Dealing with SeqScans when Time-based Partitions Cut Over

In a table with high insert frequency (~1.5k rows/s) and high query
frequency (~1k queries/s), partitioned by record creation time, we have
observed the following behavior:

* When the current time crosses a partition boundary, all new records
are written to the new partition, which was previously empty, as
expected

* Because the planner's latest knowledge of the partition was based on
its state prior to the cutover, it assumes the partition is empty and
creates plans that use sequential scans

* The table accumulates tens to hundreds of thousands of rows, and the
sequentail scans start to use nearly 100% of available database CPU

* Eventually the planner updates thee stats and all is well, but the
cycle repeats the next time the partitions cut over.

We have tried setting up a cron job that runs ANALYZE on the most recent
partition of the table every 15 seconds at the start of the hour, and
while this does help in reducing the magnitude and duration of the
problem, it is insufficient to fully resolve it (our engineers are still
getting daily pages for high DB CPU utilization).

We have considered maintaining a separate connection pool with
connections that have `enable_seqscan` set to `off`, and updating the
application to use that pool for these queries, but I was hoping the
community might have some better suggestions.

- Matthew Planchard