I responded lower, but dude! 2000 requests a second is hardly anything at all, unless the application server is doing some seriously heavy lifting in which case the architecture is wrong.
You should redo the calculations with 1gb of memory for Lambda and like 30 machines would be generous
Concurrency is key. Requests don't cost much when they're just waiting for other things, but Lambda continues to pile costs on for every increase in concurrency.
APIs should maybe use a tiny fraction actual real CPU time. Perhaps BBCs are different - In order to make an actual fair comparison and properly predict what they would need in servers, greater detail is needed than what you have available to you, but I think your estimations are off by a significant amount.
You should redo the calculations with 1gb of memory for Lambda and like 30 machines would be generous
Concurrency is key. Requests don't cost much when they're just waiting for other things, but Lambda continues to pile costs on for every increase in concurrency.
APIs should maybe use a tiny fraction actual real CPU time. Perhaps BBCs are different - In order to make an actual fair comparison and properly predict what they would need in servers, greater detail is needed than what you have available to you, but I think your estimations are off by a significant amount.