Headlines from today's edition of the

*Sim City News*:

**PH Finally Convicted in the Case of Nate's City Abandonment**

All SC4 Networks Discovered to Have Infinite Capacity

I'd like to discuss the second point first, as it lays the groundwork for the first point.

In RL, the capacity of a network is generally defined as the number of vehicles that can travel on the network without causing a noticeable delay in travel times. In practice, this means that a in a network at full capacity in RL, vehicles are generally traveling slightly below the speed limit.

In SC4, there is no speed limit as such; there is simply a network speed at which all vehicles travel. Also, unlike RL, all vehicles in SC4 are single-passenger.

In RL, as a network carries more and more vehicles beyond its capacity, traffic slows down. There is effectively a lower limit for network speeds, after which people will simply find other routes, or those on the network will leave it. For highways, as an example, this speed is about 5% of the speed limit. If no other routes are available, traffic may come to a complete halt, and network capacity temporarily drops to zero.

Things work very differently in SC4. The Congestion vs. Speed Curve (which as Alex pointed out should be more appropriately named the Traffic Volume vs. Speed Curve) slows down traffic as traffic volume increases, simulating to some extent the congestion process that happens in RL. But unlike RL, there is a lower limit on the speed of a congested network, and that limit is 30% of the network's nominal speed. As the speed of a network drops, the pathfinder will automatically try to find a faster route for the Sims, and the efficiency with which it does so is governed by the value of the pathfinding heuristic (PH). But sometimes there is no faster route. In that case, more and more Sims may be added to the existing route. Once the network speed drops to 30% of the nominal speed, adding more Sims doesn't slow down traffic any further, because it's already going at the slowest possible speed for that network. So the pathfinder can keep adding Sims to that network indefinitely, and the speed will not drop any further. (One reason this doesn't work in RL is that unlike SC4, in RL, vehicles take up physical space.) This is how networks actually have infinite capacity in SC4. This applies to all networks and all traffic simulators.

The infinite capacity of SC4 networks also explains why Simulator Z Classic (which has the capacity levels of the original Maxis simulator) can be used on a city of any size without causing abandonment due to commute time. Other problems may result from extreme congestion, but the networks will carry as many Sims as they're asked to.

There is one other important piece of information here before we look at Nate's city. Until recently, it had been generally believed (including by me) that the Commute Trip Max Time property was the maximum time that a round-trip could take, measured in minutes. However, in

this post, Lenny showed that this property actually sets a limit on the

*one-way* maximum commute time. In other words, Sims can commute twice as far as we thought they could.

This result was quite surprising to me, and you may have noticed that I have been using half of the Commute Trip Max Time value until now in this thread to describe the one-way commute time. So I constructed a very simple experiment, described in

this post, to test Lenny's results. I got the same result that he did. Furthermore, Lenny discovered that Chris (CLR1S4D) had performed experiments himself to answer this very question, and also found that this property measured the one-way commute time limit in minutes. So we have three different sets of experiments, all independently constructed and performed, coming to the exact same conclusion. I think that we can take this conclusion as fact from now on.

Now we're ready to look at Nate's city. You can find a description of his experiences

here and

here, but I'll include all the relevant information in this post so that looking at the originals is optional.

Nate started on a medium tile with a healthy city of two million Sims. He switched to a newer traffic simulator to test it out, and twenty years later, his population had dropped 60%, to about 800,000. Although this city started out with about a population almost identical to that of my Near South Side city that I've used in numerous examples, the devastation in Nate's city was far worse. As you may recall, the population actually

*increased* slightly in the Near South Side when the PH was raised, as the effects of downgrading (resulting in more Sims per building) were far greater than the results of abandonment. In Nate's city, though, abandonment overwhelms everything. The only way a traffic simulator can cause that to happen is abandonment due to commute time, and this part has never been disputed. However, there are three ways that the traffic simulator can cause abandonment due to commute time:

- The traffic simulator is unable to find suitable jobs for the Sims.
- The traffic simulator is able to find suitable jobs for the Sims, but to reach them would exceed the Commute Trip Max Time.
- The traffic simulator is able to find suitable jobs for the Sims and they can theoretically reach them within the Commute Trip Max Time, but the pathfinding heuristic is set too high, and the pathfinder can't find a suitable route.

We know that the first possibility is not the problem, since Nate's Sims had no trouble finding jobs with his previous traffic simulator. It has been generally assumed until now that the second possibility accounted for the problem, and that the lower commute time limit of the new simulator, combined with the slower travel through congested areas due to lower network capacities, prevented the Sims from reaching suitable jobs within Commute Trip Max Time. However, given the information derived in the first part of this post, it is now possible to disprove this, and show that all the abandonment was caused by the third possibility - a pathfinding heuristic that was too high for that city. In fact, given the information derived above, surprisingly little information about the city is needed to show this. We don't need to know the capacities of the networks involved, we don't need to know how much congestion there was, and we don't even need to look at the mass transit networks. All we need is a basic map of the city, the speed limits of the streets and roads, and the value of Commute Trip Max Time. From the following Traffic Volume Data view, and other pictures in the original thread, we can derive a basic map of the city roads:

The dark blue lines are roads and avenues, while the lighter lines are streets. The speed on the streets is 40 kph, while on the roads and avenues it is 60 kph. The Commute Trip Max Time is 17 minutes. This differs from the previous simulator used in this city in that the Commute Trip Max Time there was 60 minutes, and network capacities were between 50% and 100% higher. So it's easy to see why the lower Commute Trip Max Time and network capacities were suspected as the causes of abandonment. But it's also easy to prove that they're not.

Given a speed of 60 kph for roads and avenues, a car can cover 62.5 tiles in one minute. That means that the maximum range of a one-way commute is 17 times that, or 1062 tiles. For the sake of argument, let's assume that all streets and roads are at maximum congestion. (It can be shown that they weren't, but it's unnecessary to do so for this example.) That means that a car's actual range would be 30% of 1062, or 318 tiles.

*This is regardless of what the road and avenue capacities are.* This city exists on a medium-sized tile, which is 128 tiles in length. This means that the

*maximum* length of any trip is 255 tiles, and the vast majority of trips must be shorter than that. So any trip that uses only roads and avenues has more than enough time to be completed, even at maximum congestion, since 318 tiles can be covered. When you consider that some trips must use streets, you have to take into account that the Sims can cover 213 street tiles by car in 17 minutes - less than the longest possible trip. But with perfect pathfinding, which always finds the fastest path, Sims would use streets only when necessary, and use roads or avenues for the rest of the trip. For such mixed cases, as long as the street portion is less than half of maximum possible trip, or about 128 tiles, the trip can always be completed, even with maximum congestion. And looking at the map above, it should be obvious that for a path between any two points on the map, only a very small fraction of that number of street tiles is ever necessary in any trip; the fastest trip always uses roads or avenues whenever doing so shortens the trip time.

So given the properties of the traffic simulator involved, the Commute Trip Max Time is not a limiting factor - trips by car can always be completed within that time to any square on the map. And we didn't even have to consider the availability of bus or subway routes, which are present. Therefore, we can eliminate the second of the three possible causes of abandonment for this city. Since we already eliminated the first possible cause, that leaves us with the third possibility as the only explanation for the abandonment seen in this city. The pathfinding heuristic used in the new simulator was .009, while perfect pathfinding uses a value of .003. From the facts present, there can be no doubt that it was the higher value of the pathfinding heuristic, and that alone, that was the cause of all the abandonment in the city.

The point of all of this is not merely to see what happened in one city long ago. Instead, it's to demonstrate even more clearly than any other example to date the importance of the pathfinding heuristic. While a higher PH caused some abandonment and a fair amount of downgrading in the Near South Side, the overall population figures were not affected adversely. In contrast, the population here declined by 60%. For reasons such as this, I have gradually come to the conclusion that the PH is the single most important parameter in the traffic simulator.

This is not a new conclusion. Recent research has found that the first modified traffic simulator was created by the7trumpets even before the Rush Hour pack was released, and was essentially what we now call Simulator E Standard. This simulator is identical to the original Maxis simulator with one exception: The PH has been lowered from the original Maxis value of .09 to the perfect pathfinding value of .003. So I have merely rediscovered what was known more than six years ago. I would simply like to request that simulator builders consider this and other examples when deciding which values to use for their simulator.