Problem $1$: This problem compares RM and EDF schedules. Consider two tasks with

periods p$\_(1)=2$ and p$\_(2)=3$ and execution times e$\_(1)=$e$\_(2)=1.$ Assume that the

deadline for each execution is the end of the period.

$($a$)$ Give the RM schedule for this task set and find the processor utilization. How does

this utilization compare to the Liu and Layland utilization bound?

$($b$)$ Show that any increase in e$\_(1)$ or e$\_(2)$ makes the RM schedule infeasible. If you hold

e$\_(1)=$e$\_(2)=1$ and p$\_(2)=3$ constant, is it possible to reduce p$\_(1)$ below $2$ and still get a

feasible schedule? By how much? If you hold e$\_(1)=$e$\_(2)=1$ and p$\_(1)=2$ constant, is

it possible to reduce p$\_(2)$ below $3$ and still get a feasible schedule? By how much?

$($c$)$ Increase the execution time of task $2$ to be e$\_(2)=1\mathrm{.}5,$ and give an EDF schedule. Is

it feasible? What is the processor utilization?