poisson processes and queueing networks with service and synchronization nodes." Advances in Applied Probability 32, no. 3 (September 2000): 824–43. http://dx.doi.org/10.1239/aap/1013540246.

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This paper investigates the dynamics of a synchronization node in isolation, and of networks of service and synchronization nodes. A synchronization node consists of M infinite capacity buffers, where tokens arriving on M distinct random input flows are stored (there is one buffer for each flow). Tokens are held in the buffers until one is available from each flow. When this occurs, a token is drawn from each buffer to form a group-token, which is instantaneously released as a synchronized departure. Under independent Poisson inputs, the output of a synchronization node is shown to converge weakly (and in certain cases strongly) to a Poisson process with rate equal to the minimum rate of the input flows. Hence synchronization preserves the Poisson property, as do superposition, Bernoulli sampling and M/M/1 queueing operations. We then consider networks of synchronization and exponential server nodes with Bernoulli routeing and exogenous Poisson arrivals, extending the standard Jackson network model to include synchronization nodes. It is shown that if the synchronization skeleton of the network is acyclic (i.e. no token visits any synchronization node twice although it may visit a service node repeatedly), then the distribution of the joint queue-length process of only the service nodes is product form (under standard stability conditions) and easily computable. Moreover, the network output flows converge weakly to Poisson processes. Finally, certain results for networks with finite capacity buffers are presented, and the limiting behavior of such networks as the buffer capacities become large is studied.

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40

Prabhakar, Balaji, Nicholas Bambos, and T. S. Mountford. "The synchronization of Poisson processes and queueing networks with service and synchronization nodes." Advances in Applied Probability 32, no. 03 (September 2000): 824–43. http://dx.doi.org/10.1017/s0001867800010272.

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This paper investigates the dynamics of a synchronization node in isolation, and of networks of service and synchronization nodes. A synchronization node consists of M infinite capacity buffers, where tokens arriving on M distinct random input flows are stored (there is one buffer for each flow). Tokens are held in the buffers until one is available from each flow. When this occurs, a token is drawn from each buffer to form a group-token, which is instantaneously released as a synchronized departure. Under independent Poisson inputs, the output of a synchronization node is shown to converge weakly (and in certain cases strongly) to a Poisson process with rate equal to the minimum rate of the input flows. Hence synchronization preserves the Poisson property, as do superposition, Bernoulli sampling and M/M/1 queueing operations. We then consider networks of synchronization and exponential server nodes with Bernoulli routeing and exogenous Poisson arrivals, extending the standard Jackson network model to include synchronization nodes. It is shown that if the synchronization skeleton of the network is acyclic (i.e. no token visits any synchronization node twice although it may visit a service node repeatedly), then the distribution of the joint queue-length process of only the service nodes is product form (under standard stability conditions) and easily computable. Moreover, the network output flows converge weakly to Poisson processes. Finally, certain results for networks with finite capacity buffers are presented, and the limiting behavior of such networks as the buffer capacities become large is studied.

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Luo, Ya Li, and Chang Xin Zhang. "Basic Methods of Peak-Hour Traffic Generation Forecast about Urban Commercial Complex." Applied Mechanics and Materials 488-489 (January 2014): 1400–1404. http://dx.doi.org/10.4028/www.scientific.net/amm.488-489.1400.

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Based on analysis of the traffic impacts characteristics of the urban commercial complex, the article proposed that single-functional project itself generated traffic volume is related to time, and conforms to the corresponding Poisson distribution function. However, the multiple-functional complex itself generated peak-hour traffic volume is not a simple sum of each single-function peak volume, but is calculated by superposing the each function respective traffic density functions. Meanwhile, the article also explored the superposition and calculation method to obtain peak-hour traffic volume during forecasting the trip generation of the urban commercial complex.

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42

Noverola-Gamas, H., L. M. Gaggero-Sager, and O. Oubram. "Optical absorption coefficient in n-type double δ-doped layers GaAs quantum wells." International Journal of Modern Physics B 33, no. 19 (July 30, 2019): 1950215. http://dx.doi.org/10.1142/s0217979219502151.

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The superposition principle is one of the cornerstones of physics. In low-dimensional systems, it is routinely used to model the potential profile. That is the case of coupled [Formula: see text]-doped quantum wells, for which, several works have studied the transport and optoelectronic properties. However, the Poisson equation determines the potential profile is not linear, and the superposition principle is not at all valid. The aim of this work is to correct some of the inconsistencies of the mentioned models for coupled [Formula: see text]-doped quantum wells. In the framework of Thomas–Fermi approximation, we calculated the potential profile, the wave functions, the energy values and the relative absorption coefficient for the double system compared to an isolated delta system in terms of impurity density and distance between [Formula: see text]-wells. We found a red shifting in the absorption coefficient when the interlayer distances increase, in addition, an enhancement in the absorption coefficient is detected for a specific separation distance. Our results agree with ab-initio calculations reported for the electronic structure.

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RAMÍREZ CID, JUAN ESTEBAN, and JORGE ALBERTO ACHCAR. "Software Reliability Considering the Superposition of Non-homogeneous Poisson Processes in the Presence of a Covariate." Statistics 36, no. 3 (January 2002): 259–69. http://dx.doi.org/10.1080/02331880212854.

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44

Stegeman, Alwin. "Extremal behavior of heavy-tailed ON-periods in a superposition of ON/OFF processes." Advances in Applied Probability 34, no. 1 (March 2002): 179–204. http://dx.doi.org/10.1239/aap/1019160956.

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Empirical studies of data traffic in high-speed networks suggest that network traffic exhibits self-similarity and long-range dependence. Cumulative network traffic has been modeled using the so-called ON/OFF model. It was shown that cumulative network traffic can be approximated by either fractional Brownian motion or stable Lévy motion, depending on how many sources are active in the model. In this paper we consider exceedances of a high threshold by the sequence of lengths of ON-periods. If the cumulative network traffic converges to stable Lévy motion, the number of exceedances converges to a Poisson limit. The same holds in the fractional Brownian motion case, provided a very high threshold is used. Finally, we show that the number of exceedances obeys the central limit theorem.

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45

Stegeman, Alwin. "Extremal behavior of heavy-tailed ON-periods in a superposition of ON/OFF processes." Advances in Applied Probability 34, no. 01 (March 2002): 179–204. http://dx.doi.org/10.1017/s0001867800011459.

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Empirical studies of data traffic in high-speed networks suggest that network traffic exhibits self-similarity and long-range dependence. Cumulative network traffic has been modeled using the so-called ON/OFF model. It was shown that cumulative network traffic can be approximated by either fractional Brownian motion or stable Lévy motion, depending on how many sources are active in the model. In this paper we consider exceedances of a high threshold by the sequence of lengths of ON-periods. If the cumulative network traffic converges to stable Lévy motion, the number of exceedances converges to a Poisson limit. The same holds in the fractional Brownian motion case, provided a very high threshold is used. Finally, we show that the number of exceedances obeys the central limit theorem.

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46

Huffer, Fred W. "Inequalities for the M/G/∞ queue and related shot noise processes." Journal of Applied Probability 24, no. 4 (December 1987): 978–89. http://dx.doi.org/10.2307/3214220.

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Suppose that pulses arrive according to a Poisson process of rate λ with the duration of each pulse independently chosen from a distribution F having finite mean. Let X(t) be the shot noise process formed by the superposition of these pulses. We consider functionals H(X) of the sample path of X(t). H is said to be L-superadditive if for all functions f and g. For any distribution F for the pulse durations, we define H(F) = EH(X). We prove that if H is L-superadditive and for all convex functions ϕ, then . Various consequences of this result are explored.

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47

McNickle, Don. "Correlations in Output and Overflow Traffic Processes in Simple Queues." Journal of Applied Mathematics and Decision Sciences 2007 (September 24, 2007): 1–13. http://dx.doi.org/10.1155/2007/51801.

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We consider some simple Markov and Erlang queues with limited storage space. Although the departure processes from some such systems are known to be Poisson, they actually consist of the superposition of two complex correlated processes, the overflow process and the output process. We measure the cross-correlation between the counting processes for these two processes. It turns out that this can be positive, negative, or even zero (without implying independence). The models suggest some general principles on how big these correlations are, and when they are important. This may suggest when renewal or moment approximations to similar processes will be successful, and when they will not.

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48

Huffer, Fred W. "Inequalities for the M/G/∞ queue and related shot noise processes." Journal of Applied Probability 24, no. 04 (December 1987): 978–89. http://dx.doi.org/10.1017/s0021900200116833.

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Suppose that pulses arrive according to a Poisson process of rate λ with the duration of each pulse independently chosen from a distribution F having finite mean. Let X(t) be the shot noise process formed by the superposition of these pulses. We consider functionals H(X) of the sample path of X(t). H is said to be L-superadditive if for all functions f and g. For any distribution F for the pulse durations, we define H(F) = EH(X). We prove that if H is L-superadditive and for all convex functions ϕ, then . Various consequences of this result are explored.

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49

Brock, L. M. "Transient Green’s Function Behavior for a Prestressed Highly Elastic Half-Space." Journal of Applied Mechanics 68, no. 2 (August 28, 2000): 162–68. http://dx.doi.org/10.1115/1.1357167.

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A plane-strain study of a prestressed isotropic compressible neo-Hookean half-space subjected to shear and normal surface loads is performed. The loads are either stationary and applied for an instant, or travel at an arbitrary constant speed. The transient process is viewed as the superposition of infinitesimal deformations upon large, and exact expressions for the displacements, within and upon, the half-space are obtained. These, and the associated wave patterns, demonstrate the anisotropy induced by prestress. The wave speeds themselves are sensitive to prestress; in particular, Rayleigh waves disappear beyond a critical compressive prestress. A critical tensile prestress also exists, beyond which a negative Poisson effect occurs.

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Massey, William A., and Ward Whitt. "A Stochastic Model to Capture Space and time Dynamics in Wireless Communication Systems." Probability in the Engineering and Informational Sciences 8, no. 4 (October 1994): 541–69. http://dx.doi.org/10.1017/s0269964800003612.

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We construct a version of the recently developed Poisson-Arrival-Location Model (PALM) to study communicating mobiles on a highway, giving the distribution of calls in progress and handoffs as a function of time and space. In a PALM arrivals generated by a nonhomogeneous Poisson process move independently through a general state space according to a location stochastic process. If, as an approximation, we ignore capacity constraints, then we can use this model to describe the performance of wireless communication systems. Our basic model here is for traffic on a one-way, single-lane, semi-infinite highway, with movement specified by a deterministic location function. For the highway PALM considered here, key quantities are the call density, the handoff rate, the call-origination-rate density and the call-termination-rate density, which themselves are simply related by two fundamental conservation equations. We show that the basic highway PALM can be applied, together with independent superposition, to treat more complicated models. Our analysis provides connections between teletraffic theory and highway traffic theory.

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