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Aldo Nassigh edited untitled.tex
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\section{The Problem}
The offices of two corporates (A and B) are housed in similar buildings, equipped with a set of \textit{smart} elevators, that group employees before they take the elevator so as to optimize the average elevators' usage rate, that is achieved by reaching a minimum in:
\begin{itemize}
\item the number of groups per minute;
\item the service time (i.e. the time spent in the elevator by the employees).
\end{itemize}
At rush hour, however, the optimization software cannot do better than having three groups per minute with a service time of a minute and a half for each group (average values).
Either of the buildings is served by a set of five elevator, but corporate B activates one more elevator at rush hour.\\
a) You are asked to compute the average waiting time of the elevator for the corporates' employees at rush hour for both corporates.\\
Out of the peak hour, the optimization software is able to reduce the number of groups to only two per minute on average, while service time is kept constant so as to save power.\\
b) Would it be useful for corporate B to keep in service the additional elevator also in this case? \section*{Acknowledgement}
