Consider three processes, $P1,P2,$ and $P3,$ arriving in the ready queue at time $0$ in the order P$1,$ P$2,$ P$3,$ with service time requirements of $10,20,$ and $30$ units, respectively. Each process undergoes a two$-$phase execution model, allocating $20\%$ of its service time to I$/$O $($inputoutput burst time$),$ succeeded by $70\%$ of its service time dedicated to computational tasks on the CPU. The remaining portion of its service time is expended on I$/$O operations prior to process completion. Assuming concurrent execution of all I$/$O operations and incorporating a CPU scheduling overhead $=1$ unit, compute the following metrics for FCFS scheduling. $($Draw the Gnatt chart for the above question$)$

i$.$ Determine the total schedule length, reflecting the temporal extent of the entire scheduling process.

ii$.$ Calculate the average turnaround time $($TAT$),$ denoting the average time from process arrival to its completion, inclusive of waiting and execution time.

iii. Derive the average waiting time, representing the mean$-$time processes spend in the ready queue before CPU execution.

iv$.$ Evaluate the percentage of CPU idleness, indicating the proportion of time the CPU is not engaged in computational tasks