$1.$

Assume that an average process runs for time T before blocking for I$/$O $($that is$,$ the CPU burst is

T$).$ Processes are scheduled using a round$-$robin strategy with quantum Q$.$ The context switch

time is S$,$ which is pure overhead. The quantum Q does not include this overhead.

CPU efficiency is defined as follows:

$($CPU time provided to processes$)$

efficiency $=---------------------------------------------------------$

$($CPU time provided to processes $+$ overhead$).$

Note: in the following, assume that the ready queue is never empty.

For each of the following scenarios, give a formula for CPU efficiency in terms of Q$,$ S$,$ and T$.$

Be sure to simplify each formula as much as possible.

$(1)$

$(2)$

$(3)$

Q $=\backslash$infty

S $<$ Q $<$ T

Q $=$ S