Presentation at the European transport conference 2018 (Dublin) (full paper available from https://aetransport.org/past-etc-papers/conference-papers-2018?abstractId=5808&state=b)

1. Paper title: Travel demand matrix estimation methods integrating
the full richness of observed traffic flow data from congested
networks
Luuk Brederode (speaker)
Kurt Verlinden
-- DAT.mobility / Delft University
-- Significance

2. Contents
• Introduction
• Problem formulation
• Solution methodologies
• Practical insights from applications and conclusions
pagina 2

4. Motivation
Three projects where demand matrix estimation using observed flows from congested
networks played a big role:
1. Improvement of congestion modelling in LMS/NRM (DAT.Mobility / Significance 2017)
2. Development project: provincial models of Noord Brabant (Goudappel Coffeng 2018)
3. Development of a matrix estimation method for congested networks (part of my PhD)
All three projects boil down to migrating from existing capacity restrained traffic assignment
models to a capacity constrained traffic assignment model.
In these projects we use STAQ – squeezing phase*, available in OmniTRANS transport
planning software.
pagina 4
*Brederode, L., Pel, A., Wismans, L., de Romph, E., Hoogendoorn, S., 2018. Static Traffic Assignment with Queuing: model
properties and applications. Transportmetrica A: Transport Science 1–36. https://doi.org/10.1080/23249935.2018.1453561

5. 5
Static capacity restrained assignment model
Capacity = 4000 veh/h
Capacity = 6000 veh/h
Demand= 4200 veh/h
A B
Link flow values?

6. Static capacity constrained assignment model
Capacity = 4000 veh/h
Capacity = 6000 veh/h
Demand= 4200 veh/h
A B
4000
0.95
4200
  
Link flow values?
When using STAQ-squeezing phase,
reduction factors can be outputted on turn-
level.

7. Introduction: Matrix estimation framework (simplified)
pagina 7

9. • A simple corridor and merge network example:
• Bottlenecks determine what quantity we’re actually observing:
» Blue links: travel demand
» Red links: downstream capacity
» Grey links: upstream capacity
» Grey/Blue links: mix of travel demand and upstream capacity
• Only observations from blue and grey/blue links contain information on travel demand!
Observed link flows: what are we actually measuring?
pagina 9

10. Observed link flows: what are we actually measuring?
pagina 10
Based on STAQ assignment of AM peak travel demand
matrices within NRM-West base year strategic transport
model (1401 count locations in study area)

11. Problem formulation
• 91% of observed link flows contain information on travel demand
• However, for 70% of observed link flows, travel demand info is mixed with upstream
capacity
• How can we still estimate OD-demand from these mixed observations?
• What can we do with the observations on supply?
pagina 11

13. Further quantification of the corridor/merge example
pagina 13
Network, count locations, link capacities
1 lane
Count location

14. Further quantification of the corridor/merge example
pagina 14pagina 14
Assumptions w.r.t. Travel Demand:
• Stationary demand during a single time period
• Demand from origins 1+2: 1.25 lanes
>demand on links 3-7: 1.25 lanes
• Demand from origin 3: 0.50 lanes
>demand on links 8-11: 1.75 lanes
Network, count locations, link capacities
1 lane
Count location

15. Further quantification of the corridor/merge example
pagina 15
Flow
Density
link 3
link 8
link 6 link 5
Fundamental Diagram for 2 lane links
Fundamental Diagram for 1 lane links
Conditions on links 3,5,6 and 8
Assumptions w.r.t. Travel Demand:
• Stationary demand during a single time period
• Demand from origins 1+2: 1.25 lanes
>demand on links 3-7: 1.25 lanes
• Demand from origin 3: 0.50 lanes
>demand on links 8-11: 1.75 lanes
Network, count locations, link capacities
1 lane
Count location

16. Link flows as % of unconstrained link demand
Further quantification of the corridor/merge example
pagina 16
Flow
Density
link 3
link 8
link 6 link 5
Fundamental Diagram for 2 lane links
Fundamental Diagram for 1 lane links
Assumptions w.r.t. Travel Demand:
• Stationary demand during a single time period
• Demand from origins 1+2: 1.25 lanes
>demand on links 3-7: 1.25 lanes
• Demand from origin 3: 0.50 lanes
>demand on links 8-11: 1.75 lanes
Conditions on links 3,5,6 and 8
Unconstrained link demand
links 3 – 7: 1.25 lanes
Unconstrained link demand
links 8 – 11: 1.75 lanes
Network, count locations, link capacities
1 lane
Count location

17. Solution method: current (dutch) practice
pagina 17
Observed flow
Estimated link demand
Estimate unconstrained link demands from observed link flows
In the dutch LMS/NRM: ‘tonenmethodiek’:

18. Solution method: current (dutch) practice
Estimate unconstrained link demands from observed link flows
In the dutch LMS/NRM: ‘tonenmethodiek’:
pagina 18
Observed flow
Estimated link demand
Estimated reduction due to bottlenecks

19. Solution method: current practice
pagina 20
Any solver that can handle a large
sparse quadratic optimization problem
with non negativity constraints
Route fractions
Static capacity
restrained traffic
assignment model
Upper level:
Minimize differences between:
modelled / estimated link demands;
Using any OD pairs passing
ODmatrices
Lower level:
Determine relationship between
current ODmatrices and link flows
Assignment Matrices
Estimated unconstrained
link demands
Observed Link Flows
Tonen
methodiek

20. Solution method: current practice: pros and cons
Requires a traditional capacity
restrained traffic assignment
model (quick!)
Allows for use of widely available
solution methods
Fast and easy fits (on
unconstrained demand level!)
Requires a traditional capacity
restrained traffic assignment
model (not suited for cong conditions)
Accuracy of the link demand
estimates cannot be assessed, since
it cannot be measured
A good fit on unconstrained demand
doesn’t imply a good fit on observed
flow
Tractability is low: errors in input and
calibration of parameters of
assignment model and solver cannot
be isolated pagina 21

21. Alternative solution method #1:
from capacity restrained to capacity constrained
pagina 22
Static capacity
constrained traffic
assignment model
Any solver that can handle a large
sparse quadratic optimization problem
with non negativity constraints
Route fractions *
Reduction factors
Upper level:
Minimize differences between:
modelled / observed link flows;
Using non-reduced OD pairs
ODmatrices
Lower level:
Determine relationship between
current ODmatrices and link flows
Assignment Matrices
Observed
link flows

22. Alternative solution method #1: pros and cons
Requires a capacity
constrained traffic assignment
model (more accuracy)
Allows for use of widely available
solution methods
Directly compares observed
and modelled flows
Tractability is high: errors in
input, and effects of parameters
in assignment model and
solver can be isolated
Capacity constrained traffic
assignment model requires
accurate capacities and more
calculation time per assignment
Does not use information on ‘red’
and ‘grey’ links
Poor convergence when
bottlenecks switch state during
estimation iterations
pagina 23

23. Upper level:
Minimize differences between:
modelled / observed link flows;
modelled / observed link states;
Using non-reduced OD pairs
ODmatrices
Lower level:
Determine relationship between
current ODmatrices and link flows
Assignment Matrices
Observed
link flows
Observed
Bottleneck links
Alternative solution method #2:
adding information on bottleneck locations
pagina 24
Any solver that can handle a large
sparse quadratic optimization problem
with non negativity constraints
Route fractions *
Reduction factors
Static capacity
constrained traffic
assignment model

24. Alternative solution method #2:
adding information on bottleneck locations
Where do the observed bottleneck locations come from?
Either:
• Directly observed (e.g. daily traffic reports (we used ‘VID file top 50’ in the Netherlands);
• Derive indirectly from floating car data: select the node where the head of a queue is
pagina 25

25. Solution method #2: pros and cons
Requires a capacity constrained
traffic assignment model
Allows for use of widely available
solution methods
Directly compares observed and
modelled flows
Tractability is high
Uses information on bottleneck
locations
Non-convergence unlikely, as
bottlenecks are unlikely to
change state during estimation
Capacity constrained traffic
assignment model requires
accurate capacities and more
calculation time per assignment
Parameter that weighs
importance of link flow
differences with link state
differences needs to be set
carefully
pagina 26

26. Alternative solution method #3:
adds bottleneck locations as constraints, sensitivity of assignment matrices and travel times
pagina 27
Any solver that can handle a large
sparse quadratic optimization problem
with non negativity constraints and
linear bottleneck constraints
Upper level:
Minimize differences between:
modelled / observed link flows;
modelled / observed travel times
Subject to: observed link states
Using non-reduced OD pairs
ODmatrices
Lower level:
Determine relationship between
current ODmatrices and link flows
Assignment Matrices
+ sensitivities
Observed
link flows
Observed
Bottleneck links
Observed
Route travel times
Route fractions *
Reduction factors
Static capacity
constrained traffic
assignment model

27. Solution method #3: pros and cons
Requires a capacity constrained
traffic assignment model
Allows for use of widely available
solution methods
Directly compares observed and
modelled flows
Tractability is high
Uses information on bottleneck
locations
Non-convergence due to
changing link states impossible
No weight parameter to be set
for link state differences
Allows for calibration on
observed route travel times
True bi-level solution method
Capacity constrained traffic
assignment model requires
accurate capacities and more
calculation time per assignment
Implementation still in prototypical
state
pagina 28

28. Conclusions (only highlights)
• Active bottlenecks determine what quantity an observed link flow actually represents
• Current practice translates all quantities to ‘unconstrained demand’, causing
intractability to the matrix estimation process
• Links where (partial) demand is observed can be used for demand estimation. This
accounts for 91% of count locations in the congested Randstad area
• To use observed partial travel demand data, a capacity constrained assignment
model is required (otherwise only 21% of count locations is usable). No dynamic traffic
assignment model required.
• The capacity constrained assignment model also allows for
• Enforcing stability using link state constraints
• Calibration on observed travel times
• Usage of observed bottleneck locations from e.g. floating car data
pagina 29

29. Ongoing research and development
• Extension of the capacity constrained traffic assignment model with residual traffic
transfer, allowing for sequential calibration
• Relaxation of FIFO assumption within node model of capacity constrained model**,
allowing to model slip lanes without additional network coding
pagina 30
**Wright, M.A., Gomes, G., Horowitz, R., Kurzhanskiy, A.A., 2017. On node models for high-dimensional road
networks. Transportation Research Part B: Methodological 105, 212–234. https://doi.org/10.1016/j.trb.2017.09.001

30. References and Further reading
• Brederode, L., Verlinden, K., 2018. Ttravel demand matrix estimation methods integrating the full richness of observed traffic
flow data from congested networks. Presented at the European Transport Conference, AET and contributors, Dublin.
• Brederode, L., Pel, A., Wismans, L., de Romph, E., Hoogendoorn, S., 2018. Static Traffic Assignment with Queuing: model
properties and applications. Transportmetrica A: Transport Science 1–36. https://doi.org/10.1080/23249935.2018.1453561
• Brederode, L.J.N., Hofman, F., van Grol, R., 2017. Testing of a demand matrix estimation method Incorporating observed
speeds and congestion patterns on the Dutch strategic model system using an assignment model with hard capacity
constraints. Presented at the European Transport Conference, AET 2017 and contributors.
• Wright, M.A., Gomes, G., Horowitz, R., Kurzhanskiy, A.A., 2017. On node models for high-dimensional road networks.
Transportation Research Part B: Methodological 105, 212–234. https://doi.org/10.1016/j.trb.2017.09.001
• Bliemer, M.C.J., Raadsen, M.P.H., Brederode, L.J.N., Bell, M.G.H., Wismans, L.J.J., Smith, M.J., 2017. Genetics of traffic
assignment models for strategic transport planning. Transport Reviews 37, 56–78.
https://doi.org/10.1080/01441647.2016.1207211
• Brederode, L.J.N., Pel, A.J., Hoogendoorn, S.P., 2014. Matrix estimation for static traffic assignment models with queuing.
hEART 2014 - 3rd symposium of the European association for research of transportation, Leeds UK.
pagina 31

31. Thank you for your attention!
Luuk Brederode (speaker)
Kurt Verlinden
-- lbrederode@DAT.nl
-- Verlinden@Significance.nl

32. Framework and most used models in practice
pagina 33
Semi-dynamic
Unrestrained Capacity
Restrained
Capacity
Constrained
Capacity & Storage
Constrained
Simplified from:
Bliemer, M.C.J., Raadsen, M.P.H., Brederode, L.J.N., Bell, M.G.H., Wismans, L.J.J., Smith, M.J., 2017.
Genetics of traffic assignment models for strategic transport planning. Transp. Rev. 37, 56–78.
Spatial interaction assumptions
Temporalinteractionassumptions
Static
Dynamic
‘All-Or-Nothing’
(Dijkstra, 1959)
‘Macroscopic Dynamic’
(CTM, Daganzo (1994);
LTM, Yperman (2007))
‘Static Equillibrium’
(Beckmann et al, 1956)

33. Classification of traffic assignment models
pagina 34
Semi-dynamic
Unresponsive to
congestion
Route distribution
due to congestion
Vertical queues
due to congestion
Horizontal queues
due to congestion
Simplified from:
Bliemer, M.C.J., Raadsen, M.P.H., Brederode, L.J.N., Bell, M.G.H., Wismans, L.J.J., Smith, M.J., 2017.
Genetics of traffic assignment models for strategic transport planning. Transp. Rev. 37, 56–78.
Spatial interaction assumptions
Temporalinteractionassumptions
‘All-Or-Nothing’
(Dijkstra, 1959)
‘Macroscopic Dynamic’
(CTM, Daganzo (1994);
LTM, Yperman (2007))
‘Static Equillibrium’
(Beckmann et al, 1956)
Static
Dynamic
‘STAQ squeezing’
(Brederode et al, 2018)
‘STAQ queuing’
(Brederode et al, 2018)

34. Semi dynamic version of STAQ
• Add residual traffic transfer to STAQ-squeezing; not implemented yet
• Relaxes STAQ assumption of empty network before and after study period
pagina 35
Semi-dynamic
Spatial interaction assumptions
Temporalinteractionassumptions
‘All-Or-Nothing’
(Dijkstra, 1959)
‘Macroscopic Dynamic’
(CTM, Daganzo (1994);
LTM, Yperman (2007))
‘Static Equillibrium’
(Beckmann et al, 1956)
Static
Dynamic
‘STAQ squeezing’
(Brederode et al, 2018)
‘STAQ queuing’
(Brederode et al, 2018)
Unrestrained Capacity
Restrained
Capacity
Constrained
Capacity & Storage
Constrained
‘STAQ squeezing
- semi dynamic’