Poisson Process
The Poisson arrival process or Poisson process counts the number of arrivals, each of which has an exponentially distributed time between arrival. In the most general case this can be represented by the rate matrix,
![Q=\left[\begin{matrix}
-\lambda_{0}&\lambda_{0}&0&0&\dots\\
0&-\lambda_{1}&\lambda_{1}&0&\dots\\
0&0&-\lambda_{2}&\lambda_{2}&\dots\\
\vdots & \vdots & \ddots & \ddots & \ddots
\end{matrix}\right]\; .](http://upload.wikimedia.org/math/a/e/6/ae6225aa8f42684db5768c1fe10092b3.png)
In the homogeneous case this is more simply,
![Q=\left[\begin{matrix}
-\lambda&\lambda&0&0&\dots\\
0&-\lambda&\lambda&0&\dots\\
0&0&-\lambda&\lambda&\dots\\
\vdots & \vdots & \ddots & \ddots & \ddots
\end{matrix}\right]\; .](http://upload.wikimedia.org/math/4/6/8/468b7aac816a004fe208733148ff170b.png)
Here every transition is marked.
Read more about this topic: Markovian Arrival Processes
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