The 503 Service Unavailable error occurs when a new request tries to access a session where more than 16 requests are pending on that session, or an error occurred while queuing the session.
The 403 Forbidden error occurs when the client IP address or host name does not match that of the creator of the session.
A request stipulating a session that does not exist does not implicitly generate an error. It is up to the web application to detect this condition (by checking SessionID, SessionCreateTime, or SessionLastTime connection properties) and do the appropriate action.