Consider a new DISK$6521$ unit with the average seek time, rotational delay,

and block transfer times of $6\mathrm{.}5,7\mathrm{.}8,$ and $0\mathrm{.}5$ ms$,$ and consider $1+$ k$/500$ ms to move

the r$/$w head over k tracks. Suppose, initially, the r$/$w head is on track $4000.$ We want

to study performance of algorithms to schedule requests for disk I$/$Os$.$ Suppose the

followingk I$/$O requests are received by the disk controller: $(1)$ at time $0,$ request for

block on cylinder $4000$; $(2)$ at time $2,$ request for block on cylinder $6000$; $(3)$ at time

$12,$ request for block on cylinder $1000$; $(4)$ at time $17,$ request for block on cylinder

$7000$; and $(5)$ at time $26,$ request for block on cylinder $3000.$

$($a$.)$ Using the elevator scheduling method, determine when each request is served by detailed mathematic expression and steps.

$($b$).$ Answer part $($a$)$ but using the first$-$come$-$first$-$served $($FCFS$)$ scheduling method by detailed mathematic expression and steps