Time of Day and
Demand equilibrium in
large scale models
7-10-2016
Kobus Zantema
European Transport Conference
Contents
 Introduction
 Challenges
 Departure Time Choice Model
 Results of the Departure Time Choice Model
 Equilibrium Results on 3 Levels
 Conclusions
2
Introduction in BBMA
Audit 2014:
“Improve the model by including departure time choice and adding congestion
modelling”
The BBMA is: 1 consistent model system, with 1 main traffic model, modelled in
more detail in the 5 (and after the new update 6) regional models
3
4-step model
SocioData
1.Trip Choice TripGenerationModel
Departures and
Arrivals per zone
2. Mode Choice
3. Destination Choice
Gravity Model (ZKM)
OD Matrices per mode
4. Route Choice
Static Equilibrium
Multirouting
Assignment
Static AON
Assignment
Assignment
Link Flows, Link Speeds
Section/line-passenger
Section/line-speeds
Cycling Flows and
Speeds
Travel times per OD
(skim matrix)
4
4
Challenges
SocioData
 Queuing
 Departure time choice
 Convergence
1. Trip Choice TripGenerationModel
 ‘Back to the rush
Arrivals and departures
per zone
hour’-effect
2. Mode Choice
3. Destination Choice
Gravity Model (ZKM)
OD matrices per mode
4. Route Choice
Static Equilibrium
STAQ
Multirouting
Assignment
Static AON
Assignment
Assignment
Departure Time
Choice Model
Travel Times per OD
(skim matrix)
Link Flows, Link Speeds
Section/line-passenger
Section/line-speeds
Cycling Flows and
Speeds
5
Challenges2
 Adding an assignment model which includes explicit modelling of congestion
(not part of this presentation – see paper from Luuk Brederode, ETC 2016)
 Adding a departure time choice model, and finding which departure time
choice model
 Checking all iterative procedures for convergence
6
Departure Time Choice Model
Due to congestion, someone may decide to depart early or late
The model uses a preferred depart and arrival time (determined using OViN)
Deviation from these preferred time, as well as travel time are used as costs in a
utility calculation
7:00
8:00
9:00
7
Shift from the peak hour
Comparison departure and arrival times Noord-Brabant
3,50%
3,00%
2,50%
2,00%
prefered departure (arrival - ff tt)
prefered arrival (OViN)
1,50%
actual departure (OViN)
1,00%
0,50%
0:00
0:45
1:30
2:15
3:00
3:45
4:30
5:15
6:00
6:45
7:30
8:15
9:00
9:45
10:30
11:15
12:00
12:45
13:30
14:15
15:00
15:45
16:30
17:15
18:00
18:45
19:30
20:15
21:00
21:45
22:30
23:15
0,00%
Peak period AM
PM
Shift
1.36%
1.35%
8
‘Back-to-the-rush-hour’ effect
 Case study near congested location of Rosmalen
 In the reference situation, 61 vehicles, passing this
location, shift from the evening peak
9
‘Back-to-the-rush-hour’ effect
 Case study near congested location of Rosmalen
 In the variant we solve the bottleneck near
Rosmalen (still other bottlenecks exist in the
network)
 In the variant, 24 vehicles, passing this location,
shift from the evening peak
10
Departure Time Choice Model Results
11
Departure Time Choice Model Results
12
Network Model
13
Equilibrium – Assignment model
Duality Gaps alle runs + Qblok
100
10
1
0:00:00
0:30:00
1:00:00
1:30:00
2:00:00
2:30:00
3:00:00
3:30:00
4:00:00
4:30:00
5:00:00
5:30:00
0.1
0.01
0.001
0.0001
0.00001
0.000001
0.0000001
MSA-NoJM-NoSpillb
MSA-Delays-NoSpillb
MSA-JM-NoSpillb
MSA-NoJM-Spillb
MSA-Delays-Spillb
SRA-NoJM-NoSpillb
SRA-Delays-NoSpillb
SRA-JM-NoSpillb
SRA-NoJM-Spillb
SRA-Delays-Spillb
1E-08
1E-09
1E-10
1E-11
1E-12
1E-13
14
Equilibrium - ToD
•
•
iteration Morning peak Evening peak
The convergence of the
Time of Day module
In the 5th iteration the
maximum difference for
one relation, compared to
iteration 4, is
approximately 16 seconds
(evening peak)
total
2
0,028973
0,107573
0,079971
3
0,002701
0,016381
0,01126
4
0,000287
0,004201
0,002748
5
3,25E-05
0,001302
0,000829
6
3,75E-06
0,000345
0,000218
7
4,33E-07
0,000104
6,53E-05
8
3,98E-08
3,29E-05
2,07E-05
9
2,29E-09
1,07E-05
6,72E-06
10
1,89E-09
3,53E-06
2,22E-06
11
1,7E-09
1,18E-06
7,39E-07
12
1,69E-09
3,78E-07
2,38E-07
13
1,7E-09
1,21E-07
7,66E-08
14
1,69E-09
4,38E-08
2,81E-08
15
1,7E-09
1,37E-08
9,21E-09
16
1,69E-09
1,51E-09
1,57E-09
17
1,7E-09
2,18E-09
7,35E-10
18
1,69E-09
1,24E-09
1,54E-10
19
1,7E-09
1,98E-10
7,57E-10
20
1,69E-09
1,27E-09
1,43E-09
15
Equilibrium – Demand - Supply
16
Conclusions
 The proposed departure time choice model leads to an adequate amount of
traffic shifting from the rush hour
 When a bottleneck is removed, the ‘back-to-the-rush-hour’ effect is shown
 All three model converge relatively quickly, allowing for all three models to
run alongside each other within acceptable calculation time
17
Questions?
18