First large scale application of a static matrix estimation method on observed travel times, congestion patterns and link flows

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First large scale application
Ivo Hilderink (provincie Noord-Brabant)
Luuk Brederode (Dat.Mobility / TU Delft) - speaker
Multi source
matrix calibration
donderdag 15 september 2022
Matrixkalibratie met STAQ
Presentation for the 50th European Transport Conference
Milan 2022-09-07

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Introduction: results from a poll among 62 dutch
consultants and researchers in our field
Who where the respondents?
• First poll instance:
• 35 colleagues from Goudappel visiting my lunch lecture in march of 2022
• Mainly dutch consultants in transport and mobility, many of them applying strategic transport
models or using their results
• Second poll instance:
• 27 visitors of my presentation at the PLATOS colloquium in march of 2022
• Consultants and researchers in transport modelling
• In total: 62 respondents, answering two questions
Multi Source Matrix Calibration – first large scale application 2

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Q1: What is quantity best describes the amount of
congestion when conducting strategic studies?
1. Queue Lengths
1.6%
2. Travel delays / collective travel time losses
56.5%
3. Queue duration
0%
4. ‘Filezwaarte’ (=queue length * queue duration)
41.9%

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Q2: how is the accuracy of a strategic transport model
with respect to congestion assessed?
By comparing model results with:
1. Observed queue lengths
21.3%
2. Observed travel delays / collective travel time losses
13.1%
3. Observed queue duration
0%
4. Observed ‘Filezwaarte’ (=queue length * queue duration)
14.8%
5. ‘Observed’ V/C ratio’s or ‘wensvraag’ (link demands estimated from observed flows)
50.8%

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So why are we predominantly using V/C ratios
instead of delays?
Observations
Flow [veh/h/lane]
Assignment model
speed
[km/u]
Flow [veh/h/lane]
Snelheid
[km/u]

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Observations
Flow [veh/h/lane]
Assignment model
speed
[km/u]
Flow [veh/h/lane]
Snelheid
[km/u]
So why are we predominantly using V/C ratios
instead of delays?
Because a static capacity restrained traffic assignment model cannot describe links with
queues, delays from the model on or above capacity cannot be interpreted as such.

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So why can we use travel delays in the transport
model in Noord Brabant?
Because a static capacity constrained traffic assignment model STAQ is used. This model
accurately describes links with queues, allowing for direct interpretation of delays.
Observations
Flow [veh/h/lane]
Assignment model
speed
[km/u]
Flow [veh/h/lane]
Snelheid
[km/u]

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Not only delays, also congestion patterns are
more accurate, as shown in this Case study
Added lanes
Extended junction
capacity
Case study from: Brederode, L., Pel, A., Wismans, L., de Romph, E., Hoogendoorn, S., 2019. Static Traffic Assignment
with Queuing: model properties and applications. Transportmetrica A: Transport Science 15, 179–214.
https://doi.org/10.1080/23249935.2018.1453561
donderdag 15 september 2022 8

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Assignment results reference situation
Legend:
Bandwidths: flows (veh/h AM peak)
Colours: speed (as percentage of max speed)
Pie Charts: size of vertical queues (collective loss [veh*h])
Assignment results capacity restrained
Assignment results capacity constrained
80% 100%
0%
308
Uit: Brederode et al (2019)
Multi Source Matrix Calibration – first large scale application

-
1
2
4
4
3
5
6
3
4
1
2
Assignment results capacity restrained
Assignment results capacity constrained
From: Brederode et al (2019)
Legend:
Bandwidths: flows (veh/h AM peak)
Pie Charts: size of vertical queues (collective loss [veh*h])
80% 100%
0%
308
1. Bottleneck on offramp disappears
2. Bottleneck on motorway disappears
3. More traffic through Berlicumseweg
4. Increase of bottleneck severeness and
spillback downstream
5. Less delay on upstream ringroad
6. Increased flow from ringroad activates
a new bottleneck
Assignment results scenario

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Multi Source
Matrix
Calibration
First large scale application on the
strategic transport model of the
province Noord-Brabant
Development project conducted by DAT.Mobility
for the province of Noord-Brabant

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Motivation and goal of this development project
• Within the strategic transport models of the province of Noord Brabant, STAQ instead of a
capacity restrained traffic assignment model is used for road traffic.
• This increases accuracy of the assignment with respect to queuing.
• It also provides the opportunity to use observed link flows that are affected by congestion
(i.e. flow < demand) and to include data on observed congestion patterns and travel times
in the matrix estimation.
• At the start of the project, a prototypical implementation of this new matrix estimation
methodology existed and described in a scientific paper*.
• The scope of this project is to determine the practical value of this method.
*Brederode, L., Wismans, L., Rijksen, B., Hoogendoorn, S., 2020. Travel Demand Matrix Estimation for Strategic
Road Traffic Assignment Models with Strict Capacity Constraints. preprint.
https://doi.org/10.13140/RG.2.2.35478.98886

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Data preparation – observed flows
• The official data set from 2018 was used, containing observed flows on 456 locations
• Data from links on which <5% of traffic or <5% of routes was unaffected by an upstream
queue* was removed, as this data mainly discribes network supply instead of demand
% of locations
Locations with <5% unaffected flow 21 5%
Locations with <5% unaffected routes 14 3%
Locations with <5% of either quantities 21 5%
*according to assignment of the prior matrix

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Legend:
Bandwidths: flows [veh/h AM peak]
Pie charts: collective loss [veh*h]
80% 100%
0%
Data preparation –
prior assignment results
The study period duration was extended from one to two
hours to reflect actual peak period duration
STAQ assignment (1h study period duration) STAQ assignment (2h study period duration)
Run20 rerun @ 19.105

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Comparison 1h and 2h assignments
• Differences in queue lengths are large. Queues (and therefore delays for travellers) are
much larger in the 2 h assignment. This makes sense, because when doubling both OD
demand and link capacities:
• in a static capacity restrained model BPR type travel times maintain the same, whereas
• in a static capacity constrained model, duration affects queue lengths and thus travel delays
• The travel times from the 2h prior assignment results are much more in line with observed
travel times. This makes sense, as in reality (in 2018) most congestion in the AM peak
occurred for longer than 1 hour.
• Differences in bottleneck locations are very limited, apart from two locations where a
software bug caused them. The bug has been fixed (but plots haven’t been updated yet).

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Data preparation – convergence of assignment model
Original assignment (car/freight)
Converges in 8 iterations to DG < 5E-04
Calculation time: 1:28 h
PCU assignment (car+freight)
PCU 2h assignment
Conclusions
• Assignment takes around 1.5 hour.
• PCU assignment is slightly quicker as it uses less
routes
• PCU 2h is slower, because it is more sensitive due to
higher delays
For strategic applications, the model needs to
approximate the user equilibrium. In line with literature, we
consider the approximation sufficient, when the duality
gap (DG) value is smaller than 5E-04.

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Results – overview dashboard
Average deviation per count location reduces in 5 iterations
to 7%
Average deviation per observed route delay reduces from
25% to 12%
Average estimation effect per OD pair is 0.20%
Deficit (surplus) of demand on
(in-)active bottleneck locations
approaches 0
Course of objective function value bing minimized by the
upper level solver
Note: dashed lines represent
deviations from reference
estimation method.
322
90
0
Note, the max number of
iteraties is set (arbitrarily) to 5
0.13

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Results - flows
Deviation per count location – MSMC vs reference method
Prior
Reference method
MSMC (no travel times)
MSMC
Reference
Prior MSMC
(ntt)
MSMC
Official evaluation criterion:
>80% green, <5% red

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Results – Active bottleneck locations
Rang waargenomen
FileZwaarte Koplocatie
in BBMB
2018?
In pae-toedeling
BBMB 2018?
in MSMC zonder
reistijden? in MSMC?
1 A27 noord (Gorinchem) ( 303_a27_hm28.5 )
2 A2 noord (Maarheeze) ( 306_a2_hm175.6 )
3 A58 oost (Eindhoven) ( 302_a58_hm25.0 )
4 A2 noord (eindhoven) ( 306_a2_hm175.6 )
5 A16 noord (Dordrecht) ( 410_301_a16_hm44.0 )
6 A2 noord (Utrecht) ( 308_a2_hm109.7 )
7 A67 west (Eindhoven) ( 309_a67_hm27.3 )
8 A58 oost (Tilburg) ( vild093_a58 )
9 A2 zuid (Den Bosch) ( 618_a2_hm96.7 )
10 A67 west (Eindhoven) ( 311_a67_hm32.5 )
11 A58 oost (Eindhoven) ( 307_a58_hm18.5 )
12 A58 oost (Tilburg-centrum) ( 319_a58_hm44.2 )
13 A50 zuid (Oss) ( vild161_a50 )
14 A59 west (Den Bosch) ( vild820_a59 )
15 A59 noord (Nijmegen) ( vild505_a59 )
16 A50 west (Veghel) ( vild418_a50 )
Not here, but large bottlenecks
within junction Hooipolder
Bottleneck disactivates in
some iterations during matrix
estimation

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Results – observed route delays
• MSMC outperforms prior on all routes
• On average, deviations are reduced
from 25% to 12% per route
• In absolute sense, deviations are
reduced from [25 sec upto 5 minutes]
to [12 sec upto 2 minutes]
• Detailed analysis shows that
inconsistencies in observed data
prevent a bitter fit
• Note: this analysis only contains
observed routes for which delays due
to queuing occurs (according to travel
times from google)

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Results – computational requirements
• MSMC requires all five iterations to reach the fit on travel times mentioned in previous slide. This
means that MSMC is about 11% faster compared to the reference method.
• MSMC requires only three iterations to get a better fit on link flows compared to the reference
method. This means that, when not considering the fit on travel times, MSMC is about 40% faster
compared to the reference method
• There are three points of attention to be noted here:
• Unlike the reference method, MSMC only generates routes once. This is advantageous for MSMC.
• Unlike the reference method, MSMC was applied on a single class. This is advantageous for MSMC.
• Unlike the reference method, MSMC was applied on a 2h assignment. This is advantageous for the reference method
Reference method (1h, 5mln routes) Multi Source Matrix Calibration (2h, 5mln routes)
Lower level (STAQ assignment) Upper level (heuristic) Total Lower level (STAQ assignment) Upper level (solver) Total
#iterations Calculation time Iteration type Calculation time Calculation time #iterations Calculation time Calculation time Calculation time
10 04:10:00 Cong. pat. 00:09:06 04:19:06 12 02:56:36 01:10:40 04:07:16
10 03:37:58 Counts 01:56:36 05:34:34 15 02:57:30 00:59:20 03:56:50
10 03:38:44 Cong. pat. 00:09:27 03:48:11 14 02:47:04 00:45:44 03:32:48
10 03:39:53 Counts 02:00:22 05:40:15 13 02:38:49 00:20:28 02:59:17
13 02:39:51 00:00:00 02:39:51
40 15:06:35 04:15:31 19:22:06 67 13:59:50 03:16:12 17:16:02

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Conclusions (1/2)
• Wihtin this project, the prototypical implementation of Multi-Source Matrix Calibration
(MSMC) has been made suitable for application on (large) strategic transport models.
• MSMC makes use of additional information about bottlenecks from STAQ. Therefore:
• MSMC allows for direct use of observed link flows that are affected by congestion (no use of
estimated link demands (‘wensvraag’) required);
• MSMC allows to also include data on observed congestion patterns and travel times.
• MSMC also accounts for junction modelling (capacities and delays on turning movement
level, calculated within STAQ using empirical relationships from the HCM and the like)
• MSMC can be extended to be applied on multiple user classes

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Conclusions (2/2)
• In this project, MSMC was sucessfully applied on the strategic transport model of Noord-Brabant
• MSMC much better fits to observed link flows compared to the reference method
• MSMC replicates all bottleneck locations
• During matrix estimation with MSMC, deviations from observed route delays decrease from 25% to 12%
on average, which is 10 times lower compared to the reference method
• MSMC causes 23% lower prior demand deviations compared to the reference method
• MSMC (including observed delays) requires 11% less calculation time compared to the reference method
• MSMC (exluding observed delays) requires 40% less calculation time compared to the reference method
• When converting the current prototype to production code, calculation times will be further reduced
significantly (mainly because now, OmniTRANS and Matlab are interfacing through the file system :x).

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Recommendations
• Because it explicitly models queues, STAQ requires that the study period includes the
complete period during which queues occur. For the AM peak of Noord-Brabant, 7-9AM is
sufficient, but the currently used ‘representative hour’ within the AM peak yields substantial
underestimation of delays.
• To improve accuracy in areas with substantial peak spreading, a semi dynamic version of
STAQ (which transfers residual traffic to the subsequent time period) has recently been
developed. See https://shorturl.at/hILM9 for a sneak preview (a paper has not yet been
published).
• The explicit gradients that MSMC derives could be used to detect data inconsistencies.
Once removed, fits are expected to greatly improve further.

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Further reading
• Brederode, L., Pel, A., Wismans, L., de Romph, E., Hoogendoorn, S., 2019. Static Traffic Assignment with Queuing:
model properties and applications. Transportmetrica A: Transport Science 15, 179–214.
https://doi.org/10.1080/23249935.2018.1453561
• Brederode, L., Verlinden, K., 2019. Travel demand matrix estimation methods integrating the full richness of observed
traffic flow data from congested networks. Transportation Research Procedia, Modeling and Assessing Future
Mobility ScenariosSelected Proceedings of the 46th European Transport Conference 2018, ETC 2018 42, 19–31.
https://doi.org/10.1016/j.trpro.2019.12.003
• Brederode, L., Wismans, L., Rijksen, B., Hoogendoorn, S., 2020. Travel Demand Matrix Estimation for Strategic Road
Traffic Assignment Models with Strict Capacity Constraints. preprint (under review for Transportation Research: Part
B). https://doi.org/10.13140/RG.2.2.35478.98886
• Presentation (in dutch) about the methodology behind MSMC:
https://www.slideshare.net/LuukBrederode/20200311-platos2020-matrixkalibratie-op-intensiteiten-
congestiepatronen-en-reistijden-fontsembedded
• Report on complete results as created for the Province of Noord-Brabant (in dutch) available upon request

Matrixkalibratie met STAQ 26

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Waarom kijken sommige modellen naar
‘wensvraag’?
Intensiteit [vtg/u/strook]
Snelheid
[km/u]
Waargenomen intensiteit/snelheid
Gemodelleerde intensiteit/snelheid o.b.v. apriori HB matrix
Gemodelleerde intensiteit/snelheid na kalibratie op intensiteiten
De kalibratie haalt verkeer uit de matrix om de lagere gemeten intensiteit te matchen.
Maar er had verkeer bij gemoeten om file te veroorzaken!

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Waarom kijken sommige modellen naar
‘wensvraag’?
Intensiteit [vtg/u/strook]
Snelheid
[km/u]
Waargenomen intensiteit/snelheid
Gemodelleerde intensiteit/snelheid o.b.v. apriori HB matrix
Gemodelleerde intensiteit/snelheid na kalibratie op wensvraag*
De hoeveelheid ‘missend’ verkeer wordt o.b.v. vuistregels ingeschat en toegevoegd aan
de waargenomen intensiteit, in de hoop dat de kalibratie dan wel goed uit komt.
Ingeschatte wensvraag
*de gemodelleerde intensiteit/snelheid is in dit voorbeeld niet te voorspellen omdat
deze afhankelijk is van condities op omliggende wegvakken en gevoeligheid van
routekeuze

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Hoe doen we het in Noord-Brabant?
• We gebruiken STAQ om te bepalen wat de condities op omliggende wegvakken zijn
• Want netwerkcondities bepalen wat we eigenlijk meten:
• Alleen intensiteiten gemeten op blauwe en blauw/grijze wegvakken bevatten informatie over
vervoersvraag. STAQ kan met beide typen uit de voeten.
• Intensiteiten gemeten op grijze en rode wegvakken moet worden gebruikt voor netwerkkalibratie,
niet voor vervoersvraagkalibratie
Vervoersvraag
Capaciteit van stroomafwaartse bottleneck
Capaciteit van stroomopwaartse bottleneck
Mix van vervoersvraag en capaciteit van
stroomopwaartse bottleneck

First large scale application of a static matrix estimation method on observed travel times, congestion patterns and link flows

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