This is a fun experiment, but not very realistic in its current form. Handling of traffic is based on two principles. 1. Safety, 2. Efficiency.
1. Safety
In essence, aircraft separation can be either vertical (usually 1000ft) and/or horizontal (usually 5 nautical miles) .. There are variations of this, depending on radar coverage (can accept less horizontal separation with better coverage) and wake turbulence categories (large, powerful planes cause turbulence that can affect smaller planes or helicopters - more spacing can be required between a large and a small aircraft).
2. Efficiency
To be effective means not only to get all flights on the ground as soon as possible in an orderly manner, but also for the individual flight to be as cost effective as possible. What is most cost effective? Not using fuel. All commercial aircraft are built to stay in the air - and when using idle power (engines not producing significant thrust), to glide for long distances.
So all flights should follow an optimal three dimensional curve, that requires: 1. Optimal distance: To leave their planned maximum altitude for the route by simply reducing thrust, making the aircraft descend, at the optimal point where the aircraft can simply glide all the way to the runway without using additional thrust (fuel). 2. Optimal path: To minimise the amount of turns required, which causes drag, which causes the aircraft to descend faster (would have to use thrust at some point) 3. Optimal speed: To ensure the aircraft touches down on the runway with the required speed.
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An Air Traffic Controller has been trained to consider such factors, but also has the benefit of "the airspace system". Controlled airspace has predefined routes (highways in the air) which are crafted based on aircraft operational conditions. On arrival, aircraft follow a "STAR", which is a predefined route with predefined altitude requirements (cross point X with altitude Y) - usually a mix of an optimal glidepath for the type of aircraft the airport serves, surrounding airspace limitations (restricted airspace, military areas) and geographic features (nice to avoid mountains).
So to facilitate the flow of traffic, the ATC depends on using the airspace as it is designed - and deviating from that when necessary. Deviations are usually called "vectors". The ATC will instruct a flight to fly a certain heading (based on radials of 360 degrees, extending from the flight itself) .. In general "Fly heading 360" (north), "Fly heading 090" (east), "Fly heading 180" (south).. etc or more fine grained - "Fly heading 045" (north-easterly). A deviation can also be a certain flight level, or altitude. Due to traffic ATC can request a flight to descend earlier than planned, or to cross a point on a route at a certain altitude.
An air traffic controller will, traffic permitting, try to avoid deviations from the aircrafts planned route, since the planned route is the "optimal" trajectory for the flight (although constrained by airspace design). Also - placing aircraft on vectors reduces the ATCs mental capacity (the ATC has to remember to give further instructions at a later point, for the flight to return to its planned route - or some other instruction). So an ATC would try to minimise the number of flights on vectors. Unless he/she is doing approach sequencing.
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Approach sequencing.
So at the final stages of the flight, approaching the airport - the flights should as far as possible mostly following predefined routes. These routes end up going alongside the runway (in the opposite direction), and then "U-turning" into the runway direction with a nice smooth curve.
Think of a straight line extending out in the runway direction - guiding aircraft toward the runway (like the green dots you have on your example). This is the function of the localizer (https://en.wikipedia.org/wiki/Instrument_landing_system_loca...).
Aircraft turn into the localiser usually on a 30degree angle or less, to be able to properly intercept the signal and to get established.
So at this point, the ATC doing approach sequencing has to consider both the altitude, speed and heading of each aircraft that is going to land (wants to establish on the localiser) - and determine the optimal sequence based on the two principles (1. safety and 2. efficiency) ..
1. Safety: Which aircraft can safely be vectored to the runway without breaking minimal safety distances to other flights. 2. Efficiency: Which aircraft are closer to the airport (vertically and horizontally). What kind of aircraft are they, which altitudes and speeds do they currently have, and which restrictions can they tolerate (faster or slower, higher or lower).
So the ATC evaluates all this and determines a sequence.
Once a sequence is determined, the ATC takes necessary steps to ensure the safe and efficient flow of that sequence. Aircraft that are far back in sequence might be kept on a vector that takes them further away from the airport for a while, to "give enough wiggle room" to handle the aircraft further ahead in sequence. Depending on traffic, the ATC might even ask other sectors (outside of the ATCs control) to hold traffic. That can be done either by vectoring (short delay) or by instructing the aircraft to enter a holding pattern (aircraft going around in racetrack shape circles).
Anyhow.. Maybe check out some videos on sequencing on youtube, and feed your AI this info - and ask it to research for more - in order to get your sim more realistic.
Best of luck!