If you only want to run them serially, then you might already have functioning code. The SOMAXCONN argument that you are giving to the listen parameter tells the kernel to accept up to than many connections (queues them), whether or not you have accepted on them. As soon as you accept, a spot in the listen queue is opened and somebody else can connect.

However, under that senario, a client will connect and his connection will be open, but will not receive a greeting from the server until it is his turn.

An alternate solution would be to use something like the Net::Server or Net::Daemon modules. These modules are intended for handling all of the server back end for you and you simply have to deal with handling the dialog with the client. To handle only having one sleep.pl run at a time, you could use file locking to assure that only one process gets it.

For example:

#!/usr/bin/perl
package MyServer;
use Net::Server::Fork;
use Fcntl qw(LOCK_EX);
@ISA = qw(Net::Server::Fork);

MyServer->run(port => 20203);
exit;

sub process_request {
  my $self = shift;
  print STDOUT "Welcome to my server\r\n";
#  while (<STDIN>){
#    print "You said: $_";
#    last if /quit/;
#  }

  print "Waiting to get lock on file\r\n";
  my $lockfile = '/tmp/foo';
  open(LOCK, $lockfile) || die "Couldn't open [$!]"; 
  flock(LOCK,LOCK_EX) || die "Couldn't get lock [$!]";


  print "Got lock, proceeding\r\n";
  system('sleep.pl');
  close(LOCK);

  print "All done, goodbye\r\n";
}
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There are many ways to do it. Just depends on what you need.

my @a=qw(random brilliant braindead); print $a[rand(@a)];