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Revision as of 06:23, 22 April 2013
Applications of Poisson Random Variables
Student project for ECE302
by Trevor Holloway
Poisson Random Variables
In 1837, the Poisson Distribution was introduced by Siméon Denis Poisson[1]. It has the pmf
$ P(X=x)= \frac{\lambda^x e^{-\lambda}}{x!} $
This distribution models the probablility that a number of events, x, will occur within a given time period when the average rate of occurance of such events on the same time interval is $ \lambda $.
Applications of Poisson Random Variables
Poisson random variables have many applications. This arises from the fact that many events in nature can be modeled as Poisson processes. Following are some examples of modern applications of the Poisson random variable.
Optimization
Poisson random variables are often used to model scenarios used to generate cost functions in optimization problems. For example, the economic lot scheduling problem aims to optimize the production of a certain number of products on a certain number of machines given a certain demand. If this is handled as a deterministic problem, it has been shown to be np-hard by Hsu in his 1983 paper on the topic [2]. Löhndorf & Minner have used Poisson random variables to make the problem stochastic, but also more feasible [3]. It should be noted that Löhndorf & Minner used a stuttering Poisson process to model their problem. Stuttering Poisson proceses are more generalized cases of Poisson processes wherein events occur at time periods dictated by a Poisson process but the number of events occurring within these time periods followas a geometric distribution [4].
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Questions or comments on this page? Please post them below. I will try to keep up with any posts (even though only two weeks are left).
Question 1: (text)
Question 2: (text)
Question 3: (text)
References:
Retrieved from http://www.aabri.com/SA12Manuscripts/SA12083.pdf
Retrieved from http://www.jstor.org/stable/2631168
Retrieved from http://www.tandfonline.com/doi/full/10.1080/0740817X.2012.662310#tabModule
Retrieved from http://www.jstor.org/stable/3007241
