Sudden connection and load average spikes with postgresql 9.3

Hello all,
This is my very first message to the Postgresql community, and I really hope
you can help me solve the trouble I'm facing.

I've an 80 core server (multithread) with close to 500GB RAM.

My configuration is:
MaxConn: 1500 (was 850)
Shared buffers: 188Gb
work_mem: 110Mb (was 220Mb)
maintenance_work_mem: 256Mb
effective_cache_size: 340Gb

The database is running under postgresql 9.3.9 on an Ubuntu Server 14.04 LTS
(build 3.13.0-55-generic)

Two days from now, I've been experiencing that, randomly, the connections
rise up till they reach max connections, and the load average of the server
goes arround 300~400, making every command issued on the server take
forever. When this happens, ram is relatively low (70Gb used), cores
activity is lower than usual and sometimes swap happens (I've swappiness
configured to 10%)

I've been trying to find the cause of this server underperformance, even
logging all queries in debug mode, but nothing strange found so far.

I really don't know which can be my next step to try to isolate the problem
and that's why I write to you guys. Have you ever seen this behaviour
before?
Could you kindly help me suggesting any step to follow?

Thanks and best regards!
E.v.

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