$2\mathrm{.}3$ Scheduling Orders

$($a$)$ For a single$-$server CPU, where jobs arrive according to some process, let SRPT denote the preemptive scheduling policy that always serves the job with the currently Shortest$-$Remaining$-$Processing$-$Time $($assume one knows this information$).$ It is claimed that for any arrival sequence, con$-$ sisting of the arrival time and size of every job, SRPT scheduling mini$-$ mizes mean response time over that arrival sequence. Prove or disprove this claim.

$2\mathrm{.}9$ exercises $27$

$($b$)$ The slowdown of a job is defined as the job$$s response time divided by its service requirement. $($i$)$ Mean slowdown is thought by many to be a more important performance metric than mean response time. Why do you think this is$?($ii$)$ It seems intuitive that the SRPT scheduling policy should minimize mean slowdown. Prove or disprove this hypothesis.