Too many TIME_WAIT connections in PostgreSQL
1500 to 2200 concurrent connections are only useful when you need them. Otherwise, bring the total number of open connections down and start using a connection pool like pgBouncer or PgPool-II. See Number of Connections (on the wiki). We do about 2500 transactions per second on 150 connections.

Don't forget, each connection uses RAM, RAM that could be used to get some real work done. PostgreSQL gets slower when you use too many connections without a connection pool. What "too many" is depends on your hardware and workload, but it's very unlikely that your system will perform better with 2000 than it will with 100; probably much worse.