1. Paper title:. Travel demand matrix estimation methods integrating
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

4. Motivation
Three projects where demand matrix estimation using observed flows from congested networks played a big role:
Improvement of congestion modelling in LMS/NRM (DAT.Mobility / Significance 2017)
Development project: provincial models of Noord Brabant (Goudappel Coffeng 2018)
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.
*Brederode, L., Pel, A., Wismans, L., de Romph, E., Hoogendoorn, S., Static Traffic Assignment with Queuing: model properties and applications. Transportmetrica A: Transport Science 1–36.

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

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

7. Introduction: Matrix estimation framework (simplified)

9. Observed link flows: what are we actually measuring?
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!

10. Observed link flows: what are we actually measuring?
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?

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

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

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

16. Further quantification of the corridor/merge example
Network, count locations, link capacities
Assumptions w.r.t. Travel Demand:
Stationary demand during a single time period
Demand from origins 1+2: lanes
>demand on links 3-7: lanes
Demand from origin 3: lanes
>demand on links 8-11: lanes
Count location
1 lane
Conditions on links 3,5,6 and 8
Link flows as % of unconstrained link demand
Fundamental Diagram for 2 lane links
Fundamental Diagram for 1 lane links
Unconstrained link demand links 8 – 11: 1.75 lanes
link 8
link 3
Unconstrained link demand links 3 – 7: 1.25 lanes
Link 8: demand: 1.75 lanes, flow: 1.50 lanes
link 6
link 5

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

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

19. Solution method: current practice
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
Tonen methodiek
Observed Link Flows
Any solver that can handle a large sparse quadratic optimization problem with non negativity constraints
Route fractions
Static capacity
restrained traffic
assignment model

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

21. Alternative solution method #1: from capacity restrained to capacity constrained
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
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

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

23. Alternative solution method #2: adding information on bottleneck locations
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
Bottleneck links
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

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

26. Alternative solution method #3: adds bottleneck locations as constraints, sensitivity of assignment matrices and travel times
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
Bottleneck links
Route travel times
Any solver that can handle a large sparse quadratic optimization problem with non negativity constraints and linear bottleneck constraints
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

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

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
**Wright, M.A., Gomes, G., Horowitz, R., Kurzhanskiy, A.A., On node models for high-dimensional road networks. Transportation Research Part B: Methodological 105, 212–234.

30. References and Further reading
Brederode, L., Verlinden, K., 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., Static Traffic Assignment with Queuing: model properties and applications. Transportmetrica A: Transport Science 1–36.
Brederode, L.J.N., Hofman, F., van Grol, R., 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., On node models for high-dimensional road networks. Transportation Research Part B: Methodological 105, 212–234.
Bliemer, M.C.J., Raadsen, M.P.H., Brederode, L.J.N., Bell, M.G.H., Wismans, L.J.J., Smith, M.J., Genetics of traffic assignment models for strategic transport planning. Transport Reviews 37, 56–78.
Brederode, L.J.N., Pel, A.J., Hoogendoorn, S.P., Matrix estimation for static traffic assignment models with queuing. hEART rd symposium of the European association for research of transportation, Leeds UK.

31. Thank you for your attention!
Luuk Brederode (speaker)
Kurt Verlinden -- --

32. Framework and most used models in practice
Dynamic
‘Macroscopic Dynamic’
(CTM, Daganzo (1994);
LTM, Yperman (2007))
Temporal interaction assumptions
Semi-dynamic
‘Static Equillibrium’
(Beckmann et al, 1956)
‘All-Or-Nothing’
(Dijkstra, 1959)
Static
Unrestrained
Capacity
Restrained
Capacity
Constrained
Capacity & Storage
Constrained
Spatial interaction assumptions
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.

33. Classification of traffic assignment models
Dynamic
‘Macroscopic Dynamic’
(CTM, Daganzo (1994);
LTM, Yperman (2007))
Temporal interaction assumptions
Semi-dynamic
‘Static Equillibrium’
(Beckmann et al, 1956)
‘STAQ queuing’
(Brederode et al, 2018)
‘All-Or-Nothing’
(Dijkstra, 1959)
‘STAQ squeezing’
(Brederode et al, 2018)
Static
Unresponsive to
congestion
Route distribution
due to congestion
Vertical queues
due to congestion
Horizontal queues
due to congestion
Spatial interaction assumptions
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.

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
Dynamic
‘Macroscopic Dynamic’
(CTM, Daganzo (1994);
LTM, Yperman (2007))
‘STAQ squeezing
- semi dynamic’
Temporal interaction assumptions
Semi-dynamic
‘Static Equillibrium’
(Beckmann et al, 1956)
‘STAQ queuing’
(Brederode et al, 2018)
‘All-Or-Nothing’
(Dijkstra, 1959)
‘STAQ squeezing’
(Brederode et al, 2018)
Static
Unrestrained
Capacity
Restrained
Capacity
Constrained
Capacity & Storage
Constrained
Spatial interaction assumptions