boost asio async_write : how to not interleaving async_write calls?

Is there a simple way to avoid this problem ?

Yes, maintain an outgoing queue for each client. Inspect the queue size in the async_write completion handler, if non-zero, start another async_write operation. Here is a sample

#include <boost/asio.hpp>
#include <boost/bind.hpp>

#include <deque>
#include <iostream>
#include <string>

class Connection
{
public:
    Connection(
            boost::asio::io_service& io_service
            ) :
        _io_service( io_service ),
        _strand( _io_service ),
        _socket( _io_service ),
        _outbox()
    {

    }

    void write( 
            const std::string& message
            )
    {
        _strand.post(
                boost::bind(
                    &Connection::writeImpl,
                    this,
                    message
                    )
                );
    }

private:
    void writeImpl(
            const std::string& message
            )
    {
        _outbox.push_back( message );
        if ( _outbox.size() > 1 ) {
            // outstanding async_write
            return;
        }

        this->write();
    }

    void write()
    {
        const std::string& message = _outbox[0];
        boost::asio::async_write(
                _socket,
                boost::asio::buffer( message.c_str(), message.size() ),
                _strand.wrap(
                    boost::bind(
                        &Connection::writeHandler,
                        this,
                        boost::asio::placeholders::error,
                        boost::asio::placeholders::bytes_transferred
                        )
                    )
                );
    }

    void writeHandler(
            const boost::system::error_code& error,
            const size_t bytesTransferred
            )
    {
        _outbox.pop_front();

        if ( error ) {
            std::cerr << "could not write: " << boost::system::system_error(error).what() << std::endl;
            return;
        }

        if ( !_outbox.empty() ) {
            // more messages to send
            this->write();
        }
    }


private:
    typedef std::deque<std::string> Outbox;

private:
    boost::asio::io_service& _io_service;
    boost::asio::io_service::strand _strand;
    boost::asio::ip::tcp::socket _socket;
    Outbox _outbox;
};

int
main()
{
    boost::asio::io_service io_service;
    Connection foo( io_service );
}

some key points

• the boost::asio::io_service::strand protects access to Connection::_outbox
• a handler is dispatched from Connection::write() since it is public

it wasn’t obvious to me if you were using similar practices in the example in your question since all methods are public.