Problem $1$: $($use the simulation by hand format and dont copy to get like$)$ Consider the following interarrival and service times for the first $5$ customers to a single server queuing system.

$\backslash$table$[[$Customer Number,Interarrival Time $($min$),$Service Time $($min$)],[1,3,4],[2,1,4],[3,3,5],[4,1,3],[5,,2]]$

For the above table, the first customer arrives at $t=0.$ The interarrival time between customer $1$ and $2$ is $3$ minutes, and the interarrival time between customer $2$ and $3$ is $1$ minute. Suppose the simulation ends at $t=16$ minutes. Based on the above information, compute the following $($show the intermediate steps$)$:

The average number of people in queue;

The average time in system $($time in queue $+$ time in service$)$ for those who have completed service;

The average time in system $($time in queue $+$ time in service$)$ for the entire simulation run.

The server utilization.

Simulation by Hand:

$\backslash$table$[[$System$,$Clock,$B(t),Q(t),\backslash$table$[[$Arrival times of$],[$custs$.$ in queue$]],$Event calendar$],[\backslash$table$[[$Number of$],[$completed waiting$],[$times in queue$]],\backslash$table$[[$Total of$],[$waiting times in queue$]],\backslash$table$[[$Area under$],[Q(t)$