Samuel Griesemer
samgriesemer@usc.edu
University of Southern California
Jared Hwang
jaredhwa@usc.edu
University of Southern California
The way cities are structured and designed can have a massive impact on everything ranging from human health, to climate change, to societal equity. Understanding the relationship between a city's features to these qualities is paramount to designing cities according to our goals as a society. Simulation-based inference is a method in which a simulator is described by a joint distribution over some output of a simulation and some latent variables, conditioned on some input. We thereby can attempt to directly learn the relationship between the output and the input parameters. We apply this technique to A/B Street, a traffic simulation tool, by investigating the impact of one intersection's traffic light timing on the average trip time in the wider area. We find that, when applied to simulations run in the Montlake area of Seattle, that there is a meaningful relationship between the traffic stage timing and the average trip time in the area. Namely, shortening or lengthening traffic stage times corresponds with a higher probability of shorter or longer trip times respectively. We hope that these preliminary results show that for the urban planning field, simulation inference is a powerful tool that is applicable in many cases.
City and infrastructure design is only becoming more crucial as we as a society become more cognizant of out impact on climate change, public health, and racial and socio-economic equity. It is widely understood that the structural design of our cities have a marked impact on our wellbeing both individually and collectively, so it is therefore in our best interest to design and propose policy that actively strives towards "better" cities.
However, a major impedance of this goal is the number of conflating factors and differing goals (politically and technically) when considering optimal design. Each can have innumerable differences from another: their geographic topology, climate, socio-economic and race composition, historical features, and so on.
As a result, a deeper understanding of a city's design on its residents, resource usage, and so on, is extremely desirable to motivate better policy and design recommendations, but correspondingly can be difficult to pin down.
To approach this problem, we attempt to apply an inference technique developed by Papamakarios and Murray [1, 2] on A/B Street, a road/city planning simulation [3], as a proof-of-concept application of simulation inference on city planning simulations to broadly learn the impacts of traffic and road design on the efficiency and resource use of a city.
Simulators are formally treated as probabilistic programs that take a vector of parameters θ as input, internally sample a series of latent states zi ~ pi (zi | θ, z < i ), and produce a data vector x ~ p(x | θ, z) as output. As such, simulators can be described by the joint distribution p(x, z | θ) over the output x and latent variables z. This distribution captures the relative likelihoods of (x,z) pairs under fixed parameter values, embracing the relationship between θ and z explicitly. Note that this can be written as the product
p(x, z | θ) = p(x | z, θ) p(z | θ)
This expansion involves the distributions seen in the two-step sampling procedure of the simulator definition: p(z | θ) to produce latent variables from the input parameters, and p(x | z, θ) to yield the final output vector given the inputs and latents. The likelihood function p(x | θ) implicitly defined by the simulator can then be seen as a marginalization of this form with respect to the latent variables:
p(x|θ) = ∫ p(x,z|θ)dz
Note that this integral depends on all possible trajectories through the latent space. That is, for a given value of x, evaluating the likelihood at that value depends on all possible combinations of internal simulator states that could possibly lead to x as the simulator's output. For sufficiently complex latent spaces, this integral becomes intractable. Unfortunately, this is the case in most real-world settings, and where likelihood-free inference is employed.
Simulation-based inference diagram.
{width=50%} Sequential neural posterior estimation
diagram
A/B Street is a city and traffic simulator developed by Dustin Carlino, built using the Open Street Map (OSM) format [4]. It is widely flexible and supports importing any map through OSM, changing lane type (driving, bus, bike) and speed limits, traffic light timings, among others. It also has built in visualization, data aggregation, and an API through which we can control the simulation headlessly via Python code. We chose A/B Street due to these factors, contributing to its ease of using it as a black box for the simulation inference.
Traffic Simulation run in A/B Street
Editing roads in the A/B Street GUI
Understanding simulation output
To run the code, download the A/B street repository (abstreet.org) and its requirements and follow the instructions there to start a server headlessly with the desired map. Then, run the Python code provided in this repository.
Alternatively, use the provided Singularity environment definition file to build a container with the required packages, and simply run the headless Rust program in the A/B Street repository to start the server, then run the Python code here. This is particularly useful for running the inference on a high-performance cluster for faster results, as we did using the University of Southern California Advanced Reserach Computing Cluster (CARC). NOTE: currently the Singularity container does not quite work out of the box, due to some permissions errors that require extra work before and after building the container in order to have all the requisite software. This is a work in progress.
As discussed above, there are some traits of road structure that are already understood: for example, increasing number of lanes doesn't necessarily decrease trip times. Using simulation inference, we hope to gain deeper insight on the design of intersections and intra-city roads on overall travel time and throughput, which may be counter-intuitive to what we may expect.
As mentioned previously, our experiments are performed on the Montlake region within Seattle. We use the A/B Street traffic simulator to gather observational data on typical resident commutes within the area. The simulator explicitly models high-fidelity interactions between simulated individuals; there are thousands of unique residents with predetermined travel plans, and they must navigate the dynamic state of the road system as dictated by all other individuals. Our overarching goal is to better understand the dynamics of traffic signal staging and how it impacts the average commute time for residents. We focus explicitly on intersection #373 (as labeled by A/B street), pictured below:
(Intersection #373 and its stages, as shown in the A/B Street GUI)
A/B Street admits a certain level of flexibility when it comes to modeling the behavior of traffic signal stages. We focus on variable staging, where each stage's dynamics are dictated by three parameters:
- θ1: the minimum delay (in seconds) at a stage. This is a fixed amount of time that certain lanes in the intersection will have the right to drive through (i.e. a green light).
- θ2: intervallic extensiom (in seconds) to minimum delay if vehicles are waiting at the signal. If there are no waiting vehicles, the stage ends.
- θ3: maximum total extension (in seconds) to minimum delay. Places a limit on the number of additional checks for waiting vehicles that can be made in a given stage.
We then formulate a uniform prior over these parameters in accordance with our initial beliefs about reasonable values for effective throughput. Samples are drawn from this prior to parametrize the traffic simulator, and we collect the resulting average travel duration across the entire Montlake region. Note: each of the four stages (as shown in the above diagram) have shared parameters for the selected intersection.
After collecting the simulated data, we train a masked autoregressive flow to directly approximate the posterior p(θ | x). Here x∈ℝ, the average travel time (in seconds) of all trips taken in the region within a 24 hour period. Note that each simulation run has a deterministic set of trips to be taken by simulated individuals, allowing us to directly compare travel times under different traffic signal behaviors. Drawing samples from the posterior conditioned on travel times observed prior to any change (denoted xo) yields the following plot:
(Posterior over the three traffic signal parameters, conditioned on baseline travel duration; p(θ | xo))
The "dim 1", "dim 2", and "dim 3" labels in this plot (and similar plots below) correspond to parameter values θ1, θ2, and θ3, respectively. This plot shows signal staging parameter values that appear likely to yield similar travel times to our baseline data (fixed stage timing at 30 seconds per stage) under the simulator's implicit model. We observe parameter values in line with this baseline, namely θ1 centered around 30-35 seconds.
We also condition the posterior on smaller average travel times to reason about possible parameter values that lend themselves to more efficient traffic flow. Conditioning on 4 seconds below the baseline:
(Posterior over the three traffic signal parameters, conditioned on 4 seconds below baseline travel duration; p(θ | xo-4s))
Here we see a noticeable decrease in the mean of θ1, suggesting the shorter stages can yield improved traffic throughput. Conditioning on even small traffic durations (8 seconds below baseline), we see this trend continues:
(Posterior over the three traffic signal parameters, conditioned on 8 seconds below baseline travel duration; p(θ | xo-8s))
Notice in this setting we also observe more probability mass centered around the mode of marginal distributions for parameters θ2 and θ3. This suggests that particular combinations of interval extension and maximum delay extension become more impactful under tighter timing regimes. We also attempt to condition on travel times shorter than any observed average duration (minimum was ~8.5 seconds below baseline):
(Posterior over the three traffic signal parameters, conditioned on 10 seconds below baseline travel duration; p(θ | xo-10s))
This plot captures our model's generalized understanding of traffic dynamics just beyond the training data; there are no empirical data in this setting for the model to pull from. Here we see even shorter minimum stage delays, as well as shorter maximum extension times. This aligns with our original intuition that shorter stage delays likely lead to greater throughput, but it's clear the intervallic stage delays and extension times still play an important role (i.e. they don't dissolve despite their absence being supported under the prior).
As stated above, we use A/B Street and traffic light staging as a preliminary proof-of-concept on the application of simulation inference on city design. However, there are many more ways we can utilize this technique beyond just roads.
A burgeoning field is that of understanding city design on the emissions produced by a city, and understanding how the block and road structure impacts the city's contribution to climate change. Gim performed a global study of land-use on a various city's emissions, for example, congestion leading to longer trip times leading to greater emissions [5]. By using a model and performing inference on it, we can potentially understand how to more granularly change current cities or motivate future cities to reduce resource use and CO2 emissions.
Relatedly is the concept of urban heat islands--when the city itself is warmer than the surrounding areas, resulting in greater air-pollution and heat-related illnesses, among others. Understanding how building material and block structure impacts this could be of massive benefit. Gober et al. explored this for Phoenix, Arizona, by modeling three different scenarios based on gathered data [6]. We could potentially use simulation inference on their model to more fundamentally understand the land-use and heat island relationship.
Another area of interest is how policy changes can influence land-use in certain areas, thereby influencing everything about the city itself--from emissions to all the other qualities discussed above. Landis investigated this using their California Urban Futures Model, where they simulated the results of three different scenarios: "business as usual", "Maximum Environmental Protection", and "Compact Cities" [7]. By applying inference on the model, perhaps we can obtain more optimal, fine grained policy recommendations than just three scenarios would illuminate.
We've discussed several potential paths and application for this research moving forward, however, there are many more that can and should be investigated. Urban planning as a field is growing rapidly, and in turn, applications of computational techniques in the urban planning space are similarly growing. With the results we have presented here, we hope to have shown that the application of computational techniques developed for physics, math, and so on could have countless uses in urban planning, and serve to benefit society as a whole.
[1] G. Papamakarios en I. Murray, “Fast ε-free inference of simulation models with Bayesian conditional density estimation”, arXiv [stat.ML], 20-Mei-2016.
[2] K. Cranmer, J. Brehmer, and G. Louppe, “The frontier of simulation-based inference,” Proceedings of the National Academy of Sciences, vol. 117, no. 48, pp. 30055–30062, 2020.
[3] D. Carlino, “A/B Street,” June 2018. Accessed on: Dec. 12, 2021. [Online] Available: https://abstreet.org
[4] M. Haklay and P. Weber, “Openstreetmap: User-generated street maps,” IEEE Pervasive Computing, vol. 7, no. 4, pp. 12–18, 2008.
[5] T.-H. T. Gim, “Analyzing the city-level effects of land use on travel time and co2 emissions: a global mediation study of travel time,” International Journal of Sustainable Transportation, vol. 0, no. 0, pp. 1–18, 2021.
[6] P. Gober, A. Brazel, R. Quay, S. Myint, S. Grossman-Clarke, A. Miller, and S. Rossi, “Using watered landscapes to manipulate urban heat island effects: How much water will it take to cool phoenix?,” Journal of the American Planning Association, vol. 76, no. 1, pp. 109–121, 2009.
[7] J. D. Landis, “Imagining land use futures: Applying the california urban futures model,” Journal of the American Planning Association, vol. 61, no. 4, pp. 438–457, 1995.