Topic
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.
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TL;DR: Les principaux parametres interessants sont: le cout de l'algorithme (en terme du nombre d'appels a un generateur aleatoire), the hauteur du chemin a son dernier pas and le maximum du chemine.
9 citations
TL;DR: Closed polling systems with station breakdowns, under the gated, exhaustive or globally gated services regimes, are studied and analyzed and explicit formulae for the mean number of jobs, as well as for the expected cycle duration and system utilization are derived.
Abstract: Closed polling systems with station breakdowns, under the gated, exhaustive or globally gated services regimes, are studied and analyzed. Multi-dimensional sets of probability generating functions of the system’s state are derived. They are further utilized to obtain an approximate solution for the mean number of jobs residing in the system’s various queues at polling instants. The analysis is then concentrated on the case of cyclic Bernoulli polling. Explicit formulae for the mean number of jobs, as well as for the expected cycle duration and system utilization, are derived. Comparison of the throughputs of the three regimes concludes the paper.
9 citations
01 Jan 2006
TL;DR: This technical report treats some technical considerations related to the probability density function of a function of an random vector as a functionof a random vector.
Abstract: This technical report treats some technical considerations related to the probability density function of a function of a random vector.
9 citations
TL;DR: In this article, a moment identity applicable to a general class of discrete probability distributions was derived for modified power series, Ord and Katz families, which has potential applications in different fields.
Abstract: In this paper, we obtain a moment identity applicable to a general class of discrete probability distributions. We then derive the corresponding identities for modified power series, Ord and Katz families. It is noted that the proposed identity has potential applications in different fields.
9 citations
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TL;DR: In this article, a stochastic mechanics framework for chemical reaction systems is proposed that allows to formulate evolution equations for three general types of data: the probability generating functions, the exponential moment generating functions and the factorial moment generating function.
Abstract: We propose a concise stochastic mechanics framework for chemical reaction systems that allows to formulate evolution equations for three general types of data: the probability generating functions, the exponential moment generating functions and the factorial moment generating functions. This formulation constitutes an intimate synergy between techniques of statistical physics and of combinatorics. We demonstrate how to analytically solve the evolution equations for all six elementary types of single-species chemical reactions by either combinatorial normal-ordering techniques, or, for the binary reactions, by means of Sobolev-Jacobi orthogonal polynomials. The former set of results in particular highlights the relationship between infinitesimal generators of stochastic evolution and parametric transformations fo probability distributions. Moreover, we present exact results for generic single-species non-binary reactions, hinting at a notion of compositionality of the analytic techniques.
9 citations