PhD summary of Luuk Brederode, presented at 2023-10-17 to Veitch Lister Consultants

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Incorporating congestion phenomena into large scale strategic
transport model systems
Summary PhD research
Luuk Brederode 2013-2023
Summary PhD research Luuk Brederode
1
Presentation for VLC
2023-10-17
woensdag 13 maart 2024

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Contents
1. Relevance of the research / Introduction to Static Traffic Assignment with Queuing (STAQ)
(12 slides)
2. Positioning of STAQ and its Semi-Dynamic version (7 slides)
3. Matrix Adjustment using STAQ (16 slides)
4. SDTAQ - Semi dynamic version of STAQ (11 slides)
Summary PhD research Luuk Brederode 2

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1. Relevance of the
research / Introduction to
STAQ

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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

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Q1: What 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 some* dutch
strategic transport models?
woensdag 13 maart 2024 9
Because the 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]
Currently, STAQ is used in the Urban/regional models of: Eindhoven, Tilburg, Breda, Den Bosch, Noordoost
Brabant, West-Brabant, Arnhem, Nijmegen, Purmerend, the province of Overijssel, province of Noord-Brabant

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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

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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
from: Brederode et al (2019)

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1
2
4
4
3
5
6
3
4
1
2
Assignment results capacity restrained
Assignment results capacity constrained
Legend:
Bandwidths: flows (veh/h AM peak)
Colours: speed (as percentage of max speed)
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
from: Brederode et al (2019)

This also has its effects on societal cost-benefit
analysis!
13
For illustrative purposes, the annual societal value of the travel-time savings during the morning peak hour induced
by the network variant is calculated. Following Kouwenhoven et al. (2014), we assume an average value of time of
€9 per hour and an average reliability ratio of 0.6. Furthermore, we assume that per year 260 of these average
morning peak hours occur. This means that the annual societal value of the network variant would
approximately be € 240,000 according to the STA model output and € 500,000 according to the STAQ
output, an increase of 108%. These findings show that choosing an assignment method that accounts for flow
metering and spillback effects has substantial effects on the outcomes of a cost–benefit analysis for study areas
with structural congestion.
From: Brederode, L., Pel, A.J., Wismans, L., de Romph, E., Hoogendoorn, S.P., 2019. 'Static Traffic Assignment with Queuing: model properties and
applications'. Transportmetrica A: Transport Science 15(2), pp.179–214. https://doi.org/10.1080/23249935.2018.1453561

Convergence and computational requirements
models used for testing
Source: chapter 3 of my PhD thesis:
https://research.tudelft.nl/en/publications/incorporating-congestion-phenomena-into-large-scale-strategic-tra
14

Analysis (stopcriterion: relative duality gap < 1E-04)
15
Source: chapter 3 of my PhD thesis:
https://research.tudelft.nl/en/publications/incorporating-congestion-phenomena-into-large-scale-strategic-tra

Rules of thumb based on applications on these models
STAQ:
• is about 3-8 slower then a traditional (capacity restrained) static traffic assignment model
• is about 500-1200 times faster than a (macroscopic) dynamic traffic assignment model
• computation time scales proportional to the number of routes:
•Models upto 6102 TAZ where successfully run on a quadcore i7 2.67 Ghz, 4Gb laptop (my machine in 2015 ;))
•~1.25 Gbytes of memory required for every million routes
•Upto 3 minutes of additional calculation time per iteration required for every million routes
• requires around 20-30 iterations to reach a relative duality gap value of 5E-04.
•Equilibrium conditions upto 1E-05 can be reached, at the cost of (relatively many) more iterations
pagina 16

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Q&A on the first part
2023-10-17
slideshare.net/LuukBrederode
researchgate.net/profile/Luuk-Brederode
lbrederode@dat.nl / +31 (0) 6 27 36 98
30

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2. Positioning of
STAQ and its Semi-
Dynamic version
18

Classification Framework for Macroscopic
Strategic Traffic Assignment Models
Static
Semi-dynamic
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 assumptions
Temporal
assumptions
-least realistic
-most scalable / fastest
-most favorable mathematical properties
-most realistic
-least scalable / slowest
-most unfavorable mathematical properties
19

Spatial assumptions
Adopted from:
Brederode, L., Pel, A.J., Wismans, L., de Romph, E., Hoogendoorn, S.P., 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
Capacity
Restrained
Capacity
Constrained
Capacity & Storage
Constrained
Link model
Node model None (no queues, no spillback) Existent (queues, no spillback) Existent (queues, spillback)
20

Restrained
Capacity
Constrained
Capacity & Storage
Constrained
Static
Classification Framework
Semi-dynamic
Unsensitive for
congestion
Cong. influences
Route choice
+Queues due to
congestion
+spillback due to
congestion
‘All-Or-Nothing’
(Dijkstra, 1959)
‘Static Equillibrium’
(Beckmann et al, 1956)
Dynamic
‘STAQ squeezing’
(Brederode et al, 2019)
‘STAQ queuing’
(Brederode et al, 2019);
Bliemer and Raadsen 2020
Spatial assumptions
Temporal
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.
21

Temporal assumptions
Adopted 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.
Modelled Demand
‘True’ Demand
Variability
of demand
Traffic transfer None Residual traffic only All traffic conditions
Static Semi-Dynamic Dynamic
22

Restrained
Capacity
Constrained
Capacity & Storage
Constrained
Static
Starts with
empty network
Semi-dynamic
Unsensitive for
congestion
Cong. influences
Route choice
+Queues due to
congestion
+spillback due to
congestion
(Dijkstra, 1959)
‘Macroscopic Dynamic’
(CTM, Daganzo (1994);
LTM, Yperman (2007))
Dynamic
‘STAQ queuing’
‘SDTAQ squeezing’
‘SDTAQ queuing’
Spatial assumptions
Temporal
assumptions
Starts with
residual traffic
from previous
period
Start with
network
conditions from
previous period
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.
For these models, the
user equillibrium cannot
be computed (and it might
not even exist – Dafermos
1980)
23

Restrained
Capacity
Constrained
Capacity & Storage
Constrained
Static
Classification framework
On special request by Tom van Vuren: positioning of ‘hybrid’ models used in practice
Semi-dynamic
Dynamic
QBLOK network loading heuristic
PTV blocking back network loading heuristic
Spatial assumptions
Temporal
assumptions
Framework
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.
SATURN assignment model
QBLOK assignment model
PTV ICA assignment model
SATURN network loading heuristic
24

Input parameters need to be
set by trial and error
Comparison hybrid approaches to STAQ
25
Two types of flow output
(‘processed’ vs ‘demand’)
Hybrid
Heuristic
Not consistent with traffic flow
and queuing theory
Capacity +
Storage
constrained
Cannot reach user equillibrium
conditions
Includes spillback
(Differences in) output
poorly traceable
Capacity
constrained
Can reach user equillibrium
conditions
Consistent with traffic flow and
queuing theory
Input parameter values are
estimated on observed data
One type of flow (‘processed’)
+ queues
One model
Spillback only as post-
processing
(Differences in) output
easily traceable
Hybrid approaches STAQ and S-DTAQ

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Q&A on the second part
2023-10-17
30

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3.Matrix adjustment in
strategic transport models
New opportunities when using STAQ
27

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Introduction in (traditional) matrix adjustment
Upper level: OtMatrixEstimation
Minimize differences between
modelled and observed link flows
Observed
Link flows
OD matrix
Lower level: Assignment
Determine relationships between
OD-demands and link flows
Intercept information

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Matrix Adjustment with STAQ and
‘Multi-Source-Matrix-Calibration’ (MSMC)
Upper level: MSMC
Minimize differences between
modelled and observed link
flows, delays and queue locations
OD matrix
Lower level: STAQ
Determine relationships between
OD demands and link flows,
delays and queue locations
Intercept information
Observed
queue locations
Observed travel
times or delays
Observed
Link flows

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A comparison of matrix adjustment methods
Tool Implementatie
Can include observed: Takes into account:
Link flows Travel
times or
delays
Queue
locations
Blocks in
the matrix
Turncapacities
from junction
modelling
Independence
of order of
observations
1 OtMatrixEstimation
In OmniTRANS
(c++)
*
2 SigKal
Standalone
(dotNet)
*
3 Static OD Adjustment In Aimsun Next
4 T-flowFuzzy In VISUM (c++) *
5 MSMC Matlab + Ruby
6
OtMatrixEstimation
revised
In OmniTRANS
(c++)
*
* using exogenously estimated ‘link demand’ values
• Three matrix adjustment methods developed by DAT.Mobility:

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A comparison of matrix adjustment methods
Tool Implementatie
Can include observed: Takes into account:
Link flows Travel
times or
delays
Queue
locations
Blocks in
the matrix
Turncapacities
from junction
modelling
Independence
of order of
observations
1 OtMatrixEstimation
In OmniTRANS
(c++)
*
2 SigKal
Standalone
(dotNet)
*
3 Static OD Adjustment In Aimsun Next
4 T-flowFuzzy In VISUM (c++) *
5 MSMC Matlab + Ruby
6
OtMatrixEstimation
revised
In OmniTRANS
(c++)
*
• We would love to include these other methods in our comparison (but this requires licenses
and a (non-subjective) client…)
*using exogenously estimated ‘link demand’ values
• Drie eigen matrixkalibratie methoden vergeleken:

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Testbed: network and prior OD matrix: provincial
model of Noord-Brabant
1.580.764
3.920.406
OD pairs >0
Routes
145.269 Link
103.045
17.632
Nodes
Defined
Junctions
The Noord-Brabant study area contains:
• 2.5 mln inhabitants
• 4 ‘large’ cities (for dutch standards)
Comparison of study area size to Brisbane region:
Comparison picture generated using http://www.mapfrappe.com/

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Testbed: observed link flows
448 counts on major roads
Official set for the AM peak
from the provincial model of
Noord-Brabant 2015-S107

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Testbed: observed link flows
Deviations prior to matrix adjustment
More over- than underestimations
Larger overestimations
Well known-phenomenon due to
underrepresentation of trips in
survey data

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Testbed: 8 routes with observed delays
Uden – A326
A326 - Uden
A16 - Tilburg
Helmond – Den Bosch
Waalwijk – A2
Uden – Eindhoven
Tilburg - Eindhoven
Weert - Eindhoven

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Testbed: 8 routes with observed delays

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Testbed: 16 queue locations

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Results matrix adjustment (summarized)
Units
Flows
Average absolute difference as percentage
from observed link flows
Delays
Average absolute difference as percentage
from average observed delay
Queue locations
Percentage of observed queue locations that is
missing in final assignment results
Prior OD matrix
Sum of absolute differences per distance class
in percentage points
Flows
Delays
Queue
locations
Prior OD
matrix

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Results: fit on observed link flows
MSMC
OtMatrix
Estimation
-Rev
OtMatrix
Estimation

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Results: fit on observed delays
MSMC OtMatrix
Estimation
-Rev
OtMatrix
Estimation

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Results: fit on observed queue locations
Not on this node, but large
queues in upstream node
Queue present in
some iterations, but
not in final
assignment
MSMC
OtMatrix
Estimation
-Rev
OtMatrix
Estimation

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Results: differences with Prior OD matrix
MSMC
OtMatrix
Estimation
-Rev
OtMatrix
Estimation

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Results: computation time
• Lower level (the assignments) require similar amounts of computation time when
normalized to the number of iterations (==assignments)
• Large differences in computation time spent in the upper level (the solver). The MSMC
solver is much slower. Causes:
• It solves a more complicated optimization problem (due to inclusion of queues and delays)
• Queues are included as constraints to the optimization problem
• Implementation is not yet optimized (Matlab + Ruby using file based interfacing)

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Conclusions
• STAQ explicitly models queues and hence realistic delays
• This yields more realistic assignment results, but also offers the opportunity to include
observed delays / speeds and queue locations
• Based on literature research, six matrix adjustment methods where methodologically
compared
• This shows that MSMC is the only method that can include observed delays and is able to
directly include queue locations (no exogenous ‘link demand’ estimation required)
• Three matrix adjustment methods in use by Goudappel where tested on the provincial
model of Noord-Brabant
• This shows that the methods fit similarly on observed link flows, queue locations and the
prior OD matrix, but that MSMC is the only method that fits well to observed delays 44

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Q&A on the third part
2023-10-17
30

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4. Semi-Dynamic
version of STAQ
46

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Restrained
Capacity
Constrained
Capacity & Storage
Constrained
Static
Starts with
empty network
Semi-dynamic
Unsensitive for
congestion
Cong. influences
Route choice
+Queues due to
congestion
+spillback due to
congestion
(Dijkstra, 1959)
‘Macroscopic Dynamic’
(CTM, Daganzo (1994);
LTM, Yperman (2007))
Dynamic
‘STAQ queuing’
‘SDTAQ squeezing’
‘SDTAQ queuing’
Spatial assumptions
Temporal
assumptions
Starts with
residual traffic
from previous
period
Start with
network
conditions from
previous period
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.

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Implementation semi-dynamic version of STAQ
48
Run STAQ until
equillibrium Queues 𝐐𝑘 in user
equillibrium
Equilibrium link inflows 𝐮𝑘
Transfer residual traffic
Total travel demand
(𝐃𝑘+1 + 𝐐𝑘) and RouteSet
(𝐏𝑘+1) next time period
Travel demand for next
time period (𝑫𝒌+𝟏)
Route Fractions in user
equillibrium
RouteSet 𝐏𝑘
𝑘: = 𝑘 + 1
Transfer residual traffic from
queues to next time period
• Transferred traffic ‘departs’ from
the first upstream link to the queue
• When needed, routes between this
point and original destinations are
added
For each period
Run STAQ until
equillibrium
Simplified from: Brederode, L., Gerards, L., Wismans, L., Pel, A., Hoogendoorn, S., 2023. 'Extension of a static into a semi-dynamic traffic assignment
model with strict capacity constraints'. Transportmetrica A: Transport Science 0(0), pp.1–34. https://doi.org/10.1080/23249935.2023.2249118

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Application on provincial model of Noord-Brabant
1.580.764
3.920.406
OD-pairs>0
Routes
145.269 Links
103.045
17.632
Nodes
Junctions
Picture adapted from: Brederode, L., Gerards, L., Wismans, L., Pel, A., Hoogendoorn, S., 2023. 'Extension of a static into a semi-dynamic traffic
assignment model with strict capacity constraints'. Transportmetrica A: Transport Science 0(0), pp.1–34.
https://doi.org/10.1080/23249935.2023.2249118
49

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Derivation of hourly matrices
• 24h period matrix split up to 24 x 1 hour matrices using trip purpose specific hour
fractions derived from observed departure times in (OViN-)survey data:
50

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Legend:
Bandwidths: flows [pcu/h]
Colour: speed relative to speed limit [%]
Pie charts: Size of vertical queues
80% 100%
0%
51

- woensdag 13 maart 2024

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Comparison collective loss (vehicles * hours)
0
5000
10000
15000
20000
25000
30000
35000
40000
7:00
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
Collective
loss
[veh*h]
Simulation time
Static TA model
Network operator's perspective
Traveller's perspective
0
5000
10000
15000
20000
25000
30000
35000
40000
7:00
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
Collective
loss
[veh*h]
Simulation time
Semi dynamic TA model
Network operator's perspective
Traveller's perspective
Static TA model Semi-dynamic TA model Difference
Period collective loss Period collective loss absolute relative
AM peak 07:00 - 10:00 42554 07:00 - 11:00 74774 32220 76%
PM peak 16:00 - 19:00 35156 16:00 - 19:00 44560 9404 27%
24h period 00:00 - 24:00 77710 00:00 - 24:00 119334 41624 54%
Adopted from: Brederode, L., Gerards, L., Wismans, L., Pel, A., Hoogendoorn, S., 2023. 'Extension of a static into a semi-dynamic traffic assignment model with strict
capacity constraints'. Transportmetrica A: Transport Science 0(0), pp.1–34. https://doi.org/10.1080/23249935.2023.2249118

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Comparison of STAQ and its semi-dynamic
counterpart on the BBMB
Conclusions with respect to realism:
• The semi-dynamic version relaxes the empty network assumption. This yields more travel demand
and collective travel time losses during time periods to which residual traffic has been transferred.
• On the BBMB this means up to 76% more collective loss (veh*h) and (mainly AM-) peak spreading
• On 24h level, the semi-dynamic version yields 54% more collective loss.
• These substantial differences indicate that the empty network assumption in static traffic
assignment models causes a severe underestimation of delays.
• It is therefore very likely that the empty network assumption in static TA models influences (policy)
decisions based upon queue size and delay related model outcomes on congested networks.

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Effect of shift from static to semi dynamic on
computation times and convergence
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Calculation
time
[hh:mm]
Simulation timeperiod
Grafiektitel
Semi Dynamic (assignment) Semi Dynamic (traffic transfer) Static
Static Semi-dynamic Difference
Assignment Assignment Traffic transfer Total
Average 6h-20h 01:14 01:21 00:31 01:53 51%
Total 6h-20h 17:27 19:06 07:19 26:26 51%
Total 24h 28:33 30:13 07:29 37:43 32%
Numbers above bars indicate the #iterations required to reach equillibrium (Duality Gap < 1E-04)
Computational times in [hh:mm]
on a AMD Ryzen 9 3900X @3.79
Ghz with 128GB of RAM
Adopted from: Brederode, L., Gerards, L., Wismans, L., Pel, A., Hoogendoorn, S., 2023. 'Extension of a static into a semi-dynamic traffic assignment model with strict
capacity constraints'. Transportmetrica A: Transport Science 0(0), pp.1–34. https://doi.org/10.1080/23249935.2023.2249118
Up to +16% for assignment
Up to +50% for traffic transfer

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Comparison of STAQ and its semi-dynamic
counterpart on the BBMB
Conclusions with respect to computation time and convergence:
• The semi-dynamic version converges within reasonable time, so it is usable in the strategic context
• In congested time periods, the semi-dynamic model requires on average 51% more calculation time,
predominantly spent by the traffic transfer module
• But note that the STAQ implementation is optimised C++ code, whereas the residual traffic transfer
module is a prototypical implementation in Ruby using file-based data exchange with the
assignment model.
• Therefore, it is expected that the calculation time for the traffic transfer module will drop to less
than 10% when it would be merged into the STAQ codebase.

-
Opportunities of semi-dynamic STAQ that are yet
to be explored…
• Pair semi-dynamic STAQ with the matrix estimation method from Brederode et al. 2023*
yielding a whole day estimation process, allowing to include observed flows, delays, and
congestion patterns on any temporal aggregation level.
• Pair semi-dynamic STAQ with a departure time choice model to model peak spreading in
strategic context
• Further approximate dynamic models by shortening period duration lengths in busy time
periods
*Brederode, L., Pel, A.J., Wismans, L., Rijksen, B., Hoogendoorn, S.P., 2023. 'Travel demand matrix estimation for strategic road traffic assignment models with strict
capacity constraints and residual queues'. Transportation Research Part B: Methodological 167, pp.1–31. https://doi.org/10.1016/j.trb.2022.11.006
73

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31. https://doi.org/10.1016/j.trb.2022.11.006 woensdag 13 maart 2024

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