code: protected void sendOutgoingMessages (long iterStamp)
      {
          // first attempt to send any messages waiting on the overflow queues
          if (_oflowqs.size() > 0) {
              // do this on a snapshot as a network failure writing oflow queue messages will result
              // in the queue being removed from _oflowqs via the connectionFailed() code path
              for (OverflowQueue oq : _oflowqs.values().toArray(new OverflowQueue[_oflowqs.size()])) {
                  try {
                      // try writing the messages in this overflow queue
                      if (oq.writeOverflowMessages(iterStamp)) {
                          // if they were all written, we can remove it
                          _oflowqs.remove(oq.conn);
                      }
  
                  } catch (IOException ioe) {
                      oq.conn.networkFailure(ioe);
                  }
              }
          }
  
          // then send any new messages
          Tuple<Connection, byte[]> tup;
          while ((tup = _outq.getNonBlocking()) != null) {
              Connection conn = tup.left;
  
              // if an overflow queue exists for this client, go ahead and slap the message on there
              // because we can't send it until all other messages in their queue have gone out
              OverflowQueue oqueue = _oflowqs.get(conn);
              if (oqueue != null) {
                  int size = oqueue.size();
                  if ((size > 500) && (size % 50 == 0)) {
                      log.warning("Aiya, big overflow queue for " + conn + "", "size", size,
                                  "bytes", tup.right.length);
                  }
                  oqueue.add(tup.right);
                  continue;
              }
  
              // otherwise write the message out to the client directly
              writeMessage(conn, tup.right, _oflowHandler);
          }
      }
docs: Writes all queued overflow and normal messages to their respective sockets. Connections that
  already have established overflow queues will have their messages appended to their overflow
  queue instead so that they are delivered in the proper order.