Discrete-queuing models are hard to solve computationally and can become easily intractable with an increased number of state-action pairs. Markov decision processes can be employed to come up with solutions of such systems.
Fluid approximations to queuing systems, model the problem in a continuous setting and generally are useful to gain insight on the original queueing problem. In my application, I am using a fluid approximation to come up with a good approximation of a routing policy of a linear swithching curve form. Hence, fluid model gives me a reasonable approximation of the slope of that curve.
However when I analyze the discrete policy, although I see that fluid slope is a good fit, there is also an intercept - thus the switching line does not start at (0,0). How can I calculate/approximate that intercept value?
The only example I have seen in this context uses perturbation theory - on which I have very limited knowledge. I would appreciate if you could share any useful references/lectures notes.