SEVENTH FRAMEWORK PROGRAMME
THEME [SST.2010.1.3-1.]
[Transport modelling for policy impact assessments]
Grant agreement for: Coordination and support action
Acronym: Transtools 3
Full title: „Research and development of the European Transport Network Model – Transtools
Version 3
Proposal/Contract no.: MOVE/FP7/266182/TRANSTOOLS 3
Start date: 1st March 2011
Duration: 36 months
Deliverable MS55 - “Short note on traffic
assignment”
Document number: TT3_WP9_TEC_MS55 Short note on traffic assignment_0a
Workpackage: WP9
Deliverable nature: Short note
Dissemination level: N/A
Lead beneficiary: DTU, beneficiary number 1, Carlo Giacomo Prato
Due data of deliverable: [12.09.2011]
Date of preparation of deliverable: [29.08.2011]
Date of last change: [10.09.2011]
Date of approval by Commission: N/A
Abstract:
This short note introduces the main concepts behind the development of traffic assignment within
TransTools 3 (TT3). Traffic assignment models will be implemented by means of the package
Traffic Analyst developed by Rapidis on the ArcGIS platform, will account for correlation across
alternative routes and taste heterogeneity across the population, will be multi-class and multipurpose, and will use specific speed-flow curves for specific road types. Traffic assignment
models will be extremely flexible in the selection of the number of iterations, the solution method,
the definition of trip purposes and the choice of distributions of random coefficients. Traffic
assignment models within TT3 will improve existing models within TT1 and TT2 by proposing
enhancements for fast implementations and validated equilibrium solutions. This short note
delineates two directions that traffic assignment models should move toward, namely the
implementation of fast algorithmic solutions and the design of models for specific modes.
Keywords:
Traffic assignment, road assignment, rail assignment, air assignment, sea transport assignment,
fast implementation
Author(s):
Carlo G. Prato
Disclaimer:
The contents of this report reflect the views of the author and do not necessarily reflect the official
views or policy of the European Union. The European Union is not liable for any use that may be
made of the information contained in the report.
The report is not an official deliverable under the TT3 project and has not been reviewed or
approved by the Commission. The report is a working document of the Consortium.
Short note on traffic assignment
Report version 1
2011
Kgs. Lyngby
Copyright:
Reproduction of this publication in whole or in part must include the customary
bibliographic citation, including author attribution, report title, etc.
Published by:
Department of Transport, Bygningstorvet 116 Vest, DK-2800 Kgs. Lyngby,
Denmark
Content
1.
INTRODUCTION..................................................................................................................5
2.
2.1
2.2
TRAFFIC ASSIGNMENT IMPLEMENTATION ....................................................................6
Fast implementation .............................................................................................................6
Implementation issues .........................................................................................................7
3.
3.1
3.2
3.3
3.4
TRAFFIC ASSIGNMENT DESIGN ......................................................................................9
Road assignment .................................................................................................................9
Rail assignment..................................................................................................................10
Air assignment ...................................................................................................................11
Sea transport assignment ..................................................................................................11
4.
CONCLUSIONS .................................................................................................................12
Deliverable MS55 - “Short note on traffic assignment”
1. Introduction
This short note introduces the main concepts behind the development of traffic assignment models
within TransTools 3 (TT3). As the models are in their development phase, most of the ideas presented
in this note draw from the ideas illustrated in the proposal and discussed in the description of work that
was delivered to the European Commission in the early stages of the project.
The traffic assignment within TT3 departs obviously from the traffic assignment implemented by DTU
and Rapidis within TransTools 1 (TT1) and TransTools 2 (TT2). As their predecessors, traffic
assignment models will be implemented by means of the package Traffic Analyst developed by
Rapidis on the ArcGIS platform (Rapidis, 2011). As their predecessors, traffic assignment models will
be Mixed Probit models that are able to account for correlation across alternative routes and taste
heterogeneity across the population (Nielsen, 2000; Nielsen et al., 2002), will be multi-class that are
able to consider several trip purposes (see Nielsen et al., 2002), and will use specific speed-flow
curves for specific road types.
Traffic assignment models will be extremely flexible and hence it will be possible for users to change
the number of iterations, to select the solution method (i.e., Method of Successive Averages,
Incremental Loading), to define the number of trip purposes (i.e., private, work, business, vacation), to
specify the utility functions, to delineate the distributions of random coefficients (i.e., shape, variance,
correlation structure), etc. For an initial review of traffic assignment and solution methods see Sheffi
(1985), and for an initial overview of utility-based analysis see Ben-Akiva and Lerman (1985).
It is expected that the traffic assignment models within TT3 will improve existing models within TT1
and TT2 by proposing enhancements for fast implementation and validated equilibrium solutions. The
success of the work package on traffic assignment will rely on the contribution of DTU Transport as
scientific leader, Rapidis as software developer, and several partners as providers of insights into
specialised transport domains (e.g., rail, air, sea transport). Accordingly, the documentation of the
traffic assignment models (task 9.8) will be coordinated by DTU Transport with the collaboration of
Rapidis for software issues and other partners for domain issues.
This short note focuses on two directions that traffic assignment models should move toward, namely
the implementation of fast algorithmic solutions and the design of models for specific modes.
5
2. Traffic assignment implementation
Traffic assignment models within TT3 should focus on several issues concerning the improvement of
models with respect to TT2 and TT1 in terms of speed of the implementation as well as level of detail,
network calibration and software implementation.
2.1
Fast implementation
Traffic assignment models within TT2 have been proved to be efficient when considering the number
of cells, the number of purposes, the generation-attraction (GA) nature of the passenger demand
model, or more in general the dimensionality of the problem (Rich et al., 2009). However, issues exist
with respect to the calculation time of the traffic assignment models when multi-class stochastic user
equilibrium for five modes (i.e., car driver, car passenger, public transport, train, airplane) and four
purposes (commuting, business, private, vacation) is searched for.
The first issue concerns the level of stochasticity of the model. On the one hand, the model accounts
for taste heterogeneity across the population (i.e., different willingness to pay for different travellers).
On the other hand, the model accounts for similarity across alternative routes almost at the same
level-of-service. Taste heterogeneity must be considered because many real life decisions involve
differences across individuals: whether to pay the toll for an expensive bridge to save time versus a
detour; whether to save money by choosing a low-cost airline from a far-off airport versus to pay more
by choosing a conventional airline from a nearby airport; whether to use an expensive high speed rail
connection or to opt for a cheaper and slower alternative. Similarity across alternative routes must be
considered because the analysis of specific infrastructure projects cannot avoid considering realistic
routes. When these routes are similar, they should have similar market shares. However, when these
routes are dissimilar to a third route, they should have market shares that reflect their similarity and
the dissimilarity with the other alternatives in a realistic way. For a review of models able to account for
similarities across alternative routes, see Prashker and Bekhor (2004) and Prato (2009).
The second issue concerns the number of iterations of the assignment model. The trivial solution is for
a user to configure the parameter files of the model with a low number of iterations, with the possibility
that the equilibrium solution is not found because the traffic assignment models do not converge to a
solution. The less trivial solution is for the traffic assignment model to be programmed in order to
reduce the computational time through methodological improvements, rather than through simplified
behavioural assumptions or through compromises that hinder convergence.
The solutions to these issues concern the concepts of matrix thinning and efficient simulation, and
they are going to be implemented in task 9.1.
Matrix thinning is inspired by the fact that traffic assignment models assign all cells in the matrices at
each iteration of the model. However, the scale of the model within TT3 is extremely large and the
entries of most cells are either extremely small or even empty because the combination of modes and
6
distances is irrelevant (e.g., daily commuting from Denmark to Turkey by train). Accordingly, the idea
consists in removing or reallocating cells with very small entries in order to reduce the memory
requirements and hence the calculation time. Matrix thinning in combination with different number of
iterations dependent on the traffic volume has been proved to produce very efficient reductions of
calculation time. Matrix thinning in combination with different solution algorithms implemented during
the algorithm execution has been also proved to improve convergence. Tests have revealed that a
reduction of the calculation time by 90% is possible for some trip purposes in the model. It should be
noted that shortest path calculations are stopped when all destinations are reached, and since the
calculation complexity of the shortest path is proportional to the area searched, and hence to the
square of the distance searched, the immense time saving on calculation when cells connecting
distant points are removed is obvious. It should also be noted that matrix thinning is performed by
either (i) removing cells with zero traffic, (ii) redistributing cells with small entries to other origin and
destination zones proportionally, or (iii) distributing cells with small entries to neighbouring zones.
Efficient simulation is inspired by the vast amount of literature in discrete choice modelling following
the development of mixed models that do not have closed form (e.g., Bhat, 2003; Hess et al., 2006).
Monte Carlo simulations are not efficient, and alternative solutions such as Halton sequences,
scrambled Halton sequences (Bhat, 2003) and Modified Latin Hypercube Sampling (Hess et al., 2006)
could drastically improve simulation efficiency by “intelligently drawing” random numbers. Realistically,
a reduction of the calculation time by 75% is possible with Halton sequences applied to the simulation
of taste heterogeneity and link error terms. It should be noted that it is possible to reduce the taste
heterogeneity, since traffic assignment models (as passenger demand models) account for variations
of value-of-time across nations and hence the model explains variation in travellers’ preferences and
requires “less stochasticity” in the parameters. It should also be noted that tests are being conducted
on the variance of the error term in the model in order to improve convergence and consequently
reduce computational time.
2.2
Implementation issues
One issue to be considered when discussing the implementation of traffic assignment models within
TT3 is the level of detail. The traffic assignment within TT1 included an extremely detailed assignment
procedure that accounted for different times during the year (e.g., congestion during vacation in
certain regions within Europe) and different times of day during weekdays. The model implementation
would surely suffer from a drastic increase in the calculation time in the case that this level of detail will
be achieved, and hence a more aggregated design has to be conceived (task 9.5). Nonetheless,
congestion is to be modelled in project appraisal scenarios and in congestion pricing evaluations, and
hence the level of detail should be refined without hindering the speed of the implementation.
The solution to the compromise between level of detail and computational time can be achieved by
using heuristic distributions on the time of day and adopting a “pseudo-dynamic assignment”. The idea
behind this approach is that a vehicle starts its long distance trip in the morning in a certain link and
then the same vehicle will move to certain links in the afternoon where he will meet the peak during
the rush hour. The idea has been developed for the Danish National Model, and has been proved that
algorithmic refinements allow obtaining the same calculation complexity existent for the TT2 model.
7
Accordingly, the “pseudo-dynamic assignment” allows increasing the level of detail of the traffic
assignment models without increasing the computational complexity.
Another issue to be considered when discussing the implementation of traffic assignment models
within TT3 is the overall effort in calibrating the network (task 9.6) and implementing the software (task
9.7). One the one hand, a challenge consists in jointly calibrating networks that are specific to the
various domains for which traffic assignment models are designed. The challenge lies in particular in
the cross-links across the networks (e.g., access and egress trips to airports are loaded on the road
network) that need to be properly addressed in order for the implementation to be efficient. On the
other hand, a challenge consists in the overall implementation of the software and the validation of the
traffic assignment models to the 2010 network data that will be provided by the ETIS+ project and will
be tested by WP5. The challenge lies in particular in the interaction with the demand models (e.g.,
transfer of level-of-service data) that need algorithmic enhancements (e.g., outer loop for the MSA) for
the implementation to be efficient.
8
3. Traffic assignment design
Traffic assignment models will be designed for specific domains by departing from the existing models
within TT2 and addressing areas of weakness. The interested domains are road, rail, air and sea.
3.1
Road assignment
Traffic assignment models for road traffic adopt the aforementioned Mixed Probit model (Nielsen,
2000; Nielsen et al., 2002) with a pseudo-dynamic approach. The GA matrices allow significant
improvement in the realism of the traffic assignment models as route choices for both the outbound
and inbound legs of longer tours are affected by the same value-of-time calculated for the nation
where the trip occurs. The matrix thinning approach and the intelligent random number draws allow
significant savings in computational time even with the proposed approach to model congestion.
The road assignment model within TT3 allows for intrazonal traffic to be accounted for, also because
of the short distance demand model for trips below the selected threshold of 100 km that is estimated
alongside the long distance demand model for trips over the same threshold. The road assignment
model uses a set of time period factors to describe congestion for trips below 100 km and a second
set of time period factors to describe congestion for trips between 100 and 250 km.
With respect to the description of congestion, the demand model generates average daily traffic flows
that are then split into time periods according to the afore-mentioned factors. The level of detail of the
split is quite refined because the matrices are GA-based and not OD-based, and hence for example
commuting trips going out in the morning are then automatically correctly represented coming back in
the afternoon. The demand split factors are defined for (i) type-of-day within the week (i.e., four types
of day per four trip purposes plus trucks), (ii) time-of-day within the day when considering short trips
(i.e., 3 times-of-day per four trip purposes plus trucks), (iii) time-of-day within the day when
considering medium trips (i.e., 3 times-of-day per three trip purposes that exclude commuting plus
trucks), and (iv) time-of-day within the day when considering access to and egress from airports (i.e., 3
times-of-day per three trip purposes that exclude commuting).
It should be noted that the road assignment model is able to account for the type of fuels of the
vehicles on the basis of national factors for the share of car types and of the application of filter criteria
(i.e., a Spanish vehicle visiting France uses Spanish split coefficients also when driving in France),
and this is different from the traffic assignment models within TT2. It should be also noted that the
road assignment model is also able to account for revenue generation related to taxation and toll
systems. Specifically, the model considers (i) private tolls that are used for construction and
maintenance costs (e.g., Italian and French private motorways, Danish fixed links, ferries), (ii) urban
toll rings (e.g., London) and tolling systems (e.g., German Maut), and (iii) extra fuel tax beyond normal
average value-added tax. Revenue generation is defined for both passenger vehicles and trucks, and
are calculated at the NUTS3 level. It should be noted that the differentiation between the three
different revenues allows the user to forecast the traffic impacts of different policies and enables policy
9
makers to calculate the impact of revenue shares that are reinserted into a national or a regional
economy where they can be used to lower income taxes.
3.2
Rail assignment
The rail assignment model within TT2 presents several weaknesses that task 9.2 is going to address.
Firstly, passenger and freight rail network databases are stored separately. This solution is
cumbersome for users, since the maintenance of the networks should be performed simultaneously,
and is risky from the perspective of data inconsistency and capacity constraints because of passenger
and freight trains being represented separately. Secondly, capacity constraints are not represented in
the TT2 version of the models. Thirdly, the limited number of traffic counts severely restricts the
possibility of validating the rail assignment given that the rail matrices are not checked. Fourthly, the
limited availability of IPR free data limits the possibility of modelling services along the lines for
modelling average frequency and speed per link.
The rail assignment model cannot proceed without the necessary initial merging of the passenger and
freight rail networks into a unique database and hence a unique model. Consistency issues, in
particular with respect to railways that serve both passenger and freight trains, will be automatically
resolved by this joint approach.
Accounting for rail capacity complicates the rail assignment model, since capacity depends on the
number of tracks, the signal control system, the level of maintenance of the tracks, and the
composition of the services. For example, a rail line with homogeneous stopping patterns (e.g., a
metro line or a high speed line) can support a higher frequency than a rail line with a mixed operation
of fast and slow passenger trains and freight trains, since the fast trains will catch up on the slow
trains. However, even though accounting for rail capacity constitutes a challenging task, the rail
assignment models within TT3 aim at developing heuristics that to some extent can consider capacity.
Possibly, these heuristics may be inspired by the UIC (International Railway Organisation) capacity
guidelines.
The modelling of lines and services for passenger trains is also included in the rail assignment model
by acquiring information from publicly available timetables on railway websites. Most likely it is not
possible to obtain a complete description of all the lines and services in Europe, but with a dedicated
effort it is expected that it is possible to obtain these pieces of information for at least the majority of
the international connections. The modelling of lines and services for passenger trains introduces a
tremendous benefit for the reliability of passenger railroad zone-to-zone travel times, which is critical
for the quality of the level-of-service data provided to the passenger demand model.
The rail assignment model makes the best use of the improved data from the ETIS+ project, and in the
case of lines with known mixed services, different stopping patterns are approximated through the
implementation of simplified approaches (e.g., approaches adopted in the IBU Interreg project).
Similarly to the rail assignment model within TT2, the model accounts for different values-of-time and
willingness-to-pay (i.e., according to different trip purposes, different nations, and different user
segments through logarithmic normal distributions). Considering taste heterogeneity across travellers
10
has been proved to give a good model fit, for example with respect to the modelling of high speed
railways and of their feeder rail lines.
3.3
Air assignment
The air assignment model within TT2 is a multi-modal choice model that represents the choice of
airport, the choice of route in the air network, and the choice of feeder mode. This approach allows
representing the choice between a flight starting from a local airport with an intermediate stop (e.g.,
Lyon-Paris-Copenhagen) and a flight starting from a farther airport without intermediate stop that
implies a feeder mode choice (e.g., Lyon-Paris by train and Paris-Copenhagen flight). This approach
also allows representing the choice between main airports and competing airports served by low-cost
airlines. The air assignment models are based on very good data, since detailed information is
available about passenger volumes at the leg level, and since an update of the information to the year
2010 is available on the basis of the ETIS+ project.
The focus of task 9.3 is not only on the update of the model according to the additional data, but also
on the main weakness of the air assignment model within TT2 that consists in the lack of
consideration for intercontinental air transport. Data from WorldNet and ETIS+ describing
intercontinental flights are included in the model and hence improvements from this perspective are
achieved for the flight choice and the feeder mode choice. The alliances must be described in order to
better represent the airport hubs, and since their numbers is somewhat limited, it is feasible to handle
them by coding manually the relationships in the case that the data provided by ETIS+ do not account
for airline alliances. From a technical perspective, alliances are “pseudo airports” within the same
airport hub (i.e., terminals are coded as nodes), since the air assignment model within TT2 already
represents transfers between airports in towns with several airports (e.g., Guadeloupe is served from
Paris Orly, but many airports in Europe are only connected to Paris Charles de Gaulle).
3.4
Sea transport assignment
Sea transport has not been assigned within TT2 onto a dedicated network, and task 9.4 plans the
assignment of specific routes on the basis of the data provided by WorldNet through the ETIS+
project. Specific effort is necessary with respect to assigning volume dependent cost functions on
specific routes.
It should be noted that inland waterways are assigned separately. Ferries for passenger cars and
trucks, as well as RoRo ferries for trucks, are modelled within the road assignment model through the
specification of costs, frequency and other variables in the utility functions. Ferries for rail transport are
included within the rail assignment model in the rare cases that the trains run on-board the ferries.
Ferries and other vessels that carry passengers are included within the rail assignment model in the
cases that harbours are close to train stations. Hence, the task focuses on the assignment of freight
transport, which is not explicitly assigned in the traffic assignment models within TT2.
11
4. Conclusions
This short note presents the main concepts behind the development of traffic assignment models
within TT3. As the traffic assignment within TT3 departs obviously from the traffic assignment
implemented by DTU and Rapidis within TT1 and TT2, this note focuses on the predecessors and on
the directions for possible enhancement. The focus is on two directions that traffic assignment models
should move toward.
The first direction concerns the implementation of the model, in particular with respect to the speed,
but also with respect to level of detail, network calibration and software implementation. Fast
implementation will greatly benefit from matrix thinning and efficient simulation that could reduce
calculation time drastically. The compromise between level of detail and computational time will
greatly profit from heuristic distributions on the time of day and pseudo-dynamic assignment. Software
implementation will greatly benefit from joint network calibration and algorithmic enhancements for the
interaction with the demand models.
The second direction concerns the domains of road, rail, air and sea that the traffic assignment model
should focus on. Road assignment will be improved through the adoption of matrix thinning and
efficient simulation. Rail assignment will be enhanced through the simultaneous maintenance of
passenger and freight networks and the consideration of capacity constraints. Air assignment will be
enhanced through the representation of intercontinental air transport and the improvement of the hub
representation. Sea transport assignment will be included alongside ferry lines for passenger cars and
trucks and ferries for trucks that are modelled within the road assignment model.
The purpose of this note is to facilitate the discussion about the design of traffic assignment models
within meetings focusing on the related models of freight and passenger demand.
12
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