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.

Analysis of a single server queue in a multi-phase random environment with working vacations and customers’ impatience

Abstract: In this paper, we analyze an M/M/1 queueing system under both single and multiple working vacation policies, multiphase random environment, waiting server, balking and reneging. When the system is in operative phase j = 1,2,...,K, customers are served one by one. Whenever the system becomes empty, the server waits a random amount of time before taking a vacation, causing the system to move to working vacation phase 0 at which new arrivals are served at a lower rate. Using the probability generating function method, we obtain the distribution for the steady-state probabilities of the system. Then, we derive important performance measures of the queueing system. Finally, some numerical examples are illustrated to show the impact of system parameters on performance measures of the queueing system.

Applying the Moment Generating Functions to the Study of Probability Distributions

Abstract: In this paper, we describe a tool to aid in proving theorems about random variables, called the moment generating function, which converts problems about probabilities and expectations into problems from calculus about function values and derivates. We show how the moment generating function determinates the moments and how the moments can be used to recover the moment generating function. Using of moment generating functions to find distributions of functions of random variables is presented. A standard form of the central limit theorem is also stated and proved.

Calculate the Moment Generating Function for Continuous Random Variable by Using Decomposition Method

Abstract: In this paper, decomposition method is applied to develop a computational method for the moment generating function of continuous random variable. The proposed method is easy to implement from a computational viewpoint and can be employed for finding moment generating function of continuous random variable without solving any integral. Sometimes, this integral cannot be solved in general and in this case, the moment generating function remains in integral form. Some examples are illustrative for demonstrating the advantage of the proposed

Random producing method based on windows time function

Abstract: Based on the analysis of normal random producing method, this paper introduces the principle of a new method for producing random by using Windows time function and describes the procedure of this method. The random produced by this method has been proved to have perfect simulation effects.