Presentation from NORTHMOST - a new biannual series of meetings on the topic of mathematical modelling in transport. Hosted at its.leeds.ac.uk, NORTHMOST 01 focussed on academic research, to encourage networking and collaboration between academics interested in the methodological development of mathematical modelling applied to transport. The focus of the meetings will alternate; NORTHMOST 02 - planned for Spring 2017 - will be led by practitioners who are modelling experts. Practitioners will give presentations, with academic researchers in the audience. In addition to giving a forum for expert practitioners to meet and share best practice, a key aim of the series is to close the gap between research and practice, establishing a feedback loop to communicate the needs of practitioners to those working in university research.

1. Real-Time Traffic Management:
Challenges and Solutions
Ke Han
Lecturer (Assistant Professor)
Center for Transport Studies
Department of Civil and Environmental Engineering, Imperial College London
k.han@imperial.ac.uk
www.imperial.ac.uk/people/k.han

2. Outline
1. Overview
2. The CARBOTRAF Project
3. Decision Rule Approach for Real-Time Operation

3. Real-Time Traffic Management
v Challenges
Ø Timeliness of decisions
Ø Nonlinear and nonconvex objective
Ø Multiple objectives
Ø Insufficient telecom capacity (centralized vs. distributed)
Ø Uncertainties and insufficient data coverage
v New Opportunities (more challenges?)
Ø Multi-source and heterogeneous data (e.g. mobile data, social media)
Ø New collection/communication methods (e.g. crowd sourcing)
Ø Need for more robust and fundamentally new theories and methods

4. Outline
1. Overview
2. The CARBOTRAF Project
3. Decision Rule Approach for Real-Time Operation

5. The CARBOTRAF Project
“A Decision Support System for reduced emissions of CO2 and Black
Carbon through Adaptive Traffic Management”
Ø Scenario evaluation using traffic and environmental modelling tools
Ø Online status updates and decision support
Ø Ambient monitoring for evaluation, feedback and learning
Ø Two “Pilot Cities” (Glasgow and Graz)
Ø Decision Support System with GUI for Traffic Operators

6. Work Flow of The CARBOTRAF Project
Offline
modelling
&
simulation
Decision
Support
System
Online
Database
Interfacetoreal-timedata
Real-time
traffic data
ITS actions
Catalogue of
ITS actions
Traffic
simulation
Emission
models
Air quality
models
Look-up
table &
database of
traffic and
emission
scenarios
Real-time pollutant
concentration
Real-time
air quality data
Real-time
meteorology data
Offline module Online module

7. Off-Line Modeling
Microsimulation
Emission Model
Dispersion Model
• Network model
• Traffic flows
• Signal plans
• Vehicle composition
• Vehicle dynamics
• Vehicle emission
categories
• Road elevation
• Weather data
• Building heights
S-Paramics,
VISSIM
AIRE
IFDM

8. Test Site in West Glasgow
Key Performance Indicators
v Traffic
Ø Travel time
Ø Speed
Ø Delay
v Environment
Ø Black Carbon
Ø CO2
Ø Nox
v Spatial references
Ø Network wide
Ø Corridor
Ø Junction
Great W
estern Rd.
KelvinWay
University Av.
VMS
TSC
city center

9. The CARBOTRAF Project

10. Reduction of BC Concentration with ITS Actions
BC conc (µg/m3)
ITS – Base Scenario
Boundary condition 1
BC conc (µg/m3)
ITS – Base Scenario
Boundary condition 2

11. Managerial Insights Gained from Offline Modeling &
Simulation
v The effectiveness of ITS actions depends on many factors, which need to be
determined and telecommunicated in real time
Ø Dynamic demand profile
Ø Weather condition
Ø Fleet composition
v Benefits of the ITS actions are more pronounced at the local level
Ø Network level: below 3%
Ø Corridor/junction level: 5-30%
v In an urban environment, emission is closely related to
Ø Traffic flow dynamics (not merely “flow” or “volume”)
Ø Fleet composition (bus/LGV/HGV)

12. Decision Support System
v The DSS combines streaming data and the off-line LUT to rank different
candidate ITS actions
v Input:
Ø Current ITS action deployed
Ø Probability distributions of KPIs for the complete set of alternative actions
(LUT)
Ø Operational constraints on the set of ITS actions
v Minimization problem (in real time):
v Potential issues:
Ø Resolution of the Look-Up Table
Ø Expectation highly susceptible to outliers and errors
Ø Computationally expensive, with additional lags -- Traffic Prediction Tool (Min and
Wynter, 2011)

13. Outline
1. Overview
2. The CARBOTRAF Project
3. Decision Rule Approach for Real-Time Operation

14. Analytical/
closed-form
transformation
Decision Rule Approach for Real-Time Traffic Management
v Real-time control: Challenges
- Timeliness
- Nonlinear and nonconvex objective
- Distributed vs. centralized control
- Uncertainties
v Heuristic (genetic algorithm, fuzzy logic), inexact and
sub-optimal
v Decision Rule (DR) approach for real-time traffic
management
ü Historical and real-time data
ü Within-day and day-to-day variations
ü Distributionally Robust Optimization (DRO) to ensure
performance in the most adversarial situation
ü Efficient on-line operation
ü Compatible with analytical computations and microsimulation
Real-time
system state
Control
parameters
Not optimal?
Decision rule

15. Decision Rule: Concept
Off-line module
On-line module
Analytical/
closed-form
transformation
Real-time
traffic state
Real-time
decision
Decision
rule
Offline
training
Real-time
traffic state
Historical
traffic state
Look-up
table
Traffic
prediction
tool
Real-time
decision
Historical
traffic state
Offline
simulation
Decision rule approach CARBOTRAF approach
Stochastic
optimization
Offline
simulation

16. -- real-time information (flow, count, speed, queue)
-- Analytical transformation with undetermined coefficients x
-- Projection onto feasible control set
--
Network performance measure (minimize)
(congestion, emission, fuel consumption)
Real-time
Information
q
Control
u
Decision Rule
Network
performance
measure
(simulation)
Φ(q,u)
f (x,q)
u = PΩ[ f (x,q)]
Decision Rule: Deterministic Formulation
q
Deterministic Formulation
Given real-time information q, find
the best decision rule (x):
u = PΩ[ f (x,q)]

17. Linear Decision Rule
Time
Location/
data type
past T
observations
REAL-TIME DATA
CONTROL
COEFFICIENT

18. Nonlinear Decision Rule (Artificial Neural Network)
REAL-TIME DATA
CONTROL
ANN . . . . . .
Artificial Neural Network
v : a neural network with m hidden
layers and n neurons
v Activation function pre-determined (e.g.
sigmoid functions)
v x represents the weights of the
connections between neurons

19. Decision Rule: Stochastic Extension
v In reality, q is stochastic, subject to within-day & day-to-day variations
v Stochastic programming – exact probability distribution required
v Ambiguous information on the distribution with finite samples
v Distributionally robust optimization (DRO)
Ø Worst-case scenario (‘max’),
Ø among all candidate distributions
Ø Subsumes stochastic optimization
Ø Data-driven calibration of
Distributionally Robust Formulation
Given stochastic input q, find the best
decision rule coefficient x:
“Uncertain distributions (DRO)
instead of uncertain parameters (RO)”

20. Advantages of the Decision Rule Approach
v Finding the best responsive signal strategy è Finding x
v Feasible and efficient on-line operation
- Off-line: Distributionally robust optimization (expensive)
- On-line: Linear transformation and projection (inexpensive)
v Flexible sensor location, data type, and control resolution
v User-defined feasible set for signal control parameters
v Two solution procedures for the off-line problem:
- Mixed integer linear program
- Metaheuristic search
Distributionally Robust Optimization

21. v Kolmogorov-Smirnov (K-S) goodness-of-fit test (Massey, 1951; Bertsimas et al., 2013):
v Random variable: ,parameterized by
v Uncertainty set: ,parameterized by
v Fix ,and consider K samples (historical data)
v Does a distribution well capture a finite set of sampled data?
v Reject H0 at the level α if
Data-Driven Calibration of the Uncertainty Set
Set of candidate distributions

22. Formulation of the Uncertainty Set

23. Evaluating the Objective Function
v Random Variable (objective): , parameterized by
v Lower and upper bounds of : , partitioned into W intervals
v Fix (control),
g1Lf Uf
g2 gi-1 gi
. . . . . .
K-S test

24. Numerical Study, Part 1
Great Western Rd
Great Western Rd
ByresRd
City Center
University of Glasgow
§ West end of Glasgow
§ 5 signalized intersections
§ 35 directed links
§ LWR network model
Network
Data
§ Turn-by-turn flow count
§ 8-9 am, 7 June 2010
§ Daily variations are
generated synthetically,
using a variety of
distributions
Benchmarks
§ Fixed signal timing
(deterministic & DRO)
§ Field signal parameters
(Glasgow City Council)

25. Numerical Study: Part 1
Particle Swarm Optimization Great Western Rd
Great Western Rd
ByresRd
City Center
University of Glasgow
§ Zeroth-order information on the objective
and constraints
§ LWR-based network simulation model
§ Flexible trade-off between solution
quality and computational cost
§ Off-line computational time: 24h
§ On-line computational time: negligible
Criteria Deterministic
Fixed timing
DRO
Fixed timing
Field parameter
(Glasgow City)
LDR-DRO NDR-DRO
Objective (maximize) 1.61 3.81 4.14 4.28 4.34
Throughput 1498 (veh) 3382 (veh) 3576 (veh) 3910 (veh) 3951
CPU time
(offline/online)
24h/- 24h/- -/- 24h/0.01s 24h/0.03s

26. Numerical Study: Part 2
v 4-by-4 grid network in S-Paramics
v 8 zones, 56 O-D pairs
v Dynamic route assignment
v Fleet: passenger car, LGV, MGV, HGV, coach
v 4-stage signal plan at all four junctions
v 30 random seeds for generating samples
72
74
76
78
80
82
1
AverageDelay(s)
3.0% improvement

27. 210 215 220 225 230 235 240 245 250
0
1
2
3
4
5
6
7
Average Vehicle Delay (s)
Count
215
220
225
230
235
240
245
1 2
AverageVehicleDelay(s)
Numerical Study: Part 3
v West Glasgow in S-Paramics
v 21 zones, 420 O-D pairs
v Dynamic route assignment
v Fleet: passenger car, LGV, MGV, HGV, coach
v 30 random seeds for generating samples
v 80 PSO major iterations
v Signal optimization at the key junction
Byres Rd. &
University Ave.
NDR-DRO Webster
1.3% improvement

28. Numerical Study: Part 4
v The decision rule approach combined with metaheuristic methods allow for
sufficiently nonlinear and non-analytical objective functions, such as
v Emission (hydrocarbon, HC) is calculated based on vehicle speed, density, and
acceleration/deceleration derived from the kinematic wave model, and the
instantaneous HC emission model (Ahn et al., 2002)
f = w× Throughput - (1− w)× Total Emission w ∈ [0,1]
Great Western Rd
Great Western Rd
ByresRd
City Center
University of Glasgow
3100 3200 3300 3400 3500 3600 3700 3800 3900 4000
3.1
3.15
3.2
3.25
3.3
3.35
3.4
3.45
x 10
7
Throughput (veh)
TotalHCEmission(µg)
w=0.1
w=1.0
(no emission
consideration)

29. Thank you!
k.han@imperial.ac.uk