Thanks!
This is exactly when I use bash-only at the background all at once, and I received warning from the admin for causing trouble with the server! So I want to restrict the jobs less than the maximum cores of the server.
At this moment I do not care too much about the efficiency yet, although the cat/cp do eat a lot the I/O capacity.
Yes, the ln -s part is not the big deal. The real challenge is the cat and cp parts, where big files are involved to make the processes slow that's why I need parallel.
My real code is pretty much the same as the example, and here is the first several rows for the portion with cat:

Code:

# cd /storage/scottJ/data/raw_reads/resequenced
cat EMS01a_Early_Rice_*_R1.fq.gz EMS01b_Early_Rice_*_R1.fq.gz > ../Early_Rice_1_R1.fq.gz
cat EMS01a_Early_Rice_*_R2.fq.gz EMS01b_Early_Rice_*_R2.fq.gz > ../Early_Rice_1_R2.fq.gz

cat EMS02a_Early_Flax_*_R1.fq.gz EMS02b_Early_Flax_*_R1.fq.gz > ../Early_Flax_1_R1.fq.gz
cat EMS02a_Early_Flax_*_R2.fq.gz EMS02b_Early_Flax_*_R2.fq.gz > ../Early_Flax_1_R2.fq.gz
......

I was thinking the option is straight-forward, and my impression is parallel is for jobs with similar pattern of the scripts/options of the commands. I went to gnu website and other parallel tutorial, but could not spot the corresponding part for this case.
Also I found this type of work is quite common for me to process hundreds of samples, which takes at least a couple of hours when I used to do it one-by-one and let the run goes overnight. This is not good if I want the results right away, which can be achievable using 16~20 cores by parallel if the scaling is proportional as 16~20x.
Thanks again if there is option for my situation that I may have missed.

---------- Post updated at 06:51 PM ---------- Previous update was at 05:47 PM ----------

Did an experiment and found out the simple answer for my example is

Code:

cat commands_script.sh | parallel -j 16

Here is my test.

Code:

commands_script.sh:
echo test1; sleep 15s
echo test2; sleep 15s 
echo test3; sleep 15s 
echo test4; sleep 15s 
echo test5; sleep 115s  

echo test6; sleep 15s
echo test7; sleep 15s 
echo test8; sleep 15s 
echo test9; sleep 15s 
echo test10; sleep 115s  

echo test11; sleep 15s
echo test12; sleep 15s 
echo test13; sleep 15s 
echo test14; sleep 15s 
echo test15; sleep 115s

Code:

$ time cat commands_script.sh | parallel -j 16
test1
test2
test3
test4
test6
test7
test8
test9
test11
test12
test13
test14
test5
test10
test15

real    1m56.053s
user    0m0.160s
sys    0m0.132s

The order of the echoed strings is what I expected!

Code:

$ time bash commands_script.sh
test1
test2
test3
test4
test5
test6
test7
test8
test9
test10
test11
test12
test13
test14
test15

real    8m45.042s
user    0m0.012s
sys    0m0.004s

Using parallel took 1m56.053s, whereas bash-only took 8m45.042s as it is sequential sum of each process.
And I appreciate any insight/comment if I missed anything!