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Paper 4
Authors: Jason, Zhou Jingsong, Dr. Brian Vaughan, Oscar Faber Consultants
Title: JUNCTION MODELLING IN EMME/2
Abstract : In an urban environment like Singapore, the capacity and delay of a road network are usually
controlled by the performance of its junctions. As part of the model enhancement project in 1998, the Land
Transport Authority of Singapore planned to switch from a link based to a junction based modelling approach
in order to represent realistically the performance of the road network. The paper presents an iterative
approach for highway assignment taking into account the delay of turning movements at signalized junctions
using EMME/2. A conical type of turn penalty function is presented. Differences in the departure
characteristics of shared lanes are discussed such as blocking in a shared lane due to different periods of
green time, and opposed right turns (for left-hand drive). The convergence and a comparison of run-time
overhead for a large-scale network between the link and junction based approach are also presented.
Introduction
During the last decade Singapore has seen a rapid growth in car usage. This has resulted in the
expansion of the highway network and traffic control system. There are now about 1500 signalised
junctions in Singapore, which are mostly connected to GLIDE, a signal control system. The delays at
junctions are a critical factor in travel times for all road based traffic, as well as pedestrians. Historically
the Singapore strategic travel demand model has used a link based delay formulation that estimates
the junction delay based on a constrained link capacity determined from the type of downstream
junction. While such an approach is adequate for the assessment of the expressway system it is a
simplification in a highly urbanised environment, and does not reflect the accurate representation of
turning movement constraints at junctions.
As part of the model enhancement, the Land Transport Authority of Singapore (LTA) has recently
redeveloped the highway assignment module to reflect the junction constraints accurately and for each
movement at the junction. The aim of this paper is to describe an assignment approach that calculates
the junction delays separately and iteratively. It is called the iterative approach. The paper highlights
differences between this approach and the normal assignment method, and the treatment of
complicated junction situations using efficient macro capabilities of EMME/2.
The paper first presents the general approach of the new highway assignment. It then describes
improvements to the turn penalty function. The mechanism to calculate the capacity and the effective
green time for a turning movement in various situations is explained. The stopping criteria,
convergence, runtime overhead and a comparison between the link based and this approach will also
be discussed.
GENERAL APPROACH
Figure 1 below shows the general approach of the new highway assignment module of the strategic
transport model. Basically, the approach involved calculating the capacity and effective green time for
each movement in the network, which are then fed into a turn penalty function to calculate the
movement delay. The equilibrium assignment process will use the movement delay plus link delay to
assign link and turning flows which are in turns used to calculate the capacity and effective green time
in the next iteration. The iterative process is described in steps as below.
Step 1. The model calculates the capacity and effective green time of turning movements using the
EMME/2 network calculation module. The calculation is based on the free flow condition with no
opposing flow. The capacity of a shared lane is equally split among the sharing movements.
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Figure 1. Flow Chart of Iterative Highway Assignment
Module
Step 1. Calculate initial turn capacity and
effective green time for each turning
movement.
Step 3. Recalculate turn capacity and effective
green time for each turning movement using
the last assignment results. This involves
calculating opposing flow and the treatment of
various shared lane situations.
Step 2. Start the highway
assignment for N iterations
1.1.1.1.1.1N
Stopping Criteria
Satisfied?
Yes
o
Step 4. Continue to run highway
assignment for N more iterations.
Stop
Step 2. The model starts the multi-class equilibrium highway assignment for N iterations (in this module
2 iterations are adopted).
Step 3. The model checks whether the stopping criteria are met. If yes, the run will be terminated.
Otherwise it proceeds to recalculate the turn capacities and effective green times taking into account
the latest assigned result. This involves the calculation of the opposing flow and volume of turning
movements using a shared lane. Two extra turn attributes are used to store the newly calculated
movement capacity and effective green time, and update the turn penalty functions.
Step 4. The assignment preparation module is called and the option of continuing to run the highway
assignment with N more iterations is selected.
The model then goes back to the step 3. This loop will repeat until one of the stopping criteria is
reached. A set of macros has been created to carry out the whole process automatically in EMME/2.
To illustrate the approach, the next section will present relevant input data for junctions. The paper will
then discuss the turn penalty function adopted for the calculation of movement delay. The subsequent
sections will describe in details formulations used to calculate movement capacity under various
situations such as opposed flow, shared lane and combinations.
JUNCTION INPUT DATA
As part of the model enhancement, a major exercise was carried out to code junction data for all
signalised junctions in Singapore to the new highway network. Input data describing the junction
layout, lane discipline, phasing and signal timings obtained from the GLIDE system were coded into
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three user attributes, up1, up2 and up3 for each movement. Appendix 1 describes these input data in
details.
Up1 contains 6 digits used to store detailed lane layout and discipline for a movement in the following
order:
.
1st digit: number of lanes,
.
2nd digit: number of short lanes,
.
3rd digit: shared lane description,
.
4th digit: flag for signal control,
.
5th digit: opposed information,
.
6th digit: reserved for future use.
Up2 also contains 6 digits. The first three digits store the unopposed green time, while the next three
store the opposed green period. If the movement is not opposed only the first three digits are used.
Up3 contains the cycle time in seconds for the junction.
TURN PENALTY FUNCTION
Turn penalty function is used to calculate delay of each movement at junction. The general delay
formulations are based on SIDRA method (Akcelik, 1981 & 1990). The method was chosen to maintain
consistency with the practices adopted in LTA for detailed junction analysis, and also its methodology is well
documented and widely accepted.
The function adopted is of conical type. Its curve is close to a straight line when the degree of saturation,
x, is low, and asymptotically close to the deterministic line of over saturation flow when x reaches near and
beyond 1.0. This type of turn penalty functions is actually derived from a more general function form, which
embraces those delay function used in the Highway Capacity Manual, Canadian and Australian methods or
SIDRA (Akcelik, 1990)
This function has two delay components, the uniform delay and the overflow delay as below:
D = Du + D0
Where:
D - total delay of a turning movement in seconds,
Du - uniform delay in seconds, and
D0 - overflow delay in seconds.
The uniform delay Du is formulated as
c * (1-u) 2
Du = 
2 * (1 - u * x)
Where:
c – cycle time in seconds,
u – green ratio (equal to the movement green time divided by cycle time) ,
x – degree of saturation which is the ratio of arrival flow to capacity, and
x = (qc)/(sg) where
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q - movement arrival flow, and
s - base saturation flow.
The overflow delay D0 has the following form:
D0 = 900 * Tf *
z +
4*x
z + 
(Q * Tf )
2
Where:
Tf - simulation period in hours, currently set as 1,
Q - movement capacity (vehicles/hour)
x - degree of saturation of the movement, and
z = x –1.
This turn penalty functions is expected to estimate realistically the delay when the degree of saturation,
x, is closer to 1.0.
The movement capacities and effective green times, which are input to the turn penalty function, are
not fixed during the assignment process, but recalculated every time at the end of N iterations. They
form the base values for the next N iterations of assignment. The process continues until the stopping
criteria are reached. This can be done as part of the new feature of the EMME/2 Release 9. Extra turn
attributes can now be passed into turn penalty functions through three parameters, ep1, ep2 and ep3.
Even when the values of these extra turn attributes have been changed, the option of continuing the
highway assignment with more iterations is still available without the need to restart it from the very
beginning.
CAPACITY of AN Opposed MOVEMENT
The capacity of a right turn, for example, opposed by an opposing through movement is not fixed, but
will decrease if the opposing through flow increases and vice versa. Therefore it is necessary to
determine the opposing flow for each turning movement. As part of the highway network enhancement,
nodes were coded to reflect the true geographic locations of the junctions they represent. And series of
links were used to match the curve of a winding road. With this recoded highway network, it is possible
to calculate the flows of the opposing movements automatically according to their relative positions to
the opposed movement. A macro called OPPVOL.MAC created by Heinz Spiess (1994), and with
some modifications, was adopted in the new model to calculate opposing flows and save them into the
turn attributes of the opposed movement.
The saturation flow So and effective green time Go of an opposed movement during the opposed
period can be calculated using the traditional gap acceptance approach (Akcelik, 1981) as below:
q * exp( -  * q )
So = 
exp( -  * q )
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Where:
So – Effective saturation flow for the green period during which the movement is opposed
(vehicles/seconds),
q - Opposing flow (vehicles/second),
 - Critical gap (default = 4.5 seconds), and
 - Follow-up headway (default = 2.6 seconds).
And
(s*g-q*c)
Go
=
=

(s-q)
0
when x < 1 (or sg >qc) and
when x >=1
Where:
Go - Effective green time in seconds,
s - Opposing movement saturation flow (vehicles/second),
q - Opposing flow rate (vehicles/second),
g - Green time (seconds), and
c - Cycle time (seconds).
So the effective capacity of the opposed movement Qu can be calculated as:
( S0 * G o + s * g 1 )
Qu= 
c
Where:
S0 - effective opposed saturation flow,
Go - effective opposed green time,
s - base saturation flow per lane, and
g1 - green period in seconds during which the movement is not opposed by any opposing flow.
And the effective green time Gu for the movement during the whole cycle time will be
c * Qu
Gu= 
s
The effective capacity Qu and effective green time Gu of the movement will be fed into the turn penalty
function for the calculation of the movement delay.
SHARED LANE ISSUES
It is common that two movements may share a lane at a signal-controlled junction. Figures 1 and 2
below show an example of a complicated shared lane case. As shown in Figure 2, the right turn movement
has to filter through the opposing traffic in phase B and its green time is effectively reduced to Go.
Consequently the through traffic may be blocked by the right movement in the second phase and thus loses
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the capacity. The lane interaction method (Akcelik, 1990) was applied to solve this problem. This example is
used to illustrate how this situation is dealt with in the new model.
Figure 1. Example Of An Opposed and Shared Lane
Signal Phasing
1
2
1
2
3
A
B
In this example, the movements 1 and 2 share a same approaching lane.
They both have the right of way in both phases, but the right turn is opposed
by the through traffic in the phase B.
FIGURE 2. APPLICATION OF THE LANE INTERACTION METHOD
Opposing flow (3)
A
g2
B
C
Phase
Right turn (2)
Shared
lane
Go
Through traffic (1)
g1
g2
c
Green Time
Red Time
In order to apply the lane interaction method the movement flows that actually use this lane need to be
calculated. The current model adopts the following method.
Firstly the portion of a movement flow that uses the shared lane, q si needs to be calculated.
qi
qsi = 
(2 * ni - nsi)
Where:
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i - movement indicator (1 for through traffic and 2 for right turn),
qsi - part of the movement flow in the shared lane only,
qi - total flow of movement i,
ni - number of lanes including shared lanes for movement i, and
nsi - number of shared lanes for the movement i.
Secondly the proportion of each movement flows in the shared lane, p i is calculated.
qsi
pi = 
 qsi
Where:
pi – flow proportion of movement i in the shared lane, and
qsi - same as above.
And  pi = 1.
The capacity of the shared lane in the common green phase A, Qa can be calculated as:
s * g1
Qa = 
c
Where:
s - basic saturation flow per lane,
g1 - common green time in the phase A , and
c - cycle time.
During the green period Go in the phase B, the capacity of the shared lane Qb1 is calculated as:
(p1 * s + p2 * So) * go
Qb1 = 
c
Where:
p1 - proportion of the through traffic in the shared lane,
p2 - proportion of the right turning movement flows in the shared lane,
s - basic saturation flow per lane,
So – opposed saturation flows for the right turning movement,
go – opposed green time for the right turning movement, and
c - cycle time.
During the period (g2-G0), The through traffic can depart the junction before the first right turn vehicle
arrives and blocks the lane. The capacity of the shared lane during this period Qb2 is calculated as:
( s * gs )
3600 * Pd *
1 - Pd
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Qb2 = 
( Pb * c )
Where:
Pd - proportion of the through traffic in the shared lane,
Pb - proportion of the right turning movement in the shared lane (=1-Pd),
s - base saturation flow (vehicles /second),
gs - the second period in phase B (=g2-G0). It is treated as the lost time for the right turn. The through
traffic can depart until the first right turn vehicle arrives and block the lane, and
The total capacity in the shared lane Qs is calculated as:
Qs = Qa + Qb1 + Qb2
Each movement obtains the proportion of the capacity of the shared lane as below:
Qsi = Qs * pi
Where:
i - movement indicator (1 for through traffic and 2 for the right turn),
Qsi – part of the shared lane capacity dedicated to movement i,
Qs - total capacity in the shared lane, and
pi – proportion of the movement i in the shared lane.
The effective capacity and green time for each movement are saved in extra attributes, which will be fed
into the turn penalty functions through ep1, ep2 or ep3.
Convergence and Running time overhead
The stopping criteria in this approach are the same as those available in the highway assignment
module in EMME/2, i.e., relative gap, normalized gap and maximum number of iterations. Typical
criteria used in the current Strategic Transport Model are shown in the Table 2.
This iterative assignment approach is actually equivalent to applying the Jacobi method for solving an
asymmetric cost network equilibrium problem. This procedure is known to converge in most
applications. It is also the case in this model. Tests with various highway networks and demands have
been undertaken. All of them have shown able to converge quickly.
Running time overhead is another concern. Modeling the junction in details means a significant increase
in the requirement of computer space and time. New computers with large space and high speed and the
arrival of the EMME/2 Release 9 make all these achievable. The current computer system in LTA is the Sun
Ultra -10 Unix system with 8 GB of hard disk, 300 MHz CPU and one SCSI Card for a tape driver. EMME/2
macros were created to carry out a full model run automatically. They were written and tested in a way to
reduce unnecessary run time as much as possible, and managed to achieve a run-time overhead which is
not significantly longer than the normal equilibrium assignments. As shown in the table below, the average
CPU run-time per iteration in the new model is just about 17 seconds more than a normal link based
assignment, and less than 10 extra iterations are required. With the stopping criteria shown in the table, the
Singapore 1998 highway network assignment using the junction approach can be finished within half an
hour.
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COMPARISON OF THE LINK BASED AND JUNCTION BASED HIGHWAY ASSIGNMENT
APPROACHES
Model Type
Total number of zones
Number of regular nodes
Number of auto links
Turn entries
Total demand (pcu)
Relative Gap (%)
Normalized Gap (%)
Maximum No. of Iterations
Number of iterations required
Objective function (106)
CPU per iteration (seconds)
Old Model (Link based)
931
7823
17926
0
265000
0.5
0.5
200
20
10.5
88
New model (Junction Based)
931
7823
17926
13161
265000
0.5
0.5
200
24
11.2
105
CONCLUSION
The new model uses an iterative approach together with new turn penalty functions. It is able to
represent various situations at signalized junctions with effectiveness. Relatively quick convergence
has been achieved in various tests. A comparison with the link based approach shows that the
computer run-time overhead for this junction based approach is satisfactory. However, there is still
scope for further development of this junction based model to incorporate various short lane situations
and signal coordination.
Acknowledgement
Whilst the authors acknowledge the permission of Land Transport Authority to publish and present this
paper, the views presented here are those of the authors and not necessarily those of Land Transport
Authority.
References
AKCELIK, R. (1981). "Traffic signals: capacity and timing analysis". Australian Road Research Board
Research Report, ARR No.123. 109p. (ARRB: Vermont South, Vic.)
AKCELIK, R. (1990). "Calibrating SIDRA". Australian Road Research Board Research Report, ARR
No.180. 110p. (ARRB: Vermont South, Vic.)
Emme/2 Release 9 Manual (1998).
Highway Capacity Manual (1985).
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Appendix
Input of Lane Configuration
Up1
1st Digit
2nd Digit
3rd Digit
4th Digit
5th Digit
6th Digit
Description (for left-hand drive)
Number of lanes allocated for the specific movement (including shared and short lanes).
Number of short lanes.
Shared lane information:
0= no shared lanes,
1= 1 lane shared with left turn only,
2= 1 lane shared with straight movement only,
3= 1 lane shared with right turn only,
4= 1 lane shared with U-turn only,
5= 1 lane shared with more than one movement, and
6= 2 shared lanes (applies to straight-ahead movement, with one shared lane on the left
and another on the right).
Is movement signal controlled? (1=yes, 2=no).
Give way /opposed flow information:
0= not opposed,
1= opposed by pedestrian,
2= right turn opposed by oncoming vehicles,
3= right turn opposed by oncoming vehicles and pedestrian,
4= left turn giving to the traffic from right,
3= left turn giving to the traffic from right and pedestrian.
Reserved for future use ( left blank)
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