How to input many big static json files into logstash? - out-of-memory

Question

My inputs are hundreds of big 1-line json files (~10MB-20MB).
After getting out-of-memory errors with my real setup (with two custom filters), I simplified the setup to isolate the problem.
logstash --verbose -e 'input { tcp { port => 5000 } } output { file { path => "/dev/null" } }'
`
My test input is a multi-level nested object in json:
$ ls -sh example_fixed.json
9.7M example_fixed.json
If I send the file once, it works fine. But if I do:
$ repeat 50 cat example_fixed.json|nc -v localhost 5000
I get the error message:
Logstash startup completed
Using version 0.1.x codec plugin 'line'. This plugin isn't well supported by the community and likely has no maintainer. {:level=>:info}
Opening file {:path=>"/dev/null", :level=>:info}
Starting stale files cleanup cycle {:files=>{"/dev/null"=>#<IOWriter:0x6f51765 #active=true, #io=#<File:/dev/null>>}, :level=>:info}
Error: Your application used more memory than the safety cap of 500M.
Specify -J-Xmx####m to increase it (#### = cap size in MB).
Specify -w for full OutOfMemoryError stack trace
I have determined that the error triggers if I send the input more than 30 times with a heap size of 500MB. If I increase heap size, this limit goes up accordingly.
However, from documentation I understand logstash should be able to throttle the input when it cannot process the events quickly enough.
In fact, If I do a sleep 0.1 after sending new events, it can handle up to 100 repetitions. But not 1000. So I assume this means the input is not being throttled properly, and whenever the input rate is higher than the processing rate, it's a matter of time before the heap is filled and logstash crashes.