Problem $2$: Consider the following two queueing systems: M$/$G$/1/$FCFS$($First$-$Come$-$

First$-$Served order of service$)$ and M$/$G$/1/$PS $($Processor Sharing$).$ Answer the following

questions in terms of the coefficients of variation of the corresponding service times:

$($a$)$ For what distributions of the service time does M$/$G$/1/$FCFS provide lower average

system time?

$($b$)$ For what distributions of the service time does M$/$G$/1/$PS provide lower average sys$-$

tem time?

$($c$)$ When are the average system times provided by both the M$/$G$/1/$FCFS and M$/$G$/1/$PS

the same?