Analysis of Queueing Systems by J.A. White (Auth.)

By J.A. White (Auth.)

Publication by means of White, John A., and so forth

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If X is the random variable used to describe the outcome of the experiment, then X is a discrete random variable that may assume the values zero or one. Let the probability of the first outcome (zero) be 1 — ρ and let ρ be the probability of the second outcome (one). 22) Binomial distribution. Let an experiment consist of η independent Bernoulli subexperiments; that is, the result of each subexperiment is one of two outcomes to which we assign either a zero or a one. After conducting η such subexperiments, we count the number of ones occurring.

However, the time spent with each client is exponentially distributed. 033εΓ · *, 0 033 0 < χ < oo where χ is measured in minutes. If he schedules appointments every 30 minutes, what is the probability that a client will have to wait to see the tax consultant, if he arrives for his appointment on time, and if the preceding client saw the tax consultant on schedule? 6 A certain part is produced on one of two manufacturing lines. The time, in hours, to produce a part on the first line is exponentially distributed with parameter 10.

K on the interval (0, t). , x . , y is given by l9 2 k k l9 fc / ( ) Ί ^ 2 » . . 87) Thus, given a Poisson process and the occurrence offcevents in time t then the times of occurrence of thesefcevents are uniformly distributed over the interval (0, t). 9 TRANSFORM METHODS Functional transformations play an important role in nearly all of the physical and engineering sciences. Transforms commonly encountered include the Fourier (Giffin, 1971; LePage, 1961; Schmidt, 1974), Laplace (Giffin, 1971; Hall et al, 1959; LePage, 1961; Schmidt, 1974), Mellin and Ζ transforms (Brown, 1963; Giffin, 1971; Schmidt, 1974), the characteristic function (Lukacs, 1960; Parzen, 1960, 1965; Schmidt, 1974), moment generating function (Freeman, 1963; Giffin, 1971; Parzen, 1960;Wilks, 1962), and generating function (sometimes called the geometric transform) (Brown, 1963; Giffin, 1971).

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