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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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Proceedings ArticleDOI
07 Apr 2008
TL;DR: This paper considers a discrete-time queueing model with infinite storage capacity and one single output line, which can for instance be applied to study the traffic of a file server, where one file download by a user corresponds to one session.
Abstract: This paper considers a discrete-time queueing model with infinite storage capacity and one single output line. Users can start and end sessions during which they are active and send packets to the queueing system. Each active user generates a random but strictly positive number of packets per time slot: this results in a session-based arrival process of packets. This model can for instance be applied to study the traffic of a file server, where one file download by a user corresponds to one session. The steady-state probability generating functions of the number of active sessions, buffer occupancy (number of packets stored in the buffer) and packet delay are derived. We also derive an approximation for the tail probabilities of the buffer occupancy. This allows us to study the influence of the different system parameters: some examples are presented.

10 citations

Journal ArticleDOI
TL;DR: In this article, the weighted distributions of a bivariate three-parameter logarithmic series distribution were derived with weight W(x,y) = x[r] y[s].
Abstract: In this paper, we are interested in the weighted distributions of a bivariate three parameter logarithmic series distribution studied by Kocherlakota and Kocherlakota (1990). The weighted versions of the model are derived with weight W(x,y) = x[r] y[s]. Explicit expressions for the probability mass function and probability generating functions are derived in the case r = s = l. The marginal and conditional distributions are derived in the general case. The maximum likelihood estimation of the parameters, in both two parameter and three parameter cases, is studied. A procedure for computer generation of bivariate data from a discrete distribution is described. This enables us to present two examples, in order to illustrate the methods developed, for finding the maximum likelihood estimates.

10 citations

Journal ArticleDOI
TL;DR: In this paper, a geometrical and statistical-mechanical interpretation of the problem is suggested and used for obtaining the asymptotic properties of the occupation and first-passage probabilities.
Abstract: A method is presented which yields the exact solution of the generating function for the first-passage probability and related observables, for a one-dimensional random walk with random hopping rates on each site. A geometrical and statistical-mechanical interpretation of the problem is suggested and is used for obtaining the asymptotic properties of the occupation and first-passage probabilities. The class of values with the property of self-averaging is found.

10 citations

Journal ArticleDOI
TL;DR: In this article, the authors considered a discrete time Markov chain whose state space is the nonnegative integers and whose transition probability matrix possesses the representation of a sequence of non-negative real numbers satisfying, and a corresponding sequence of probability generating functions.
Abstract: Consider a discrete time Markov chain { Z n } whose state space is the non-negative integers and whose transition probability matrix ║ P ij ║ possesses the representation where { P r }, r = 1,2,…, is a finite or denumerably infinite sequence of non-negative real numbers satisfying , and , is a corresponding sequence of probability generating functions. It is assumed that Z 0 = k , a finite positive integer.

10 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20236
202211
20217
202014
201912
20188