How to model aircraft fuel consumption during the approach? I am trying to write an algorithm modelling the 'Airplane landing problem'. The aim is to land a sequence of airplanes while minimizing the operating costs and respecting constraints such as the separation between consecutive airplanes.
Hence, I need to be able to quantify these operating costs in particular fuel consumption.

Basically, in my simulation - it's a very simple approach - airplanes can be in 3 different regimes :


the aircraft can be asked to fly faster than it's preferred speed, it's called time advance and it's one of the tools used to reduce congestion
the aircraft can of course fly at it's preferred speed
the aircraft can be asked to fly a holding pattern


I would like to elaborate a function that would give the fuel consumption in function of the time for every mode.
I absolutely don't know where to start. The only information that I find deal with the preferred speed consumption.
How can I model the two others regimes ?

Edit : Indeed, the part concerning holding patterns is similar to this other question. However, I don't think any information on time advance has been given so I would like to focus my question on this. Also, if anyone has more information on fuel consumption in holding patterns than would by very helpful.
Thank you very much
Approaches take relatively little time, and have various throttle ranges, from idle to slow level flight. I would simply model as if the aircraft were flying level for the distance of the approach, you will over estimate fuel consumption for the approach itself, but for even a 60 minute flight the error would be tiny. You simply cannot accurately predict what is going to happen.