Scheduling Parallel Jobs Using Migration and Consolidation in the Cloud

Algorithm 3

REASY Backfilling.

 Input :  𝐽_fg: jobs running in fg VMs;

     𝐽_bg: jobs running in bg VMs;

     𝐽_𝑞: jobs waiting in the queue.

(1) begin

(2) /^* Make reservation for the first job in 𝐽_𝑞∪𝐽_bg, then backfill^*/

(3)  let 𝑇_𝑆 = 0 (shadow time), 𝑁_𝐸 = 0 (extra fg VM number);

(4)  𝐻𝑑𝐽𝑜𝑏 ← first job in 𝐽_𝑞∪𝐽_bg; 𝑁_𝑅 ← process number of 𝐻𝑑𝐽𝑜𝑏;

(5)  𝑁_future ← current idle fg VM number;

(6)  if  𝐻𝑑𝐽𝑜𝑏∈𝐽_𝑞  then

(7)   Sort 𝐽_fg in ascending order of their termination time;

(8)    for  𝑒𝑎𝑐ℎ𝑗𝑜𝑏𝑗𝑖𝑛𝑡ℎ𝑒𝑠𝑜𝑟𝑡𝑒𝑑𝐽_fg   do

(9)   𝑁_𝑗 ← processe number in 𝑗; 𝑁_future=𝑁_future+𝑁_𝑗;

(10)      if   𝑁_future≥𝑁_𝑅   then

(11)       𝑇_𝑆 = the termination time of 𝑗; 𝑁_𝐸 = 𝑁_future − 𝑁_𝑅;

(12)       break;

(13)  else

(14)    𝐽^fg_ℎ ← the jobs running in the foreground VMs of 𝐻𝑑𝐽𝑜𝑏;

(15)    𝑆𝑢𝑚𝑆𝑖𝑧𝑒 ← the size sum of jobs in 𝐽^fg_ℎ;

(16)    𝑇_𝑆 = last termination time of jobs in 𝐽^fg_ℎ;

(17)    𝑁_𝐸 = 𝑁_future +𝑆𝑢𝑚𝑆𝑖𝑧𝑒 − 𝑁_𝑅;

(18)  /^* Backfill runnable jobs^*/

(19)  for  𝑒𝑎𝑐ℎ𝑗𝑜𝑏𝑗𝑖𝑛𝐽_𝑞∪𝐽_bg  do

(20)    𝑁_𝑗 ← processe number 𝑗; 𝑁_idle ← idle fg VM number;

(21)    if   𝑁_𝑗>𝑁_idle   then

(22)     continue;

(23)    𝑡_𝑟 ← the runtime of 𝑗; 𝑡_𝑐 ← current time;

(24)    if   (𝑡_𝑟+𝑡_𝑐≤𝑇_𝑆) or 𝑁_𝑗≤𝑁_𝐸   then

(25)      if Deploy (j, 'R')  then

(26)      remove 𝑗 from 𝐽_𝑞 or 𝐽_bg, insert it into 𝐽_fg;

(27)     if   𝑡_𝑟+𝑡_𝑐>𝑇_𝑆  then

(28)      𝑁_𝐸 = 𝑁_𝐸 − 𝑁_𝑗;