Showing papers on "Probability-generating function published in 2010"

Synthesizing Nonstationary, Non-Gaussian Random Vibrations

Abstract: This paper presents a novel technique by which non-Gaussian vibrations are synthesized by generating a sequence of random Gaussian processes of varying root mean square (rms) levels and durations. The technique makes use of previous research by the authors which shows that non-Gaussian vibrations can be decomposed into a sequence of Gaussian processes. Synthesis is achieved by first computing a modulation function which is produced from the rms and the segment length distribution functions, both of which were developed in previous research. This is achieved by first generating a sequence of uniformly distributed random numbers scaled to the range of segment length, which itself is a function of the desired total duration of the synthesized process. In order to transform a uniformly distributed random variable into any arbitrary non-uniform distribution, the cumulative distribution function is established and used as a transfer function applied to the uniformly distributed random variable. This modulation function is applied to a Gaussian random signal itself generated by a standard laboratory random vibration controller (RVC) by means of a purposed-designed variable gain amplifier system. In order to counteract the feedback function of the RVC, a second variable gain amplifier is introduced into the system in order to attenuate the feedback signal in inverse proportion to the gain applied to the command signal. This result is a nonstationary, non-Gaussian random signal that statistically conforms to the desired PSD as well as the RMS distribution function. Copyright © 2010 John Wiley & Sons, Ltd.

Two-point generating function of the free energy for a directed polymer in a random medium

Abstract: We consider a 1+1 dimensional directed continuum polymer in a Gaussian delta-correlated space-time random potential. For this model the moments (= replica) of the partition function, Z(x,t), can be expressed in terms of the attractive delta-Bose gas on the line. Based on a recent study of the structure of the eigenfunctions, we compute the generating function for Z(x_1,t), Z(x_2,t) under a particular decoupling assumption and thereby extend recent results on the one-point generating function of the free energy to two points. It is established that in the long time limit the fluctuations of the free energy are governed by the two-point distribution of the Airy process, which further supports that the long time behavior of the KPZ equation is the same as derived previously for lattice growth models.

M/g/m queue with two stage heterogeneous service compulsory server vacation and random breakdowns

Abstract: We analyze a single server queue with Poisson arrivals, two stages of heterogeneous service with different (arbitrary) service time distributions subject to random breakdowns and compulsory server vacations with general (arbitrary) vacation periods. After first-stage service the server must provide the second stage service. However, after the completion of each second stage service, the server will take compulsory vacation. The system may breakdown at random and repair time follow exponential distribution. The time dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results have been obtained explicitly. Also the average number of customers in the queue and the average waiting time are derived.

Mathematical Modeling of Bivariate Polymer Property Distributions Using 2D Probability Generating Functions, 1 – Numerical Inversion Methods

Abstract: This is the first of two papers presenting a new mathematical method for modeling bivariate distributions of polymer properties. It is based on the transformation of the infinite mass balances describing the evolution of a two-dimensional distribution using 2D probability generating functions (pgf). A key step of this method is the inversion of the transforms. In this work, two numerical inversion methods of 2D pgfs are developed and carefully validated. The accuracy obtained with both methods was very satisfactory. The inversion formulas of both methods are simple and easy to implement. A simple copolymerization example is used to show the complete procedure from the derivation of the pgf balances to the recovery of the bivariate molecular weight distribution.

Continuous time random walk with generic waiting time and external force.

Abstract: We derive an integrodifferential diffusion equation for decoupled continuous time random walk that is valid for a generic waiting time probability density function and external force. Using this equation we also study diffusion behaviors for a couple of specific waiting time probability density functions such as exponential, a combination of power law and generalized Mittag-Leffler function and a sum of exponentials under the influence of a harmonic trap. We show that first two waiting time probability density functions can reproduce the results of the ordinary and fractional diffusion equations for all the time regions from small to large times. But the third one shows a much more complicated pattern. Furthermore, from the integrodifferential diffusion equation we show that the second Einstein relation can hold for any waiting time probability density function.

Sudden Extinction of a Critical Branching Process in a Random Environment

Abstract: Let T be the extinction moment of a critical branching process $Z=(Z_{n},n\ge 0)$ in a random environment specified by independent identically distributed probability generating functions. We study the asymptotic behavior of the probability of extinction of the process Z at moment $n\rightarrow \infty ,$ and show that if the logarithm of the (random) expectation of the offspring number of a particle belongs to the domain of attraction of a non-Gaussian stable law, then the extinction occurs at time moment T owing to a very unfavorable environment forcing the process, having at time moment $T-1$ an exponentially large population, to die out instantly. We also give an interpretation of the obtained results in terms of random walks in a random environment.

Performance evaluation of self-similar traffic in multimedia wireless communication networks with power saving class type III in IEEE 802.16e

Abstract: In this paper, we present a theoretical analysis to numerically evaluate the system performance of multimedia wireless communication networks with power saving class type III in IEEE 802.16e for self-similar traffic. Our model is based on system operations using a batch arrival, and we suppose the batch size to be a random variable following a Pareto(c, α) distribution in order to capture the self-similar property. By using a discrete-time embedded Markov chain, we derive the probability generating functions of the number of data frames and batches for when the busy period begins and for when the system is in a busy cycle. Using the first and higher moments of the probability generating functions, we give the averages and the standard deviation for the system performance in the diffusion approximation for the operation process of the system. In numerical results, we show the performance measures such as the energy saving ratio, plus the average and the standard deviation for the handover ratio with different system parameters as examples.

PDF estimation via characteristic function and an orthonormal basis set

Abstract: The efficacy of estimating the probability density function through, first, reconstruction of the characteristic function and, second, through use of a series approximation based on a Hermite orthonormal basis set, is shown. Both approaches yield a lower integrated error than a benchmark uniform kernel density function for the case of a probability density function with a significant tail. For a Hermite series it is shown that a scaling parameter can be set according to the root mean square value of the data to obtain optimum error performance. The Hermite series estimator is applied to approximating the probability density function evolution of a generalized shot noise process and to estimation of a bimodal probability density function.

Apparatus and method for processing a set of data values

Abstract: An apparatus for processing a set of data values, a data value representing a physiological measure of a body fluid at a time instant, comprising: an estimated probability function calculator (3 a) for calculating an estimated probability function associated with the set of data values; a transform calculator (3b) for calculating a non-linear transform rule using a predetermined target probability function being different from the estimated probability function, so that the probability function of a set of transform data values is closer to the target probability function than the estimated probability function; and a transformer (3 c) for applying the transform rule to the set of data values or to at least one further data value not included in the set of data values and sampled at the different time instant from the time instants for the set of data values to obtain at least one transformed value representing the physiological measure.

The Random Function in Matlab

Abstract: In the practice simulation and testing environment,the random function is widely used.Due to the use of random physical method for faults cannot applied to general research.To meet the demand of computer simulation research,the people to study with various probability distribution algorithm simulation of pseudo random sequence.This paper is making a comprehensive analysis based on the random in Matlab.

On the (")-stable of composed random variables

Abstract: Let be a random variable (rv) with the characteristic func- tion'(t) and be a rv with the generating functiona(z), is independent of It is known (see (1)) that the composed rv of and (denote by = ) is the rv having the characteristic function (t) = a('(t)) The rv is called to be the first component of and is called to be the second component of In this paper, we shall investigate the changes of the distribution function of the composed rv if we have the small changes of the distribution function of the first component or the second component of

Performance analysis for power saving class type III of IEEE 802.16e in WiMAX

Abstract: In this paper, we present an effective method to analyze the performance of the networks using the power saving class type III based on the IEEE 802.16e standard in WiMAX with self-similar traffic. We characterize the self-similar traffic in multimedia wireless communication networks as a batch arrival and suppose that the batch size is a random variable following a Pareto(c, α) distribution. By using the discrete-time embedded Markov chain, we analyze the probability generating functions of the numbers of data frames and batches when the busy period begins, the queueing length, the waiting time and the busy cycle for the networks using the power saving class type III. Moreover, we give the formulas for the system performance in terms of the energy saving ratio, the handover ratio, the system utility and the response time of data frames. We also construct a cost function to determine the optimal sleep window lengths to make the cost of the system whole into the minimum. Numerical results are given with analysis and simulation to show the performance measures and optimal results with different degrees of self-similarity and different sleep window lengths.

Stability Boundaries between Non-Saturation and Saturation Regimes for IEEE 802.11e EDCA

Abstract: In this paper we investigate the transition between non-saturation and saturation regimes for the EDCA function within the IEEE 802.11e standard. We develop queueing and Markov chain models for node operation, and demonstrate interaction among traffic classes in transition from non-saturation to saturation regime. We derive probability generating functions (PGFs) for the probability distributions of packet service time and buffer occupancy. We also derive Laplace-Stieltjes transform (LST) for the probability distribution of frame response time and show stability limits for each traffic class.

Apparatus and method for processing a set of data values

Abstract: An apparatus for processing a set of data values, a data value representing a physiological measure of a body fluid at a time instant, comprising: an estimated probability function calculator (3 a) for calculating an estimated probability function associated with the set of data values; a transform calculator (3 b) for calculating a non-linear transform rule using a predetermined target probability function being different from the estimated probability function, so that the probability function of a set of transform data values is closer to the target probability function than the estimated probability function; and a transformer (3 c) for applying the transform rule to the set of data values or to at least one further data value not included in the set of data values and sampled at the different time instant from the time instants for the set of data values to obtain at least one transformed value representing the physiological measure.

The discrete-time Geo/G/1 queue with N-policy and synchronized reneging

Abstract: In this study, we consider a discrete-time Geo/G/1 queueing system with N-policy and synchronized reneging. In such-system, whenever the busy period ends, the server is immediately deactivated until N customers are accumulated. If the number of customers in the queue becomes N, each customer independently decides whether to leave the system with probability η or to stay in the system with probability (1?η ) . Then, the busy period begins with the customers who do not renege. We present the probability generating functions of the queue length and the sojourn time, respectively. We also analyze the long-run average cost function per unit time using the result of the cycle analysis. Some numerical examples of this model are presented.