Heroku seems to encourage responses of 500 ms or less . Since they do not mention changing the request timeout on this page, I assume that they do not support changing it (although you can ask for Heroku support).
What work do you do for your report?
Can you run the calculation work in the background job and save the result? (for example, in memcache, in another table in your database, etc.) How relevant is the information that should be?
Can you expedite the request? What does your query plan look like? Is there room for improvement by changing the way we query data or add indexes?
Would an approach like streaming HTTP message help?
I would suggest trying 1 or 2 first and see if they help. If you give us more details about what you are doing, we can help more.
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