...
gzip_func() {
started=0
threads=4
for filename in `ls -1 ${EXP_DIR}/*.dmp`

Not only is -1 unnecessary, but so is ls itself. Also, ls will break your script if there are any spaces in the filenames.

Code:

for filename in ${EXP_DIR}/*.dmp

do
 if [[ ${started} -lt ${threads} ]]; then
  let started=started+1

Use standard syntax:

Code:

 if [ ${started} -lt ${threads} ]; then
 started=$(( $started + 1 ))

  echo "gzip ${filename}"
  ( $GZIPCMD ${filename} ) &

Quote the variable, or your script will break if there are spaces in the filename (and there's no need for the parentheses):

Code:

  $GZIPCMD "$filename" &

  list_of_pids="${list_of_pids} $!"
 else
  print "wait ${list_of_pids}"
  wait ${list_of_pids}
  list_of_pids=""
  started=0
 fi
done
}
...
my_binary_file_creation_process
...
while [ `find ${EXP_DIR} -name \*.dmp|wc -l` -gt "0" ]; do

What wrong with:

[code]
for

 gzip_func
 print "wait ${list_of_pids}"
 wait ${list_of_pids}
 list_of_pids=""
done

Your code looks far more complicated than it needs to be.

It's not clear from your code how you tell whether a file is finished being written to so that you can compress it.

Do you have any control over the process that is writing the binary files?