Junction Modelling in a Strategic Transport Model

Wee Liang LimHenry 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

BackgroundSingapore

• 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

Trip Generation

Trip Distribution

Mode Split

Peak Hour Factors

Trip Assignment

Model Inputs Model OutputsModel Step

iteration

HBW (car, m/c, taxi, LRT, MRT, bus, c/o bus) HBS (car, LRT, MRT, bus, school bus) HBB, HBL, NHB

Daily OD matrices by mode and trip purpose

- travel times- highway volumes- transit volumes- other performance measures for downstream analysis(e.g. financial, economic analysis)

Model outputs

- car, m/c, taxi- LRT/MRT- c/o bus, school bus- bus

Peak hour matrices, AM, PM & OP by mode

HBW (highway, transit) HBS, HBB, HBL, NHB

Trip distribution matrices by trip purpose and main mode

HBW, HBS, HBBHBL, NHB

Daily trip ends by purpose

OVERVIEW OF LTA STRATEGIC TRANSPORT MODEL

- Planning Data: population, employment, school enrolment.- Car ownership, - Dwelling types & others

Land use data

Trip rate data

From assignments- Car, m/c, Taxi- LRT/MRT/Bus

Skims of time and cost

From HIS and traffic count data

Peak hour factors by trip purpose, mode and area

- tourist trips, airport trips- goods vehicle trips

Special trip matrices

- links, junctions- travel time, delay functions- transit services

Network

From HIS and SP survey

Mode split parameters

Trip distribution functions

HIS data

Junction Modelling - Iterative Approach

Review Standard

Calculate link delay

Assign Traffic

Start

Check Convergence

No

END

Yes

Calculate link delay

Calculate Junction delay

Calculate movement capacity & effective green time

Iterative Approach

Run assignment for N iterations

Start

Check Convergence

No

END

Yes

Assignment Procedure

Iterative Approach Review

• 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

Junction Coding

Iterative Approach Review

• Delay function was based on SIDRA Formulae

• Delay = uniform delay + Overflow delay

• Function of cycle time, green split, arrival flow and movement capacity

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4V/C

Del

ay (

min

ute

s)

Delay Function for Signalised Movement

D(delay) = c/2*(1-u)2/(1-u*x)

+ 900*(x-1 + Sqr((x-1)2 + 4x/C))

Iterative Approach Review

• 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.

Movement Capacity

Assignment & convergence instability. Factors identified:

(i) Steep junction delay curve

(ii) Iterative calculation of movement capacity

Junction Delay Function

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

V/C

De

lay

(m

inu

tes

)

Iterative Approach Review

Limitations

1st Iteration

3rd Iteration

2nd Iteration

4th Iteration

REVISED JUNCTION MODELLING

Revised Approach

• To represent realistically the junction delay in a strategic network

• To improve model convergence and therefore assignment stability and accuracy

Objectives

Junction Modelling - Revised ApproachAssignment Procedure

Calculate link delay

Calculate Junction delay

Calculate movement capacity & effective green time

Iterative Approach

Assign Traffic

Start

Check Convergence

No

END

Yes

Calculate link delay

Calculate Junction delay

Calculate movement capacity & effective green time

Revised Approach

Assign Traffic

Start

Check Convergence

No

END

Yes

Revised Approach

To reduce the steep gradient of the iterative delay curve

Junction Delay Function

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 v/c

dela

y(m

in)

Current delay function

Revised Delay Function

Revised Delay Function

Delay = {0.25 + 0.25 (V/C)}*{c-g} for V/C <1 {0.5 + 1.5 (V/C-1)}*{c-g} 1 < V/C < 2 {2 + 2 (V/C - 2)}* {c-g} 2 < V/C

Source:V/C < 1: uniform delayV/C > 1: calibration of the base model

Revised Approach

• Different base saturation flow (veh/hour)

Left Through Right

1700 1960 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)

Revised & Improved Calculation of Movement Capacity

COMPARISON OF PERFORMANCE RESULTS

Comparison of movement delays

Left Movement

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

35.0%

40.0%

45.0%

50.0%

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 0.9-0.10

>1.0

Delay(min)

Perc

en

tag

e o

f Ju

ncti

on

Iterative Revised

Iterative: Ave 16.8 sec

Revised: Ave 22.2 sec

32% increase

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

35.0%

40.0%

45.0%

50.0%

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 0.9-0.10

>1.0

Delay(min)

Per

cen

tag

e o

f Ju

nct

ion

Iterative Revised

Iterative: Ave 30.0 sec

Revised: Ave 27.0 sec

10% reduction

Through Movement

Comparison of movement delays

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

35.0%

40.0%

45.0%

50.0%

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 0.9-0.10

>1.0

Delay(min)

Perc

en

tag

e o

f Ju

ncti

on

Iterative Revised

Iterative: Ave 38.4 sec

Revised: Ave 43.2 sec

12.5 % Increase

Right Movement

Comparison of movement delays

Comparison of network travel time

1999 Network - AM peak

Link Travel time Junction Delay Total Travel TimeIterative Method (hrs) 68411 13845 82255Revised Method (hrs) 67409 15717 83126Difference (hrs) -1002 1873 871% Change -1.5% 13.5% 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

Comparison between modelled and observed travel time

Improvement in model convergence

Comparison of model running time on the 2015 network

The revised approach has improved model convergence through reducing number of iterations & running time.

Unix system(450 MHz)

Pentium 4(2400 MHz)

Stopping criteria

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

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.