implement the procedure in python to simulate a GI$/$GI$/1$ with Gamma$(2,1)$ inter$-$arrival times and Gamma$(2,1\mathrm{.}2)$ service times.

You can start the system empty at time $0$ and generate the system dynamics on time interval $[0,5000].$ Report you estimation of the following quantities and explain how you compute these estimates from the simulation data.

$($i$)$ Mean waiting time of customers. $($hint: Don$$t use Lindley$$s equation. Instead, map

each customer$$s arrival event to the corresponding service completion event.$)$

$($ii$)$ Time$-$average queue length.

$($iii$)$ Average queue length observed at customer arrivals.