I'm pretty confident AWS's product for this use case would be Lambda and the new on-demand DynamoDB.
Is there actually a use case in analytics that requires a server that accepts connections from multiple clients, and then has to have <60ms latency including state over the wire and executing sophisticated business logic, between those clients, for time periods longer than 5 seconds? I.e. something that resembles a video game?
Because if there isn't, if your goal is to scale, why have containers at all?