Probability-generating function

About: Probability-generating function is a research topic. Over the lifetime, 752 publications have been published within this topic receiving 9361 citations.

Discrete-time ATM Queues with Independent and Correlated Arrival Streams

Abstract: In this tutorial paper, we present a set of fundamental techniques of analysis for discrete-time queueing models with either independent or correlated arrival streams, deterministic service-time distribution and one or more equivalent servers. The main characteristic of our approach is that it is almost entirely analytical (except for a few minor numerical calculations) and that an extensive use of probability generating functions is being made. The analysis leads to simple and accurate (exact or approximate) formulas for a wide variety of performance measures of practical importance, such as mean and variance of buffer occupancies and cell delays, cell loss probabilities, delay jitter, etc. The theory developed in the paper is also applied to the detailed performance evaluation of ATM multiplexers and ATM switching elements with dedicated-buffer output queueing arrangements.

Family of Pearson discrete distributions generated by the univariate hypergeometric function 3F2(α1, α2, α3; γ1, γ2; λ)

Abstract: In this work we present a study of the Pearson discrete distributions generated by the hypergeometric function 3F2(α1, α2, α3;γ1, γ2; λ), a univariate extension of the Gaussian hypergeometric function, through a constructive methodology. We start from the polynomial coefficients of the difference equation that lead to such a function as a solution. Immediately after, we obtain the generating probability function and the differential equation that it satisfies, valid for any admissible values of the parameters. We also obtain the differential equations that satisfy the cumulants generating function, moments generating function and characteristic function, From this point on, we obtain a relation in recurrences between the moments about the origin, allowing us to create an equation system for estimating the parameters by the moment method. We also establish a classification of all possible distributions of such type and conclude with a summation theorem that allows us study some distributions belonging to this family. © 1997 by John Wiley & Sons, Ltd.

Multiple roots in some equations of queueing theory

Abstract: Examples are given of probability generating functions K(z) for which has nonhero multiple roots in 1. Cases in which the roots can be proved to be simple are also discussed

On a Class of Estimates of the Probability Density Function and mode based on a Random Number of Observations

Abstract: The estimate of the probability density function, based on a fixed number of observations, studied by Yamato (1971) and Davies (1973), has been extended to the case when the number of observations is random. Asymptotic properties of the estimates of She d:osity function and its derivatives, as also of the estimate of the mode, have been studied under appropriate conditions.

A points estimation and series approximation method for uncertainty analysis

Abstract: The objective of this article is to present an algorithm for moment evaluation and probability density function approximation of performance function for structural reliability analysis. In doing so, a point estimation method for probability moment of performance function is discussed at first. Based on the coherent relationship between the orthogonal polynomial and probability density function, formulas for point estimation are derived. Vector operators are defined to alleviate computational burden for computer programming. Then, by utilizing C-type Gram—Charlier series expansion method, a procedure for probability density function approximation of the performance function is studied. At last, the accuracy of the proposed method is demonstrated using three numerical examples.