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Under the assumptions 1. and 2. above, the problem is made analytically tractable.\\  \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 \textit{group} 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} 
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