CPU scheduling is the basis of multi$-$programmed operating systems. By switching the CPU among processes, the operating system can make the computer more productive. The following questions are about CPU scheduling.

Consider the following set of processes with the length of the CPU$-$burst time given in milliseconds:

Process

Burst Time

Priority

$q,$

$q,$

$q,$

P$1$

$7$

$3$

P$2$

$1$

$1$

P$3$

$2$

$4$

P$4$

$5$

$2$

The processes are assumed to have arrived in the order P$1,$ P$2,$ P$3,$ P$4,$ all at time $0.$

a$.$ Draw four Gantt charts illustrating the execution of these processes using FCFS$,$ SJF$,$ a non$-$preemptive priority $($a smaller priority number implies a higher priority$),$ and RR $($quantum $=2)$ scheduling.

b$.$ Calculate the average waiting time.