If all priorities are unique, the sorting can be done very simply with reverse:

#!/usr/bin/perl -w
use strict;

my %input = (
  PR1     => 2,
  PR2     => 4,
  PR3     => 1,
  PR4     => 3,
);

my %by_priority = reverse %input;
foreach (sort keys %by_priority) {
  print $by_priority{$_}, "\n";
}
[download]

Which gives:

$ ./foo.pl
PR3
PR1
PR4
PR2
[download]

After sorting, I would use a hash of code references (as in davorg's reply) to execute the actual processes.