experilous Design: Traffic Simulation Tradeoffs

[Andy Gainey 6]

Continuing on with I'd like to discuss traffic simulation this time.  I've spent the past couple weeks working on a prototype simulator to get a feel for what is technically achievable.  (I'll have some preliminary results posted later this week; you can read about of my few early bugs on my blog.)  But more important than technical feasibility would be practical value:  How much (and what kind of) detail would actually maximize entertainment, in the face of certain tradeoffs?

 

I would classify the tradeoffs into three broad categories:  Performance, Interface, and Mechanics.  On the performance side, naturally the more detailed a simulation gets, the slower it will run when attempting to run as fast as possible.  For interface, it's sort of a tradeoff between ease-of-use and and creative power.  And for mechanics, it's largely a matter of feedback from the game to the player:  Can a player understand what's happening in the simulation, why it is working well or poorly, and what one could try in order to improve traffic problems?

 

Running at max speed, how long would you be willing to wait for the simulation to process one in-game year?  (What counts as an in-game year can be fuzzy, but you can loosely base it on other city builders you've played.)  Would you be more forgiving if it were a large city?  For example, what if a city of 100,000 people could simulate a year in 1 minute, but a city of 10 million, while playable, would take nearly 2 hours?  Or would you prefer the SimCity 4 style where you could focus on just one segment of the city at a time, and thus get more predictable performance regardless of how large the overall city were?  The tradeoff would be that the simulation for most areas of the city would be frozen or vastly simplified during that time.

 

Regarding interface, I'm not sure I have any specific questions at this early stage.  The ideal is obviously to achieve both ease-of-use and creative power simultaneously.  I am optimistic that with effort, and with a lot of feedback and ideas from players, the ideal can be accomplished.  But for now I think that just having an idea of priorities would be helpful to me.  Judging from past discussions and player activity, it seems clear that a capable interface for designing highway interchanges, rail yards, bus/subway routes, and similar complex structures would be very welcome.  What type of transit-related structures would you most like to see have a well designed interface?

 

Finally, I have a concern that if the game mechanics contain too much complexity, even if the computer is able to process all the details, and even if the interface allows easy creation of complex transit networks, the result will be an incomprehensible mess of data, and an overwhelming array of options available to the player.  But I also suspect that different types of players will judge this point of excess quite differently:  Aesthetic builders would love to have a myriad of options.  Functional tinkerers on the other hand would probably do better with just enough options to provide proper control over the behavior of the simulation.  So from this suggested distinction, which transit network features would you like to have mostly for aesthetic purposes, and which are desired primarily for behavioral control?  Which ones are important for both reasons?  (For example, I suspect highway interchanges would be.)  Other features to consider might include rail yards, lane count, intersection styles, road surface styles, specialized lane use (bus lanes, no trucks, et cetera), pedestrian routes, and I'm sure many more.

[Tysons4 68]

The traffic simulator has always been the hardest part for city simulators, but i have a few ideas on how it should be... my dream have you

 

lets say you have 4 types of automobile used networks street, road, and highway (one way roads) and specials

 

street would allow cars to park on the side. roads would be wider and allow more traffic. and highways would be high volume in one direction, the specials would allow on and off ramps, not creating intersections but allow traffic to merge onto a network

 

I always liked how in simcity 3000 when your dragged 2 roads next to each other they would create an avenue, but i always wanted to take it a step further. dragging a street next to a road would allow parking on the side of the road you placed it against. dragging 2 roads next to each other would create an avenue (like simcity 3000)3 roads, an even wider road, 4 roads and streets on either side and an extra wide avenue with parking ect.  highways would have to be built one side and then the other and could go under or over any network, or use them as one way roads in a cities core. and the special road network would be there to create slip lanes and on/off ramps.

 

as for the simulator side, i think simcity 4 got it right. have it display roughly how much traffic is using that corridor, and when you route query show how much traffic and where it's headed.

 

as for other forms of transport:

pedestrian only networks, footpaths and crosswalks, footbridges and what have you. 

rail: above, below ground at various levels and elevated at various levels with 2 different types for the sims and their freight

 

keep the network interface simple but make the mechanics complex so we can have fun seeing what develops when we drag a road on either side of a street with a rail next to it and a highway going overhead with special lanes connecting it together.

 

ill keep my ideas simple for now, but really want to see you create something amazing for this community that is dying for an honest city simulator... i wouldn't even care if a city ran in real time and projects took as long as they do in real life as long as we had a planning mode to get all our ideas out and then let the sims get to work when i decided to let the simulation run

[Andy Gainey 6]

Thanks for the thorough reply!

 

Modularity sounds like a major component of your interests.  Mine too.  Your approach to breaking down the different categories of modular pieces is very interesting.  For example, the way streets add street-side parking to whatever they're attached to is fascinating; I would have never thought of that possibility.

 

Oh man I love the traffic query tool of SimCity 4.  If I can't at least get that level of information out of my system, I'll be sorely disappointed. 

 

I would like to have at least enough detail in the simulation to more reasonably fake the real-time display of cars whenever the player slows the game down to near-real-time speeds.  The cars in SimCity 4 provided an at-a-glance indication of congestion, but the fading into/out of existence really bothered me.  Sure, it was just a surface detail that didn't really impact the simulation, but we each have our psychological weaknesses. 

[Ocram's Razr 964]

I think that if you go with a grid, make the grid small (like 5x5 meters) and let paths (roads, rail, etc) be able to go at any angle as long as their start and end points are exactly on the 5 meter grid.

--Ocram

[Cool_Z 1,547]

The way SC4 handles the simulation is the way to go I think. There's no need to reproduce the flow of vehicles itself, just use it for the simulation and represent it on screen in a realistic way.

 

Sure the appearing/disappearing cars in SC4 can look a bit weird, but there is certainly a way to have more persistent automata following some paths around the city, building denser traffic where is needed but without trying to simulate every damn car in town

 

It's not truly part of the traffic simulation mechanism, but as was mentioned, seeing vehicles park would be awesome !

[APSMS 1,893]

As regards Cool_Z's comment, I would say that this enters the realm of agent vs. Statistical simulation, and while agent based is cool, it has modern hardware limitations that I think are unbefitting a city simulator; of course, an agent representation of statistical data (i.e. for persistent cars and route trips, etc.) would be very cool, and would perhaps have the added benefit (unlike the glassbox model) of making "people" psedo-persistent, rather than disappear everytime they leave the view.

 

As for network options, I think the current NAM is a good indicator of networks that are in many ways both functional and aesthetic. Defining bus routes for people like in Cities XL would be preferred, though I doubt doing the same for rail networks, where the nature of the network causes routes to be largely self-governed, would be as necessary. I think mapping train journeys is something best left to Cities in Motion (1 or 2).

 

So, for options, I would say:

Rail, both ground and elevated

Subway, and corresponding surface light rail/el-rail

Highways/freeways, with modular highway interchanges, if possible, or perhaps for a future release/update/expansion (even though I hate expansions) RHW, as frustrating as it is, is one of my favorite components of the NAM, though it may be biased since I'm from CA.

A lane-based approach to road networks sounds like a neat idea, esp. for more options in transit networks, though implementation would be tricky, especially to keep it to a manageable and fun level for the less dedicated players. You don't want to go bankrupt because the casual player can't figure out your game (Maxis didn't have much luck on that front).

Pedestrian Only city-centers would be really cool as well. Turning lanes as well should be a must, if only for the sake of being an easy way to add capacity to impacted non-turn lane intersections (which could be like a base option, and have the turning lanes be upgrades that don't really take up extra room).

 

If you go with a grid-based system, a very small grid would, I think, suit a number of options like curvy roads and terrain hugging networks. SC4's grid is way to large to do anything more than approximate reality, no matter how hard the NAM team tries.

 

And Finally, whether you choose a spline-based approach (which, if you do, please don't make it the backbone of the whole deal; creating stuff in the middle of nowhere is still a strong suit of SimCity 4 and a major weakness of SC2013), or go for a grid-based system for networks and zoning, make sure that the networks are fully 3d, and not merely camera tricks to fool the user (which is what SC4 has, and what, as a first, SC2013 got right).

 

         Potentially boat traffic, though this is optional to me, and generally is very little used in most demonstrations of Sim City 4 on this site. Much of the boat traffic I see is eye-candy only.

 

This sounds like a very cool project, and I'm glad to see some seriousness on this level. Will be following this project closely.

[Cool_Z 1,547]

As regards Cool_Z's comment, I would say that this enters the realm of agent vs. Statistical simulation, and while agent based is cool, it has modern hardware limitations that I think are unbefitting a city simulator; of course, an agent representation of statistical data (i.e. for persistent cars and route trips, etc.) would be very cool, and would perhaps have the added benefit (unlike the glassbox model) of making "people" psedo-persistent, rather than disappear everytime they leave the view.

 

Well... that's the way to go maybe...

 

100% fully persistent automata but only for the part of the city that the player sees, drawn accordingly to the city's statistical traffic calculations. Best of both worlds

[MandelSoft 2,775]

Hello, a Transport & Planning university student here. May I have a few semi-professional words on traffic modeling here?

Right, first off is of course the trade off between computation time and performance. This completely depends on what simulation model choices you make. I'd recommend to take a look at aggregated models instead of agent-based models. Aggregated models are often less complex than agent based models and therefore take less computation time while still being a good approximation.

Furthermore, you should also know how a transport model works. One of the widely used approaches is the so called 4-step model. Below is a scheme that explains in brief how it works:

Now I could write pages about what models there are, but Wikipedia can explain better what methods there are. I can only give you some recommendations:

• Trip Generation. I'd recommend a simple linear regression method here to save computation time.
• Trip Distribution. I'd recommend the Gravity Model here.
• Mode Choice. I'd recommend a Logit Model here. Frankly, it's not on the other page.
• Assignment. I'd either go for a Waldrop Equilibrium/DUE assingment, or (maybe more logical) or iterative assignment (add one or multiple vehicles on the network and calculate the effect on the network to get the new delays and start over again for the next set of vehicles). The latter one is probably the method SimCity 4 is using and it's more logical to have that one in a dynamic simulation.

One thing that's annoying in SimCity 4 is the so-called Eternal Commuter bug. This bug is caused by a lack of simulation in the region. However, if we can simulate the rest of the region while playing in just one city tile by taking the rest of the region into account when it comes to trip distribution, it may be possible that sims will travel multiple city tiles to reach their work, making commute distances a bit more realistic. Of course, opportunities closer to home are more attractive, but it makes the destination choice more robust and flexible. However, you do need to keep track of which jobs are occupied and which jobs are free, so two sims cannot claim the same job...

Anyway, these were my thoughts. I hope this will help you out

Best,

Maarten

[Andy Gainey 6]

The way SC4 handles the simulation is the way to go I think. There's no need to reproduce the flow of vehicles itself, just use it for the simulation and represent it on screen in a realistic way.

 

Sure the appearing/disappearing cars in SC4 can look a bit weird, but there is certainly a way to have more persistent automata following some paths around the city, building denser traffic where is needed but without trying to simulate every damn car in town

 

As regards Cool_Z's comment, I would say that this enters the realm of agent vs. Statistical simulation, and while agent based is cool, it has modern hardware limitations that I think are unbefitting a city simulator; of course, an agent representation of statistical data (i.e. for persistent cars and route trips, etc.) would be very cool, and would perhaps have the added benefit (unlike the glassbox model) of making "people" psedo-persistent, rather than disappear everytime they leave the view.

 

Yeah, at this point I am definitely considering ways to create a statistical simulation that can be conveniently and believably translated into a visual representation when needed.  I remember when I learned how SimCity 2000 chose the density of its marching ants, based on proximity to traffic generators.  Drove me crazy seeing a long highway with heavy traffic near the origin and destination, but nothing in between.  That's a system I emphatically do not want to resort to. 

 

 

 

A lane-based approach to road networks sounds like a neat idea, esp. for more options in transit networks, though implementation would be tricky, especially to keep it to a manageable and fun level for the less dedicated players. You don't want to go bankrupt because the casual player can't figure out your game (Maxis didn't have much luck on that front).

 

While I do want to make the game relatively easy to play for more casual players, I do have the luxury of prioritizing complexity more than Maxis, as I don't have to sell something like 2 million units just to consider the project a financial success.  Heck, 10,000 purchases in a year would be a definite success for me; 100,000 would be wildly successful.  So I think my approach will be to ensure early on that the core of the simulation supports a relatively high level of complexity.  From there I can incrementally improve the interface and balance the game to be playable and enjoyable even when only utilizing just the simpler game features.

 

(As you might infer from this approach, my current plan is to pursue an alpha-funding approach, releasing the game for a cheap price as soon as it provides a sufficiently playable and fun experience, and then improving it from there.  Existing players would receive all updates for free, and the price for new players might increase over time with major updates until reaching whatever I might consider to be an appropriate full price.)

 

 

 

If you go with a grid-based system, a very small grid would, I think, suit a number of options like curvy roads and terrain hugging networks. SC4's grid is way to large to do anything more than approximate reality, no matter how hard the NAM team tries.

 

And Finally, whether you choose a spline-based approach (which, if you do, please don't make it the backbone of the whole deal; creating stuff in the middle of nowhere is still a strong suit of SimCity 4 and a major weakness of SC2013), or go for a grid-based system for networks and zoning, make sure that the networks are fully 3d, and not merely camera tricks to fool the user (which is what SC4 has, and what, as a first, SC2013 got right).

 

Indeed, even though the grid gets in the way of the numerous non-conforming parts of a city, it is super convenient for the majority transit network design.  (Or at least would be if it could handle straight diagonals better.)  I want to get away from the traditional fixed grid altogether, to properly enable the freedom that a gridless system can provide.  But the convenience of the grid must still somehow be maintained.

 

I had an idea a while back about letting the player configure virtual grids that could be used for snapping roads to them.  After watching some Let's Plays of SimCity 2013, I realized that the guideline system moves in that direction, but I think it's too simplistic to really capture the balance of power and convenience provided by SimCity 4.  I might talk about that more in the future, but the core of the idea is that virtual grids will work like guidelines, but will be configurable (angles, curvature, distance between each cell, blending style with nearby virtual grids, et cetera), can be present even in the absence of existing roads (or when overlapping non-conforming roads), and can persist for future design work that should properly match the flow and alignment of the existing city.

 

 

 

Hello, a Transport & Planning university student here. May I have a few semi-professional words on traffic modeling here?

Right, first off is of course the trade off between computation time and performance. This completely depends on what simulation model choices you make. I'd recommend to take a look at aggregated models instead of agent-based models. Aggregated models are often less complex than agent based models and therefore take less computation time while still being a good approximation.

Furthermore, you should also know how a transport model works. One of the widely used approaches is the so called 4-step model. Below is a scheme that explains in brief how it works:  ...

 

Holy awesome information, thanks!

 

So far I've been focused almost purely on route assignment, working under the assumption that I could come up with simplistic but sufficient models for the other three steps.  (Not that I was aware of this 4-step model before now, but I can see how a lot of my thoughts fit very naturally into this model.)  My assumptions may be off, however.  I'll be studying this stuff in more depth!

 

I'll admit that I'd been wanting to do an agent-based system, because I really want to have the simulation generate emergent behavior, rather than fake it based on patterns we've already observed in the real world.  But I'm probably overlooking a large selection of statistical and/or aggregate models that still have plenty of internal feedback and can generate the type of emergent behavior I'm looking for.  I also need to keep in mind this advice originating from Sid Meier:  "The player should have the fun, not the designer or the computer."  You all can keep me in check. 

[MatlockMan 370]

How about a turn-based city sim? ^{don't kill me}

[Andy Gainey 6]

How about a turn-based city sim? ^{don't kill me}

 

Haha, don't worry; no death threats from me.  I love turn based.

 

But I don't believe I've ever really considered doing a city sim using a turn based model before.  On a technical level, many of the options I'm considering would work out to be more or less turn-based (the traffic simulation among them), but I still always envisioned typical real-time style of presentation.  Making it truly turn-based would have some interesting implications.  Off the top of my head, I imagine that the variety of available player actions and the scale of a single turn would need to be balanced so as to reduce the number of turns where the player does nothing but hit [End Turn] again.  Otherwise, the game would frequently feel pointlessly tedious.

 

Then again, even if I stick with a real-time presentation, thinking about it from a turn-based perspective could help inspire some solutions to the already existing problem of waiting for things to happen.  If the game runs fast enough, sure, you can just run it at cheetah speed for a minute or so and then get back to spending money doing stuff, but it still feels a bit like you just wasted all that time in your city's in-game history.  Finding meaningful ways for a player to always be doing something relevant and engaging is on my list of design considerations, and with the turn-based perspective, I think you've given me another tool in my toolbox!

[Darth Apple 54]

Honestly a lot of people complain about Cities XL/Simcity's whole issue with cars and pedestrians spawning and despawning. To me, visible traffic really just seems like an abstract concept to make the underlying traffic engine look more realistic. 

 

Of course I'm still entertained by the visual simulations, but as far as the visuals are concerned, I don't really care that much about the semantics to be honest. As long as it's not something like the notorious bug in Cities XL that caused all cars to stop at highway interchanges and jam up traffic, I think any model that is well planned will do fine for the most part. What I'm more concerned about is the underlying model for traffic congestion, etc... There needs to be a good (and realistic) pathfinding algorithm. It is important that the algorithm is not simply based on which route is the shortest, and not only based on time, but also on the overall desirability of a route. For example, I will gladly go a few minutes out of my way to take a better road rather than taking a very curvy, rural road that is in the middle of nowhere. A realistic traffic simulation in a city simulator would take similar considerations into account (within reason, of course. Computers still have processing power limitations too. )

 

I think Cities XL and the NAM-free Simcity were too far on each end of the spectrum, personally. Simcity's pathfinding engine (without the NAM or patches) only searched for the shortest possible route, whereas Cities XL searched for the fastest possible route, but sometimes the fastest route isn't the route that most drivers would have any desire whatsoever to take. A good balance that is also conscious of computer resources is the idea solution, in my opinion.  

 

Also, it would be really neat to see traffic that shows up for things other than just the commute. It'd be nice to add some light traffic for shopping, leisure, parties, etc... as well. Outside of that, how traffic spawns visually, how long a car stays on the road, to which degree visual congestion should be shown, etc... is rather secondary in my opinion. 

[MandelSoft 2,775]

Of course I'm still entertained by the visual simulations, but as far as the visuals are concerned, I don't really care that much about the semantics to be honest. As long as it's not something like the notorious bug in Cities XL that caused all cars to stop at highway interchanges and jam up traffic, I think any model that is well planned will do fine for the most part. What I'm more concerned about is the underlying model for traffic congestion, etc... There needs to be a good (and realistic) pathfinding algorithm.

The Four-step model deals with that with feedback loops. After the assignment, new resistances are calculated, which influences the rest of the steps. With the DUE assignment, but also with the incremental assignment, congestion will occur and traffic will act on this, since everyone wants to get the shortest route. Within the DUE, an equilibrium occurs when no-one can improve their travel time by switching routes. A similar thing will happen with incremental assignment, since it recalculates the resistances after a group of vehicles is assigned.

It is important that the algorithm is not simply based on which route is the shortest, and not only based on time, but also on the overall desirability of a route. For example, I will gladly go a few minutes out of my way to take a better road rather than taking a very curvy, rural road that is in the middle of nowhere. A realistic traffic simulation in a city simulator would take similar considerations into account (within reason, of course. Computers still have processing power limitations too. )

By fun coincidence I did some research on that very subject the last months with a group and we came to the conclusion that this effect is hardly significant over other effects and it's hard to isolate the effect...

[Andy Gainey 6]

Also, it would be really neat to see traffic that shows up for things other than just the commute. It'd be nice to add some light traffic for shopping, leisure, parties, etc... as well. Outside of that, how traffic spawns visually, how long a car stays on the road, to which degree visual congestion should be shown, etc... is rather secondary in my opinion. 

 

Very valuable feedback in general, thanks!  As for the specific of more types of traffic, I'm in agreement.  Freight in SimCity 4, for example, was nice, but not all freight leaves the city.  Businesses and industries are shipping stuff between locations all the time.  Certain commercial services are making house calls in residential areas.  School buses are everywhere.  Shopping is constantly happening.  (I was surprised when I discovered that commercial zones SimCity 4 do well only if people drive by them on their way to work.  Huh?)

 

In addition, I think it would be fascinating to have other events too, stuff that isn't just routine day-to-day traffic.  Weekend traffic is different from weekday traffic.  Holidays can have various effects on traffic patterns.  Seasonal patterns are often relevant.  One-off tourist events (Olympics, anyone?).  Heavy construction.  Snow storms, heavy rain, dense fog, or other "minor" disasters.  None of that is going to ruin a city necessarily, but how the traffic network is able to adapt to those various events can definitely affect citizens' opinion of the city and their quality of life.

 

The trick of course would be to enable the player to comprehend the affects of these various events.  But I think something as simple as providing a list of recent events and being able to limit any particular graph or map overlay to a specific event would be sufficient.  For example, if you look at the congestion map, it will by default show the average congestion over the last n simulated days.  If you want to just look at weekday congestion, that'd be an option.  Or you see that their was a snow storm recently; limit the congestion map to show what congestion was like on the day of the storm.  (Depending on randomness, it was most likely a weekday, but might've been a weekend, which would change how congestion was affected.)

 

My hope would be that this would give each city a strong sense of personality and history; each city could feel more unique.  Trying to experience the joys of creativity usually fails if you don't feel as though you can create something that is unique in some relevant way.

[MatlockMan 370]

 

How about a turn-based city sim? ^{don't kill me}

 

Haha, don't worry; no death threats from me.  I love turn based.

 

But I don't believe I've ever really considered doing a city sim using a turn based model before.  On a technical level, many of the options I'm considering would work out to be more or less turn-based (the traffic simulation among them), but I still always envisioned typical real-time style of presentation.  Making it truly turn-based would have some interesting implications.  Off the top of my head, I imagine that the variety of available player actions and the scale of a single turn would need to be balanced so as to reduce the number of turns where the player does nothing but hit [End Turn] again.  Otherwise, the game would frequently feel pointlessly tedious.

 

Then again, even if I stick with a real-time presentation, thinking about it from a turn-based perspective could help inspire some solutions to the already existing problem of waiting for things to happen.  If the game runs fast enough, sure, you can just run it at cheetah speed for a minute or so and then get back to spending money doing stuff, but it still feels a bit like you just wasted all that time in your city's in-game history.  Finding meaningful ways for a player to always be doing something relevant and engaging is on my list of design considerations, and with the turn-based perspective, I think you've given me another tool in my toolbox!

 

Yeah, the continual pressing of next turn in even Civilisation 5 does irritate me, so I don't know if turn based Simcity would even work. It's just an idea of how one could overcome the issue of processing - by continually pausing. Not sure if it would work, but its something to think about.

Very valuable feedback in general, thanks!  As for the specific of more types of traffic, I'm in agreement.  Freight in SimCity 4, for example, was nice, but not all freight leaves the city.  Businesses and industries are shipping stuff between locations all the time.  Certain commercial services are making house calls in residential areas.  School buses are everywhere.  Shopping is constantly happening.  (I was surprised when I discovered that commercial zones SimCity 4 do well only if people drive by them on their way to work.  Huh?)

Freight in Simcity 2013 I believe is sorta more realistic. Doesn't freight from industry ship to commercial within in the same city? (I haven't played enough to understand if Glassbox does actually simulate this far).

 

The trick of course would be to enable the player to comprehend the affects of these various events.  But I think something as simple as providing a list of recent events and being able to limit any particular graph or map overlay to a specific event would be sufficient.  For example, if you look at the congestion map, it will by default show the average congestion over the last n simulated days.  If you want to just look at weekday congestion, that'd be an option.  Or you see that their was a snow storm recently; limit the congestion map to show what congestion was like on the day of the storm.  (Depending on randomness, it was most likely a weekday, but might've been a weekend, which would change how congestion was affected.)

 

My hope would be that this would give each city a strong sense of personality and history; each city could feel more unique.  Trying to experience the joys of creativity usually fails if you don't feel as though you can create something that is unique in some relevant way.

Simcity 5 touched lightly on one-off traffic through the use of stadium and expo centres. They added tourism traffic to a city. However, one could very easily see no gigantic problems because they didn't add that much to the traffic.

 

However, if you went into events such as the Olympics (don't use the Olympics specifically, or the IOC's lawyers will find you and end you), that would add such tasks as building huge amounts of infrastructure that previously wasn't present. I'd make such events a kind of 'disaster' or surprise, where your city wins the Games unexpectedly and suddenly has a 7-10 year period to build the necessary infrastructure (venues for games, hotel capacity and methods of transport for getting into and around your city).

 

As for seasons, I'd love the idea of a harsh winter changing a variable in the capacity of the roads. In summer, roads are 100% efficient - in a warm winter, roads are 85% efficient, normal/average would be 70% efficient, harsh winters 50%. Simulating individual days and snow storm events would be very demanding and complex I'd imagine.