There is a problems with
ifup (or some scripts it calls).
Do the following:
create two ppp connections
on the same ttyS port.
Then start first one,
after then start second (because the modem is busy,
it will print that the ttyS is busy).
But it prints this at huge rage to /var/log/messages
without any stop.
In less than 10 minutes
the /var/log/messages file on my computer
grew so big, that there is no disk space left.

A delay in at least several seconds
should be put in between attempts to activate a link.