IMPLEMENTATION OF ROAD PRICING MODEL
WITH THE EMME/2 MACRO LANGUAGE
Jamie Wheway (Director)
Karl Cheuk (Transport Analyst)
Wilbur Smith Associates Limited
(Hong Kong)
Tel: (852) 2359-5700
Fax: (852) 2385-7215
E-mail: [email protected]
1st Asian EMME/2 Users Conference
Shanghai
August 23-24, 1999
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ABSTRACT
Traffic congestion, in Hong Kong, is a serious problem and is unlikely to be solved by
adding more road capacity. Due to spatial limitation in the most congested areas and
latent demand induced by the added capacity, transport planners and economists have
shifted their focus from the supply side to the demand side for tackling traffic
congestion. Road pricing can form part of a traffic demand management strategy to
provide an efficient, equitable and flexible solution to handle traffic congestion
problems in the long term.
Hong Kong Government appointed a consultancy to investigate the requirement for
electronic road pricing (ERP) system implementation, the social impacts and its
implications. As a part of the study requirement, A discrete choice model with
multinomial logit formulation was developed in order to assess major behavioural
change in traveller responses due to ERP. From a review of the previous Hong Kong
ERP study and other worldwide experience, the most likely responses of travellers to
ERP are identified as paying the road pricing charge, changing the time of travel,
changing the route taken, switching to other modes, switching to use Park and Ride
facility, increasing vehicle occupancy for ERP cost sharing and suppressing of trip
making.
A stated preference (SP) survey was designed to collect information upon individuals’
likely responses to the alternative ERP responses defined above. The SP survey
results were analysed to derive the ERP assessment model coefficients. The model
was integrated with an existing multi-modal, four-step model to produce a tool
capable of analysing alternative ERP strategies by using EMME/2.
INTRODUCTION
Over the past years, the number of vehicles on the road has increased at a rate much
faster than the rate of transport infrastructure to be built and conventional traffic
management schemes, such as first registration taxation and fuel taxation, are able to
accommodate. Hong Kong Government considers that road pricing, it might provide a
more efficient, equitable and flexible solution to deal with traffic congestion in long
term.
It was concluded from a review of worldwide studies of road pricing and the 1985
Hong Kong Pilot Scheme that the introduction of electronic road pricing schemes
(ERP) would cause major behavioural changes on travel decisions. From the transport
modelling point of view, the existing strategic transport model (ECTS-2 Model) that
was originally developed to handle various traditional transport policy tests is unable
to model the possible behavioural changes of travellers due to the road pricing. A
discrete choice sub-model was therefore introduced for this purpose and named ERP
Assessment Model. Only the assessment model for car and taxi trips will be discussed
in following sections.
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This paper is divided into four parts that includes overviews of the ECTS-2 model,
structure of the assessment model, implementation of the assessment model and
conclusion.
OVERVIEW OF ECTS-2 MODEL
The ECTS-2 Model is a part of a series of comprehensive transport models that have
been developed by Hong Kong Government for more than 20 years to plan transport
infrastructures and to assess various transport policies. The ECTS-2 Model was
developed during the Model Enhancement Study 1993 - 1995 and is a four-step model
comprising trip generation and attraction, trip distribution, modal split and trip
assignment. The structure of the model is illustrated in Figure 1.
The ECTS-2 Model was originally developed using WSA’s transport planning
package WAYS. The model was converted to EMME/2 on a module-by-module basis
to ensure that the conversion was able to reproduce ECTS-2 results at each stage of
the model process.
The model was calibrated using data collected in the 1992 Travel Characteristics
Survey Study (TCS) and validated against observed traffic count and public transport
usage data. Further model updating and refinement were performed in order to
replicate 1996 traffic conditions. The updating of model involved assembling and
inputting 1996 land use planning data, transport networks and transport costs. The
model refinement, on the other hand, included disaggregating the home-based work
trip into three different income bands instead of two used in the ECTS-2 Model,
enchancing the car availability model to handle zonal monthly usage costs, enhancing
the peak model and introducing more traffic analysis zones for auto assignment.
STRUCTURE OF ERP ASSESSMENT MODEL
The assessment model is constructed by considering the four key issues:




the behavioural segments for which equation coefficients are developed;
the behavioural choices for which equation coefficients are developed;
the independent variables to be used in the utility functions; and
the mathematical formulation of the model.
Behavioural Segmentation
Income is the one of the most important socioeconomic factors and it is incorporated
into various model segments in different ways. For home based work trips the model
is segmented by three income levels:


low income (below HK$25,000 per month);
medium income (between HK$25,000 and HK$40,000 per month); and
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
high income (above HK$40,000 per month).
Tests on other socioeconomic factors were undertaken on such variables as household
size, vehicle ownership per household and age. No significant or only marginal
improvements in statistical sense on the model fit were found. In order to maintain the
model simplicity and maximize the computational efficiency, none of these variables
were selected in the model.
Home to work and work to home trips are found to have similar sensitivities to travel
time, cost, and trip start time, and the two trips are consequently combined into a
single work segment. Because of the similarities of the home to school trips with the
above work-related trips, the home to school trips were merged into the work segment
for estimating the model coefficients. Only one coefficient that differed between work
and school trips, travel time, was specifically estimated for the two trips.
Similarly, the home based other segment was created by merging the home to other
and other to home trips. Employer’s business trips and non-home based trips each
differs in time and cost sensitivity from each of the previously described model
segments. These two trip purposes comprise two additional model segments.
According to the above analysis, the final model segmentations are categorized as
follows:







Home based work – low income;
Home based work – medium income;
Home based work – high income;
Home based school;
Home based other;
Non home based ; and
Employer’s business.
Behavioural Choices
According to our worldwide experiences in congestion pricing studies and reviewing
the previous road pricing study in Hong Kong, several possible travel behavioural
choices were identified as follows:







paying the road pricing charge;
changing the time of travel;
changing the route taken;
switching to other modes;
switching to use Park and Ride facility;
increasing vehicle occupancy for ERP cost sharing; and
suppressing of trip making.
For car trips, six of the above choices are modelled in the assessment model. The
route choice option is installed in the auto assignment model. For the taxi trips, only
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three options, paying the road pricing, changing the time of travel and switching to
alternative public transport modes, are implemented in the assessment model. This
was concluded from taking the existing travel pattern and behaviour into account.
Similar to car trips, the route choice option for taxi trip is also installed in the
assignment model.
Independent Variables
Characteristics of trips being made and of the modes that are available for the trip are
described in utility functions for the choice alternatives. The utility functions are
modelled as affecting choice probabilities through the multinomial logit model in
functional form. Separate utility functions are specified in the model for each possible
alternative choice. Coefficients of the variables in all utility functions were estimated
by using maximum likelihood estimators from the data collected from a stated
preference (SP) survey.
The specifications of utility functions were developed in a series of tests involving
each of the classes of factors that affect mode choices. A total of 140 tests were
performed and the final utility formulation is a linear combination of variables
included travel time for auto and transit modes, ERP charge, out-of-pocket
expenditures including fuel costs and road tolls, and transport fares.
Constant terms of the linear utility functions were individually investigated in order to
improve the model fit. The final model adopts constant terms for the alternative
choices of occupancy shifting, public transport mode, Park and Ride facility and trip
suppression.
Mathematical formulation of the model
The mathematical formulation of the model is determined by whether the model
structure is nested or not, a nested structure implying a certain degree of sequential
choices in the process of decision making. Several nesting structures were statistically
analysed and the estimated nest coefficient “thetas” were not statistically significant
different from zero. It is concluded that the simplest multinomial logit structure was
appropriate for the behavourial choices among the possible alternatives.
The probability of each prescribed alternative choice are calculated by using the
multinomial logit formulation that is one of the most popular tools used in discrete
choice modelling. The model formulation among the choice probabilities is recorded
below:
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pij Z 
e
  U ijZ
e
  U ijk
all Modes k
where
Pij(Z)

U ,U
Z
k
ij
ij
is the probability that alternative Z will be chosen for origindestination movement from zone i to zone j,
is an adjustment factor and
are utility functions for alternatives Z and k.
The utility functions in the above formulation are individually described below:
U ijERP  Tij 
Cij
VoTk
U ijtime  Tij 
U ijocc  Tij 

Cij
VoTk
Cij
VoTk
ERP Feeij
VoT ERPk

ERP Feeij*
VoT ERPk
 0.6 
 k1  T 
ERP Feeij
VoT ERPk
 k2
U ijnotrip  k3
U ijPnR  Tij 
Cij
VoTk
 PTTij 
PTCij
VoTk
 k4
U ijPT  PTTij 
PTCij
U ijERP
is the utility for ERP choice;
VoTk
 k5
where
U
time
ij
is the utility for time shift choice;
U
occ
ij
is the utility for occupancy shift choice;
U
notrip
ij
is the utility for no trip choice;
U
PnR
ij
is the utility for Park and Ride choice;
U
PT
ij
is the utility for Public Transport choice;
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Tij
is the travel time in minutes skimmed from highway network;
PTTij
is the travel time in minutes skimmed from transit network;
Cij
is the travel cost in dollars skimmed from highway network;
PTCij
is the travel cost in dollars skimmed from transit network;
VoTk
is the value of time for out-of-pocket costs by purpose k;
VoT ERPk
is the value of time for ERP by purpose k;
ERP Feeij
is the ERP charge in dollars between zone i and j;
*
ij
ERP Fee
T
is the ERP charge in time period moved into between zone i
and j;
is the number of minutes time switching by;
K2
K3
is the change in time choice constant, purpose K;
is the occupancy shift choice constant, purpose K;
is the no trip choice constant, purpose K;
K4
K5
is the Park and Ride choice constant, purpose K; and
is the transit mode choice constant, purpose K.
K1
IMPLEMENTATION OF ERP ASSESSMENT MODEL
The ERP assessment model has been coded in EMME/2 macro language with three
macros that correspond to three model stages:



calculation of slice matrices by trip purpose and by mode (slice macro);
calculation of utility matrices by trip purpose and by mode (utility macro); and
calculation of trip demands for all alternative behavioural choices (logit macro).
The order of these macros within the model and the interaction between the
assessment model and the ECTS-2 model is illustrated in Figure 2. These interactions
are summarised as follows:


Daily car and taxi trip matrices by trip purposes are extracted from the databank
for the ECTS-2 Model and temporarily stored in the databank for the slice macro.
This macro outputs 98 car and taxi time slice matrices: 14 slices by 7 trip
purposes;
Auto and public transport time and cost skim matrices are extracted from the
databank for the ECTS-2 Model and temporarily stored in the databank for utility
macro. The macro also considers the parameters derived from the SP survey and
computes the utilities for each behavioural choice by time slices by trip purposes
for car and taxi modes. There are totally 588 skim matrices for car trips (6 choices
by 14 slices by 7 trip purposes) and 298 skim matrices for taxi trips (3 choices by
14 slices by 7 trip purpose) generated.
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

The matrices created from the above two stages are then imported into the
databank for the macro logit. It calculates probabilities of each possible choice and
derives choice matrices that are totally 588 car matrices and 298 taxi matrices as
described above.
The final step is to produce car and taxi trip tables by 6 periods by trip purpose
which are sent to the databank for assignment process.
The macro running sequence of the ERP assessment model is illustrated as Figure 3.
The macros for slice, utility and logit are sequentially executed in the order for a
particular time slice and for a journey purpose prior to any computation of next time
slice and purpose. Starting with journey purpose 1, the model first creates the 14 time
slice trip tables and then calculates the utilities and choice probabilities for the first
time slice trip matrices. The model then iterates around ‘loop A’ for the other 14 time
slices. Once this has been completed, the model iterates around ‘loop B’ for the
journey purpose 2 and the process continues up to the 14th time slice for the 7th trip
purpose matrices.
Slice Model
In the model daily car and taxi matrices by trip purpose from the ECTS-2 model are
disaggregated into 14 slices by trip purpose.
The daily production-attraction trip tables for each purpose is split into AM and PM
peak period origin-destination matrices in similar fashion to the ECTS-2 Model. Also,
subtracting the total peak demands from the daily matrices derives the off-peak
matrices. The period definition for car and taxi trips is



AM Peak from 07:45 to 09:30;
Off peak from 09:30 to 16:45; and
PM Peak from 16:45 to 18:30.
The period matrices are then sliced into 14 components by applying the time slice
factors by trip purposes that are derived from the data extracted from the 1992 Travel
Characteristic Survey Study.
Utility Model
The calculation of linear utilities for all choices by modes and by trip purposes is
performed in this macro. The mathematical formulation is recorded in the section of
the mathematical formulation of assessment model.
Logit Model
The logit model calculates the probability of each behavioural choice and its demands
by time slice, by trip purpose and by mode.
The resultant matrices are then processed in the macro with steps:
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



The park and ride choice slice matrices are split into trip leg matrices for car and
public components and combined to produce time period matrices.
the ERP choice slice matrices are aggregated into six period matrices while the
trip demands with choice of time shifting and the auto legs from Park and Ride
choice demands are added with the ERP choice period matrices in appropriate
time periods. The definition of time periods is named as AM shoulder, AM peak,
Off-peak, PM peak, PM shoulder and Night.
The occupancy and trip suppression choice slice demands are only reported to
ASCII files that are prepared for input to spreadsheets for further analysis.
The public transport choice slice demands with transit legs from Park and Ride
choice demands are aggregated into period matrices and delivered to the ECTS-2
model.
CONCLUSION
The road pricing assessment model is a short-term strategic transport model
improvement developed in the course of the Electronic Road Pricing Feasibility
Study. The model is an add-on component to the ECTS-2 model and overcomes the
existing model restriction such as its ability to handle Park and Ride trips, time
shifting effect due to congestion or road pricing, etc.
The assessment model and the ECTS-2 model have been successfully implemented
under the EMME/2 platform and macro language. The model has been examined by
undertaking several hundred sensitivity tests on various transport policy assumptions
that includes various road pricing structures.
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Goods Vehicle
Model
Highway
Data
Public
Transport Data
Planning Data
Auto Network
Model
PT Network
Model
Household
Income Model
Car Availability
Model
Cost Model
Cost Data
Trip
Distribution/
Modal Split
Model
Trip Generation
Model
Trip Attraction
Model
Special Travel
Model
Car/Taxi
Model
PT Sub-Modal
Split Model
ERP
Assessment
Model
PT Peak Model
Auto
Assignment
Model
PT
Assignment
Model
Analysis and Evaluation
Figure 1
ECTS-2 Model Structure
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ECTS-2
Model
ERP Assessment
Model
Daily Trip
Matrices by
Purposes
Slice
Macro
Demand Matrices
by Purposes and
Time Slices
Cost Skims by
Modes and
Purposes
Utility
Macro
SP Model
Parameters
Utilities for Each
Choice, by
Purposes and by
Time Slices
Logit
Macro
Assignment
Routines
Trip Tables for
Each Choice, by
Purpose and by
Time Slices
Figure 2
Relationship between ECTS-2 Model and ERP Assessment Model
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SLICE
MACRO
UTILITY
MACRO
LOGIT
MACRO
‘LOOP A’
Slices 1 to 14
‘LOOP B’
Purpose 1 to 7
Figure 3
ERP Assessment Model Macro Running Sequence
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