Event are send by thousands of visitors and we are not able to bulk insert
You need to either bulk insert or shard the data. I would be tempted to try the bulk insert route first.
That you think you can't suggests these events are being created by autonomous processes - you just need to funnel them through an intermediary rather than direct to the database. And it would be easiest to implement that funnel as an event based server (rather than a threaded or forking server).
You don't say what the events are nor where they originate - which has some impact on the details of implementing a solution.
Both rsyslog and syslogng will talk to a MySQL backend - hence you can eliminate the overhead of establishing a new connection per message - but I don't know if either implements buffering / bulk inserts. It would certainly be possible to tail the files they produce with a single process and create bulk inserts from there.
It would relatively simple to write a funnel using this event based server, this buffer tool along with a bit of code to implement asynch mysqli calls and a watchdog. Or you could use node.js with an async mysql lib. There's also tools like statsd (again using node.js) which can also perform some aggregation on the data on the data.
Or you could just write something from scratch.
A write-only database is a useless piece of hardware though. You've not provided any details of how this data will be used - which has some relevance to designing a solution. Also since ideally the data feed would be a single process / DB session, it might be a beter idea to use MyISAM rather than InnoDB (I see in your later comment you said you had problems with MyISAM - presumably this was with multiple clients).