Junction Modelling in a Strategic
Transport Model
Wee Liang Lim
Henry Le
Land Transport Authority, Singapore
Outline
• Background
• Objective
• Overview of the LTA Strategic Transport
Model
• Review of iterative junction modelling
• Revised junction modelling
• Comparison of performance results
• Conclusions
Background
Singapore
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A city state
648 km2 area ; 4.1 mil population.
109 km rail lines (MRT/LRT), 150 km expressways
575 km major arterial roads, 1500 signalised junctions
EMME/2 Strategic Transport Model
Used widely to forecast travel demand for planning &
design of transport proposals, also calculate user benefits
Enhanced over the years
Incorporated “iterative” junction modelling in 2000
Recently revised junction modelling
Objective
• To present a review of the iterative
approach in junction modelling and its
limitations.
• To present a revised & simpler approach in
junction modelling and its improvements in
model convergence
OVERVIEW OF LTA STRATEGIC TRANSPORT MODEL
Model Inputs
Land use data
- Planning Data: population,
employment, school enrolment.
- Car ownership,
- Dwelling types & others
Model Step
Daily trip ends by purpose
Trip Generation
Trip rate data
Trip distribution functions
HIS data
Trip Distribution
HBW (highway, transit)
HBS, HBB, HBL, NHB
Daily OD matrices by mode and trip purpose
Mode Split
Mode split parameters
From HIS and SP survey
Peak hour factors by trip purpose,
mode and area
HBW, HBS, HBB
HBL, NHB
Trip distribution matrices by trip
purpose and main mode
Skims of time and cost
From assignments
- Car, m/c, Taxi
- LRT/MRT/Bus
Model Outputs
HBW (car, m/c, taxi, LRT, MRT, bus, c/o bus)
HBS (car, LRT, MRT, bus, school bus)
HBB, HBL, NHB
Peak hour matrices,
AM, PM & OP by mode
Peak Hour Factors
From HIS and traffic count data
- car, m/c, taxi
- LRT/MRT
- c/o bus, school bus
- bus
Special trip matrices
- tourist trips, airport trips
- goods vehicle trips
Network
- links, junctions
- travel time, delay functions
- transit services
Model outputs
Trip Assignment
iteration
- travel times
- highway volumes
- transit volumes
- other performance measures
for downstream analysis
(e.g. financial, economic analysis)
Junction Modelling - Iterative Approach Review
Assignment Procedure
Standard
Iterative Approach
Start
Start
Calculate movement capacity &
effective green time
Calculate
link delay
Calculate link delay
Calculate Junction delay
Assign
Traffic
Run assignment
for N iterations
Check
Convergence
Yes
END
No
Check
Convergence
Yes
END
No
Iterative Approach Review
Junction Coding
• Turn penalty (delay) function (tpf):
• User defined turn data
– UP1: 6 digits to store
1: No. of lanes
2: No. of short lanes
3: Shared lane description
4: Signal control or not
5: Opposed information
6: unused
– UP2: unopposed green time & opposed green time
– UP3: cycle time
• Extra user turn data: effective green time & capacity
Iterative Approach Review
Delay Function for Signalised Movement
3.5
Delay (minutes)
3.0
2.5
2.0
D(delay) = c/2*(1-u)2/(1-u*x)
1.5
1.0
+ 900*(x-1 + Sqr((x-1)2 + 4x/C))
0.5
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
V/C
• Delay function was based on SIDRA Formulae
• Delay = uniform delay + Overflow delay
• Function of cycle time, green split, arrival flow and
movement capacity
Iterative Approach Review
Movement Capacity
• Unopposed Movement
– Capacity = Saturation flow*green
time/cycle time
• Opposed Movement:
– Opposing movement & flow
– Effective saturation flow
– Effective capacity for opposed
movement
• Movement in a shared lane:
– Capacity is proportioned to the ratio of
its flow over total lane flow.
Iterative Approach Review
Limitation
s
3.5
Junction Delay Function
3.0
Delay (minutes)
2.5
2.0
2nd Iteration
4th Iteration
1.5
1.0
1st Iteration
0.5
3rd Iteration
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
V/C
Assignment & convergence instability. Factors identified:
(i) Steep junction delay curve
(ii) Iterative calculation of movement capacity
REVISED JUNCTION
MODELLING
Revised Approach
Objectives
• To represent realistically the junction delay in a
strategic network
• To improve model convergence and therefore
assignment stability and accuracy
Junction Modelling - Revised Approach
Assignment Procedure
Iterative Approach
Revised Approach
Start
Start
Calculate movement capacity &
effective green time
Calculate movement capacity &
effective green time
Calculate link delay
Calculate link delay
Calculate Junction delay
Calculate Junction delay
Assign
Traffic
Assign
Traffic
Check
Convergence
Yes
END
No
Check
Convergence
Yes
END
No
Revised Approach
Revised Delay Function
Junction Delay Function
Revised Delay Function
3.5
To reduce the steep gradient
of the iterative delay curve
Current delay function
3.0
Delay =
{0.25 + 0.25 (V/C)}*{c-g} for V/C <1
delay(min)
2.5
2.0
{0.5 + 1.5 (V/C-1)}*{c-g} 1 < V/C < 2
1.5
1.0
{2 + 2 (V/C - 2)}* {c-g}
2 < V/C
0.5
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
v/c
Source:
V/C < 1: uniform delay
V/C > 1: calibration of the
base model
Revised Approach
Revised & Improved Calculation of Movement Capacity
• Different base saturation flow (veh/hour)
Left
1700
Through
1960
Right
1800
• Simplified calculation for shared lane movements
Saturation flow = base saturation flow/no. movements
• Added calculation for short Lane
Saturation flow = storage length/(vehicle space* mov. green time)
(Capacity  400 veh/hr)
• Simplified calculation for opposed movement
Saturation flow = base saturation flow/3
(Capacity  200 veh/hr)
COMPARISON OF
PERFORMANCE RESULTS
Comparison of movement delays
Left Movement
50.0%
45.0%
Iterative: Ave 16.8 sec
Percentage of Junction
40.0%
35.0%
Revised: Ave 22.2 sec
30.0%
32% increase
25.0%
20.0%
15.0%
10.0%
5.0%
0.0%
0.0-0.1 0.1-0.2 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9
Delay(min)
Iterative
Revised
0.90.10
>1.0
Comparison of movement delays
Through Movement
50.0%
45.0%
Iterative: Ave 30.0 sec
Percentage of Junction
40.0%
Revised: Ave 27.0 sec
35.0%
30.0%
10% reduction
25.0%
20.0%
15.0%
10.0%
5.0%
0.0%
0.0-0.1 0.1-0.2 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9
Delay(min)
Iterative
Revised
0.90.10
>1.0
Comparison of movement delays
Right Movement
50.0%
Iterative: Ave 38.4 sec
Percentage of Junction
45.0%
40.0%
Revised: Ave 43.2 sec
35.0%
30.0%
12.5 % Increase
25.0%
20.0%
15.0%
10.0%
5.0%
0.0%
0.0-0.1 0.1-0.2 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9
Delay(min)
Iterative
Revised
0.90.10
>1.0
Comparison of network travel time
1999 Network - AM peak
Iterative Method (hrs)
Revised Method (hrs)
Difference (hrs)
% Change
Link Travel time Junction Delay
68411
13845
67409
15717
-1002
1873
-1.5%
13.5%
Total Travel Time
82255
83126
871
1.1%
Observations:
• Junction delay increased despite delay curve smoothened
• Link travel time reduction => more efficient route choice,
more converged assignment
Comparison between modelled and observed
traffic volumes
Modelled Traffic Flows VS Traffic Count Data
10000
9000
Modelled Flows 1999 (PCU/hr)
8000
7000
6000
5000
y = 0.9495x - 60.367
R2 = 0.9016
4000
3000
2000
1000
0
0
1000
2000
3000
4000
5000
6000
Traffic Count for Year 1999 (PCU/hr)
7000
8000
9000
10000
Comparison between modelled and observed
travel time
Modelled versus Observed Travel Time
60
Modelled Travel Time (mins)
50
40
y = 1.1582x + 0.2609
2
R = 0.9416
30
20
10
0
0
10
20
30
Observed Travel Tim e (m ins)
40
50
Improvement in model convergence
Comparison of model running time on the 2015 network
Stopping criteria
Unix system
(450 MHz)
Pentium 4
(2400 MHz)
Stopping Gap 0.5
Stopping Gap 0.1
Iterative Approach
34 hrs
(38)
9.5 hrs
(120)
Revised Approach
23 hrs
(30)
7.2 hrs
(94)
Difference
-32%
(-21%)
-24%
(-22%)
Note: (38) number of iterations per highway assignment
The revised approach has improved model convergence
through reducing number of iterations & running time.
Conclusion
• Junction delay is a major contributor to a journey time in an
urban network.
• Full incorporation of SIDRA to a strategic transport model
may not suitable.
• Revised and simpler approach to calculation of junction
delay was presented
• The revised model represents realistic movement delays,
travel times and traffic demand in a network.
• Model converges faster and predicts stable travel time &
saving for transport schemes.