A simple queuing system is given as follows. Also given are random variate streams for both the arrival and service times $($in minutes$).$ Assume the first arrival occurs at time $0$ and has a processing time of $1$ minute. After this, customers arrive and are processed according to the following inter$-$arrival and service times. Simulate the process by hand until TimeNow $=30$ minutes.

$\backslash$table$[[,$Sarvice timectraye$],[3,11],[1,1]],[1,6],[$il$,2],[1,$T$],[32,5]]$

a$.$ Draw a plot of work$-$in$-$process over the $30$ minutes.

b$.$ Calculate the average flow time and waiting time in queue $($only for completed parts in the $30$ mins$)$

c$.$ Calculate the average server utilization and queue length over the $30$ minutes.