I think you need to read up about the modem you're using. Most of the smart modems these days don't really need to use the handshake controls.

You don't need to assert/de-assert RTS for each character - most modems have a resonable buffer built in. If this modem buffer gets full, it will drop CTS telling you to hold off. RTS tells the modem that 'I want to send' and it replies with CTS saying 'yes you can send', when it drops CTS it's telling you to 'wait'. Since most data sent across the modem is in small data packets, the modem normally will not need to tell you to wait.



To directly answer your question - RTS is not used by the modem for sending you (DTE) data. DTR and DSR handle this.