When HTTP requests arrive faster than your application can process them, they can form a large backlog on a number of routers. When the backlog on a particular router passes a threshold, the router determines that your application isn’t keeping up with its incoming request volume. You’ll see an H11 error for each incoming request as long as the backlog is over this size. The exact value of this threshold may change depending on various factors, such as the number of dynos in your app, response time for individual requests, and your app’s normal request volume.
2010-10-06T21:51:07-07:00 heroku[router]: at=error code=H11 desc="Backlog too deep" method=GET path="/" host=myapp.herokuapp.com fwd=188.8.131.52 dyno= connect= service= status=503 bytes=
The solution is to increase your app’s throughput by adding more dynos, tuning your database (for example, adding an index), or making the code itself faster. As always, increasing performance is highly application-specific and requires profiling.