After adding the index for "last_activity_at", we did not see a noticeable improvement in response time and the 95th percentile was still unusually high. There was a significant improvement in the error rate. The chart below shows a visual correlation between spikes and the response time. Upon inspecting these remaining errors, it was found that they all shared the "asc" sort field in common. This could explain the unexpected response time where we were expecting an improvement.
