At rush hour, the traffic intensity is \(a = 4.5\) Erlangs1. 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 \(T_w=2'\) \(17''\), that is, it is longer than the average service time (\(W_s=1'\) \(30''\)). The time needed on average by the employees to reach their floors \(T_w + W_s\) is \(3'\) \(47''\).
By adding one more elevator, so that \(c=6\), the management of corporate B decreases the average server utilization to \(\rho = 4.5 / 6 = 0.75\). The average waiting time \eqref{Tim} is \(T_w=25''\), that is, it is one third of the average service time (\(W_s=1'\) \(30''\)). The time needed on average by the employees to reach their floors \(T_w + W_s\) is \(1'\) \(55''\)
The management 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 time needed on average by the employees to reach their floors.
\(3\) groups per minute times \(1.5\) minutes service time↩