Certainly. The given/when (or for/when) construct is cleaner, but there's no reason you can't fall back on a series of if/elsif/else. (Though I'd recommend looking at the dispatch table concept first.) In your sample data, the fields appear consistent up to the 'directional' field you're looking at, so you could:

while(<DATA>){
  chomp;
  my( $month, $day, $time, $host, $ppid, $date, $time2, $something, $d
+irection, $remainder ) = split ' ', $_, 10;
  if( $direction eq '<=' ){
    # go left
  } elsif( $direction eq '=>' ){
    # go right
  } elsif( $direction eq '==' ){
    # do a third thing
  } elsif( $direction eq '**' ){
    # do a fourth thing
  } else {
    # fall back on a default behavior
  }
}
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