deletions | additions       diff --git a/The_analysis_confirms_the_qualitative__.tex b/The_analysis_confirms_the_qualitative__.tex  index 1528b35..85df788 100644  --- a/The_analysis_confirms_the_qualitative__.tex  +++ b/The_analysis_confirms_the_qualitative__.tex 
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The analysis confirms the qualitative discussion based on the analytical formulas \eqref{ErlangC} and \eqref{Tim}  presented in section 3. With five elevators, when the number of groups per minute exceeds a threshold that lies approximately at $2.75$, the increase in average waiting time is very sharp since the average server utilization is very high. For reference, at the threshold ($\lambda=2.75$) $\rho=0.825$\\ With six elevators, the threshold level is raised above $\lambda=3$ groups per minute (outside the chart). For reference, the average waiting time is more than $1'$ if $\lambda$ exceeds the threshold of $3.4$ groups per minute (that is $\rho=0.850$), so that the average server utilization lies below $30''$ also in the \textit{rush-hour} state of the system.