Problem $4(15$ pts$)$

Suppose in the distributed system, we have $7$ independent jobs $\backslash (\backslash \{$J $1,$ J $2,$ J $3,$ J $4,$ J $5,$ J $6,$ J $7\backslash \}\backslash )$ and $3$ machines $\backslash (\backslash \{\backslash$mathrm$\{$M$\}1\backslash ),$ M$2,$ M$3\backslash \}.$ The processing ability of machines are the same. The completion time of the $7$ jobs are $\backslash (\backslash \{2,14,4,16\backslash ),\backslash (6,5,3\backslash \}\backslash ).$ How to schedule them so that the entire execution time is the shortest.

$(1)$ Please draw the scheduling order on the three machines

$(2)$ Please calculate the shortest time of the entire execution $($in other words, how long does it take run the $7$ jobs on the $3$ machines$)$

$($Reference paper: Omega: flexible, scalable schedulers for large compute clusters; Large$-$scale cluster management at Google with Borg$)$

Answer:

Examples:

M$1$

Job$\_$i Job$\_$j

M$2$

M$3$