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Unformatted text preview: 1 ms 1500 2000 3 2 ms 1750 2000 7 4 ms CS 522, v 0.94, d.medhi, W’99 T 13 7. On exponential distribution
This is a good time to quickly go over a couple of things about exponential distribution. The pdf of the
exponential distribution with parameter is given by f x = e,x x 0 : The mean and the variance are given by
1
V X = 2 : 1
E X = 8. Poisson Process
A purebirth homogeneous process, i.e., j A stochastic process fAtjt
with rate if
1. =0 j = , is a Poisson process. Another way: 0g taking nonnegative integer values is said to be a Poisson process fAtg is a counting process. 2. The number of arrival that occur in disjoint time interval are independent.
3. The number of arrivals in interval of length is Poisson distributed with parameter PrfAt + , At = ng = exp, n=n! n = 0 1 :::
Note that exp is the exponential function, expx = ex , where e is the Euler number (=2.718281828...).
Important properties of a Poisson process:
1) Interarrival times are independent and exponential...
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This document was uploaded on 03/19/2014 for the course CS 6030 at Western Michigan.
 Fall '08
 Staff
 Computer Networks

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