Having had the Arcology built for the last few days, I've been studying what exactly its doing.
Here's the current stats of my Arcology:
Operating/Constructing
Arcology costs 1,000,000 (just one city pays this fee) and requires 1,000 Alloy, 2,800 Metal, 60,000 TVs (entire region can help with goods) to construct.
One thing to remember is each city in the region processes the Arcology separately. I had to load each of my regional cities to get it "built" in each city. To get it operating you need 300 MW/hr power and 120 kGal/hr water available in the region.
While building the Arcology, it doesn't directly update its required goods very consistently. A lot of people on the forums are complaining it's not working, but it worked for me relatively fine (except for a few goods-eating bugs).
Benefit
Arcology provides 3 direct benefits. Arcology fills the need for residential buildings. With Arcology in place, you could technically create a city without residential zones since all your shoppers, workers commute in. It's an absolute absurd notion, but that's what it claims.
1) Shoppers
The first benefit is shoppers commuting in to fill gaps in your Commercial demand. At level 8 I have 3,125 Shoppers available at the Arcology. I think these numbers are for the whole region. I don't know what would happen if two people both requested the maximum number of shoppers/workers from the Arcology. I suspect it would grant both cities what they wanted. Anyways, the shoppers commute in and look for shopping. They fill the gap of Commercial needing shoppers if you have one there. You will still have businesses complaining about needing shoppers but they will be eased a bit. ALSO: looking at my numbers it seems Arcology shoppers don't replace your city's shoppers. I think they have some kind of priority over shoppers from Arcology. I think this is true for workers as well.
2) Workers
This is the most important benefit of the Arcology by far since getting that RCI just right is hard. If you look at the above population breakdown you see that I have huge numbers commuting to work. Before I had the Arcology up, I needed $ and $$ workers, but they are filling the gap in my RCI. My needed jobs is staying at 0, while unemployment is staying at 0. Very few $$$ workers are commuting in so I assume most or ALL of the Arcology residents are $ and $$. Just recalling from memory but I think I am receiving 10,000 $ Workers and 10,000 $$ Workers after building the Arcology.
Basically the Arcology floods your city with unemployed agents walking around/using mass transit or cars to find/fill jobs.
3) Students
I just watched a morning rush hour and didn't notice any school buses or cars coming in and headed to school. Unless they are all on mass transit and only going to the college/university they aren't coming in. All buses I followed coming in from Arcology seemed to drop off unemployed worker agents, but its possible students were on those buses too. In any case, there's not much need for extra students filling up your schools, so that would be a drawback. I have an extra amount of schools for this city and I haven't noticed any extra filling of my schools. Just taking a look at my community college shows very little regional impact:
Drawbacks/Impact
The drawbacks of the Arcology after being built are pretty singular, in my opinion. The only problem Arcology causes is it has the potential to put extra strain on a city in the form of Traffic.
You can see the huge spike in Visitors to my city. That equals traffic. Look at it like this: All those unfilled jobs you had before, all those shops that needed to sell goods got serviced by new people because the Arcology supplied and fixed the gap. IMO, if you have a city that has bad traffic problems Arcology could potentially make it worse. If you have a city that is OK on traffic but needs help in the RCI department (particularly for $/$$$) then Arcology is GOOD. As for your Residental concerns, I don't see ANY impact on the residental in my city, the only thing that is happening is Arcology is flooding my city with Unemployed Workers and Shoppers with money. The students I don't know about so much. In your 2 scenarios the 2nd one is definitely true. Arcology is all about filling the RCI gap (just the CI part) in the form of Shoppers/Workers, not devaluing or replacing your residental need. I can't speak to what would happen if you had very high unemployment and you built the Arcology. And the way the Industry/Commercial need workers at the moment I don't know why you would have Unemployment unless you're trying to game the system with 100% residental city.
Tourists
Just one last update. It was suggested that you receive tourists from the Arcology. I can't see any proof at all of this. In fact my tourism industry is flailing in the wind and seems unaffected by Arcology being built. I think any shopper from another city is labeled a "tourist", which is true. However, it won't help your Tourism industry, only local commercial.
You have a problem with people turning left at that first intersection. If everyone turns the same way, it effectively turns the road into a single lane road. Address this by making sure that people who turn right and go straight can still reach destinations on the left. Cars do not always take the shortest route, so some will take the alternate routes.
Do you see that square at the entrance? That's a conversion intersection between a heavy avenue and a streetcar avenue. Making a streetcar avenue at that point is useless - people aren't just going to jump out of their cars and ride it. Since you can't upgrade the entrance road to streetcar avenue, downgrade the road between the conversion intersection and your first turning intersection to heavy avenue.
Add destinations that incoming sims will want before the first turning intersection.
I landed in a similar situation in my game today. Here's a shot of the commuters. It's a nice mix of workers and shoppers which have founded a bumper-to-bumper parking lot outside my city. 9pm? That's not a rush hour, it's a way of life.
Everyone is turning right at the first intersection. I tried various things to solve it. Reducing the number of commuters. Adding a commuter train. Adding 48 commuter buses (at ~5000 simolean monthly cost). Nothing stuck, so I removed those buses and made the roads "worse". Here's a shot of the solution, along with a nice long column of flowing traffic. It's 8 o'clock and I don't know where the traffic went.
The fix addressed two issues.
Cars were turning right at that first intersection and immediately getting hit with another stoplight. Throughput was limited by the synchronization of those stoplights. In my fix, there are a few 2-way intersections after that right turn. 2-way intersections (and conversion intersections) have no stop mechanism: cars just flow through. That driver may turn right, but it will be a long time before he hits another stopping mechanism.
But that's not enough. By itself this would just move the problem to the end of that long street. I moved the right turn forward, and made cars have to drive back to reach places near the entrance. Cars also would enjoy a shorter trip to places in the back of the city if they just would go straight through that first intersection. This had the affect of dividing the traffic. In that first intersection, get 3/4 of the traffic to go straight (using three lanes!) and 1/4 to turn (using one lane).
Breaking the grid this way made the drivers do what I want, even though they could have done it themselves. Now, they have a longer commute, but less time spend parking during it.
Best Answer
The calculation you're asking for actually works the other way around in SimCity, the number of agents is taken and then run through a function to return a 'fudged' population figure.
The function in game that returns the population is as follows;
This works out as follows;
a
is less than/equal to 500, returna
a
is greater than 501 but less than 40845, return(a-500)^1.2 + 500
a
is greater than 40845, return8.25 * a
Here is a graph of how the actual population relates to the displayed population;
To work out the number of agents that makes up your displayed population, you would use one the following formula (courtesy of OrigamiRobot@The Bridge), depending on the size of your population;
if
population
is:(population - 500)^(5/6) + 500 = a
population/8.25
This would return the number of actual agents present for your current population.