1. Introduction Our Approach Results Conclusions Appendix
Context-based Traffic Flow Parameter
Estimation:
A Case Study of Nairobi, Kenya
Daniel Emaasit1,2
1Research Intern
Mobility Team
IBM Research | Africa, Nairobi, Kenya
daniel.emaasit@ke.ibm.com
2PhD Student
Civil and Environmental Engineering Department
University of Nevada, Las Vegas, USA
emaasit@unlv.nevada.edu
August 25 2016
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2. Introduction Our Approach Results Conclusions Appendix
Introduction
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3. Introduction Our Approach Results Conclusions Appendix
Background (1/2)
Road traffic congestion in developing cities results in:
massive delay, unpredicted travel times, increased fuel
consumption, man-hour and monetary loss.
In Kenya, inefficient travel squanders economic productivity,
wastes fuel and produces unnecessary pollutants, which
results in:
the loss of US$ 250M (or 3% of GDP) every year1
Prolonged commute times frustrate Nairobi drivers (the
world’s 4th most painful commute2).
1
Kenya Ministry of Planning (2010).
2
IBM Commuter Pain Survey (2011).
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4. Introduction Our Approach Results Conclusions Appendix
Background (2/2)
(a) Traffic congestion. (b) Traffic disruptions.
(c) Dynamic usage. (d) Foreign delegates.
Figure 1: Typical traffic conditions in a developing city.
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5. Introduction Our Approach Results Conclusions Appendix
The Research Problem (1/3)
There’s no robust method that incorporates a wide range of
contextual factors local to Nairobi to estimate traffic flow
parameters.
1. Traffic incidents (crashes, . . . )
2. Pavement conditions (potholes, . . . )
3. Weather conditions (rainy, flooding . . . )
4. Socio-political events (riots, sports, . . . )
5. Land use information (commercial, residential, . . . )
Related Work: Other studies by Box & Waterson3, Fowe et
al.4, Kwon & Murphy5 do not take into account local
contexts.
3
Method for state estimation of a road network, 2013.
4
Dynamic location referencing segment aggregation, 2015.
5
Modeling freeway traffic with coupled HMMs, 2000.
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6. Introduction Our Approach Results Conclusions Appendix
The Research Problem (2/3)
Definition of traffic flow parameters/conditions (Speed,
Density, Flow):
Greenschield’s fundamental diagram(s) of traffic flow6
Figure 2: Flow Vs Density.
6
Foundations of Traffic Flow Theory: The Fundamental Diagrams,
Journal of the Transportation Research Board (2008).
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7. Introduction Our Approach Results Conclusions Appendix
The Research Problem (3/3)
However, local transport authorities in Nairobi do not have
the necessary data (Typical of developing cities)
Look for alternative sources of data
(a) Speeds from "Twende,
Twende and Access Kenya".
(b) Road quality data from "IBM
StreetSense Project".
Figure 3: Available data sources.
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8. Introduction Our Approach Results Conclusions Appendix
Research Question
How can we use the available road quality &
camera-speed data to estimate traffic flow
parameters (speed) in Nairobi?
We do not know the true traffic speeds. We only have speeds
(from cameras) with some unknown observation error.
This observation error must be accounted for when analyzing
the true speed dynamics.
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9. Introduction Our Approach Results Conclusions Appendix
Our Approach
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10. Introduction Our Approach Results Conclusions Appendix
Step Process (1/2)
1. For this study, take a roadway as a case study
2. Then select a segment from that roadway
Figure 4: Roadway segment.
3. Then segment the 24 hour camera speed observations into
5-min time intervals (T = 288 time intervals)
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11. Introduction Our Approach Results Conclusions Appendix
Step Process (2/2)
4. For each segment, develop a probabilistic model7 of the true
trajectory of traffic speeds.
Figure 5: Factor Graph of the
proposed model.
where:
θt = latent speed at timet
θ0 = initial latent speed
xt = road quality observations
yt = camera speed observations
P(θt|xt) = Prob. of latent speed
given the road quality
P(yt|θt) = Prob. of camera speed
given the latent speed
P(θt|θt−1) = Prob. of latent speed at
timet given latent speed at timet−1
7
Bishop, C. M. (2013). Model-Based Machine Learning.
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12. Introduction Our Approach Results Conclusions Appendix
Data Preparation - speed data (1/2)
Speed Data Source: Access Kenya Data
55,511,370 speed observations, 5246 distinct road segments.
Case Study: Uhuru Highway
Figure 6: Speed distributions at study segment. 12 / 27

13. Introduction Our Approach Results Conclusions Appendix
Data Preparation - speed data (2/2)
Data was segmented into 5-min intervals/windows per day
The average speed in the interval was used as the observation
Figure 7: 5-minute time intervals
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14. Introduction Our Approach Results Conclusions Appendix
Data Preparation - road quality
(a) Road quality categories in
overall dataset
(b) PMF for road quality at
study segment
Figure 8: Properties of road quality data.
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15. Introduction Our Approach Results Conclusions Appendix
Learning & Model Evaluation
Condition the observations to their known quantities
Figure 9: Incorporate observed data.
Then perform exact inference8 to learn model parameters.
posterior probability distributions of latent speeds
8
Stan Development Team (2016a). The Stan C++ Library, version 2.10.0.15 / 27

16. Introduction Our Approach Results Conclusions Appendix
Results
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17. Introduction Our Approach Results Conclusions Appendix
Discussion of Results (1/2)
Measured predictive accuracy: by predicting on new data9
Overall Average Error = 3.63 kph (Recall: T = 288
intervals/windows)
Table 1: Sample predicted mean latent speeds (kph) from new data
Predicted Observed Error
1 30.4 29.1 1.3
2 30.6 28.9 1.7
3 29.8 27.7 2.1
4 24.9 27.2 2.3
5 22.6 20.7 1.9
6 23.5 20.8 2.7
.. .... .... ....
9
Andrew Gelman (2013). Understanding predictive information criteria
for Bayesian models. arXiv:1507.04544v4 [stat.CO]
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18. Introduction Our Approach Results Conclusions Appendix
Discussion of Results (2/2)
Probability distributions of (some) parameters
to show the uncertainities
(a) Latent speed at t = 1
(b) Latent speed at t = 259
Figure 10: Distributions of some parameters.
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19. Introduction Our Approach Results Conclusions Appendix
Conclusions
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20. Introduction Our Approach Results Conclusions Appendix
Contributions
Journal papers:
1. Emaasit D., Walcott-Byrant A., Tatsubori M., Byrant R.
E., Osebe S., & Wamburu J. (2016). “Context-based Traffic
Flow Parameter Estimation: A Case Study of Nairobi,
Kenya”. Journal of Transportation Research Part B. (In
Progess)
2. Walcott-Byrant A., Byrant R. E., Tatsubori M., Emaasit
D., Osebe S., Wamburu J., & Fobi S.(2016).“The Living
Roads Project: Giving a Voice to Roads in Developing
Cities”. 96th Annual Meeting of the Transportation Research
Board(TRB). (Under Review)
Patent:
3. Emaasit D., Walcott-Byrant A., Tatsubori M., Byrant R.
E., & Amayo P. (2016). System and Method for Intelligent
Decision Making in a Threatening Event for a Self Driving
Car. (In Progress)
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21. Introduction Our Approach Results Conclusions Appendix
Potential Benefits
Road users provided with an accurate view of the current
& future traffic flow conditions.
make travel plans in advance of commutes
motorists divert to avoid congestion, thereby reducing the
period of congestion.
Traffic operators can use this information to make traffic
control plans:
allowing traffic to be controlled to reduce the impact of
congestion,
operators can prioritize on “crutial” road segments
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22. Introduction Our Approach Results Conclusions Appendix
Future Work
Estimate other parameters of traffic flow (Density &
Flow)
Expand to more roadways.
possibly the entire roadway network in Nairobi
Incorporate more local context factors.
to improve accuracy of traffic flow estimation
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23. Introduction Our Approach Results Conclusions Appendix
Appendix
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24. Introduction Our Approach Results Conclusions Appendix
Other Contributions
Road quality affects driver behavior10
(a) Swerving Vs speed bumps (b) Swerving Vs potholes
Figure 11: Road quality Vs driver behavior.
10
Walcott-Byrant A., Byrant R. E., Tatsubori M., Emaasit D., Osebe S.,
Wamburu J., & Fobi S.(2016).“The Living Roads Project: Giving a Voice to
Roads in Developing Cities”. 96th Annual Meeting of the Transportation
Research Board(TRB). (Under Review)
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25. Introduction Our Approach Results Conclusions Appendix
Methodology Used: Model-Based Machine Learning
A different viewpoint for machine learning proposed by
Bishop (2013)11, Winn et al. (2015)12
Goal:
Provide a single development framework which supports the
creation of a wide range of bespoke models
The core idea:
all assumptions about the problem domain are made
explicit in the form of a model
11
Bishop, C. M. (2013). Model-Based Machine Learning. Philosophical
Transactions of the Royal Society A, 371, pp 1–17
12
Winn, J., Bishop, C. M., Diethe, T. (2015). Model-Based Machine
Learning. Microsoft Research Cambridge. http://www.mbmlbook.com.
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26. Introduction Our Approach Results Conclusions Appendix
Misc - Notes
Why probabilistic modeling?
to account for noisy data & uncertainity
to incorporate our domain assumptions
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27. Introduction Our Approach Results Conclusions Appendix
Model Development
The model can be described as follows:
"data {
int<lower=0> T; // the number of time steps
vector[T] y; // the observation vector for camera speeds
int<lower=0> N; // the number of categories/classes in road quality
int<lower=0,upper=2> x; // the observation vector for road quality
simplex[N] beta_x; // simplex for the prob dbn for road quality
real<lower=0,upper=80> theta_init; // Initial state speed
}
parameters {
real<lower=0> sigma_theta; // SD of state process
real<lower=0> sigma_y; // SD of observation process for camera speeds
}
transformed parameters {
vector<lower=0>[T] theta;
}
model {
theta_init ~ uniform(0, 10); // Priors
sigma_theta ~ uniform(0, 10);
sigma_y ~ uniform(0, 10);
for (n in 1:N)
x[n] ~ multinomial(beta_x); // Likelihood for road quality observation
y ~ normal(theta, sigma_y); // Likelihood for camera speed observation
theta[1] ~ normal(theta_init, sigma_theta); // State process
for (t in 2:T)
theta[t] ~ normal(theta[t-1], sigma_theta); 27 / 27