Why are you actually using a HoHoH?
Is there more information besides the time?
If not you could say:

$HoHoH->{"alice"}{"aaaa"} = "20:00:00";
# instead of
# $HoHoH->{"alice"}{"aaaa"}{"time"} = "20:00:00";
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and later:

foreach my $user ( sort keys %$HoHoH ) {
  print "$user\n";
  for my $text
      ( sort {$HoHoH->{$user}->{$a}
              cmp
              $HoHoH->{$user}->{$b}
             }
       keys %{$HoHoH->{ $user }} ) {
...
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