Problem $1$:$($simulation by hand$)$

Consider the following interarrival and service times for the first $5$ customers to a single

server queuing system.

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, and so on$.$ Suppose the simulation ends at $t=16$ minutes. Based on the above

information, show the following $($show the intermediate steps$)$:

Construct the $N(t)$ plot, where $N(t)$ is the number of customers in system $($those

in queue $+$ those in service$).$

The average time in system $($time in queue $+$ time in service$)$ based on the $N(t)$

plot.

The average number of people in system $($those in queue $+$ those in system$)$ based

on the $N(t)$ plot.

Construct the $B(t)$ plot.

The server utilization based on the $B(t)$ plot.