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\section{Discussion and Conclusios}  Following the main results outlined above, the target of the wise building manager is to avoid that the average server utilization becomes too high at rush hour, so as to prevent the divergence of the average waiting time.  \subsection{Question a}  The traffic intensity is $a = 4.5$ \textit{Erlangs}\footnote{$3$ groups per minute times $1.5$ minutes service time}. With $c=5$ elevators, the average server utilization of corporate A is very high: $\rho = 4.5 / 5 = 0.9$. The average waiting time \eqref{Tim} is $2'$ $17''$, that is, it is \textbf{ longer} than the average service time ($W_s=1'$ $30''$). The overall time needed on average by the employees to reach their floor $T_w + W_s$ is $3'$ $47''$\\ $47''$.\\  By adding one more elevator, so that $c=6$, the building manager of corporate B decreases the average server utilization to $\rho = 4.5 / 6 = 0.75$. The average waiting time \eqref{Tim} is $25''$, that is, it is \textbf{one third} of the average service time ($W_s=1'$ $30''$). The overall time needed on average by the employees to reach their floor $T_w + W_s$ is $1'$ $55''$\\  The building manager of corporate B was able to take advantage of the non-linearity of the problem: the increase by $20\%$ in the number of elevators translate into the decrease by $50\%$ of the overall time needed on average by the employees to reach their floor.   
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