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Aldo Nassigh added subsection_The_Distribution_of_Arrival__.tex
almost 9 years ago
Commit id: 314c2de6c560f5d48715928b7099a3319d02f7c3
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\subsection{The Distribution of Arrival Time}
We introduce the count of arrival per minute $k = 1,2,3, ...$ where $k$ is incremented by one each time the optimization software creates a new group of employees, that will be carried by the same elevator. Probability of arrivals is:
\begin{equation}\label{Poisson}
P(k) = \frac{\lambda^k \cdot e^{- \lambda}}{k!}
\end{equation}
where $\lambda$ is the mean arrival count.
The plot below shows the probability mass function (\textit{pmf}) under the Poisson distribution in three cases ($\lambda=1$, $\lambda=4$ and $\lambda=10$).
