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I am trying to come up with a cost function that I could minimize/maximize. This would be a two variables function: number of requests per second and latency in ms. What we observed is that the more requests we serve, the higher the latency. We want to find the right balance.

What would be the formula? Is this simply a linear function?

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First, there's a third variable somewhere: cost. What's the cost of not serving someone? What's the cost of latency? –  Neal Jul 31 '12 at 13:10
    
Second, the latency(RPS) formula depends on your empirical observations. It will probably be simplest to model it as linear, but if the latency response is actually nonlinear, if RPS changes from average too much, your model will no longer describe the situation and you may find that the cost-benefit calculation shifts. (I don't know what is the most realistic model -- a hyperbola?) –  Neal Jul 31 '12 at 13:12

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