Actually a simple boss/worker model should be easy enough. This wont scale to multiple computers but its a starting point. Note that this code was torn from a larger fully functional threaded program I have. The code below is not complete and not even tested but it should demonstrate all the concepts you need.

For example, how can I avoid a race condition when I'm filling up the result data structure (for the table) if the results themselves come in asynchronously?

You can put your work back into a queue to avoid a race condition. Alternatively look into lock(). Just make a variable called $lock then you can control access to your output structure. by doing something like this..

my $lock : shared;
{
lock($lock)
...do something that only 1 thread at a time should do...
}
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How do I tell which thread is busy and which one is available?

You shouldn't need to. In the scheme below using a queue an idle thread will pick up a unit of work if it can, if there is no more work it will exit and if no work exists yet it will wait.

use threads;
use threads::shared;
use Thread::Queue;

my $max_threads = 8;
my $queue = Thread::Queue->new();

print "Spawning threads...";
for(1...$max_threads){
       threads->create(\&thread_main)->detach();
}
print "Done!\n";

...Do what you need to do to get a work unit...
$queue->enqueue("SOME_WORK_UNIT");

#Signal to the threads they're done.
   for(1...$max_threads){
       $queue->enqueue("DONE");
  }

wait_on_threads();

exit 0;

sub thread_main(){
 while(1){
 my ($work)  = $queue->dequeue());
 # If end-of-queue marker reached then cleanup and exit.
        if($app eq "DONE"){
            return 0;
        }
 ...do processing work...
 }
}

sub wait_on_threads(){
    #Dont even start printing messages until our queue is near deplete
+d.
    while($queue->pending() > $max_threads){
        sleep 1;
    }

    my $cnt  = 0;
    my $wait = 5;
    while(my $items = $queue->pending() > 0){
        # Fortunatly on AIX sleep doesnt seem to put ALL the threads t
+o sleep.
        # whew! This is a non-portable loop though ;)
        if ($cnt++ > $wait){
            print "Please wait. $items items still in progress.\n";
            $cnt = 0;
            $wait++;
        }
        sleep 3;
    }
}
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