Veröffentlichung / Publication
Modelling Through Traffic Prohibition
Autoren / Authors:
Markus Friedrich
Eileen Mandir
Gerd Schleupen
Lehrstuhl für Verkehrsplanung und Verkehrsleittechnik, Universität Stuttgart
[email protected]
Veröffentlicht in / Published in:
Friedrich, M., Mandir, E., Schleupen, G. (2008): Modelling Through Traffic
Prohibition, Proceedings of 10th International Conference on Applications of
Advanced Technologies in Transportation, 2008, Athens, Greece.
Universität Stuttgart
Institut für Straßen- und Verkehrswesen
Lehrstuhl für Verkehrsplanung und Verkehrsleittechnik
www.isv.uni-stuttgart.de/vuv/
MODELLING THROUGH TRAFFIC PROHIBITION
Markus Friedrich1, Eileen Mandir2, Gerd Schleupen3
ABSTRACT. With increasing traffic volumes the importance of measures to reduce noise
and air pollution grows continuously. A possible measure is through traffic prohibition in
which transit routes through densely populated urban areas are banned for HGV traffic. The
paper shows an approach to modelling through traffic prohibition and introduces a general
solution which includes different types of prohibition strategies (cordon wise or road wise)
also taking into account the origin-destination information in order to determine the set of
trips a prohibition applies to. In addition the paper examines suitable multi-class assignment
procedures for LDV and HGV.
INTRODUCTION
Traffic related emissions of noise and particulate matter are a major concern for cities. The
EU Environmental Noise Directive (2002/49/EC) requires that noise maps and action plans
are developed by European cities and the European Commission has set limits for the
emissions of PM10. The enforcement of a tolling system for HGV over 12 tons on German
motorways in 2005, however, has caused a shift of HGV traffic towards the secondary road
network in some places, thus increasing the emission problems. Facing these problems the
City of Stuttgart has enacted a through traffic prohibition in 2006 for the whole city area for
external HGV traffic over 3.5 tons and additionally for several inner city districts banning the
city’s internal HGV traffic from those critical neighbourhoods.
This paper reports on transport modelling methods which were applied to understand and
forecast the impacts of the through traffic prohibition. The results from the model provided
the input for a comprehensive noise abatement plan.
In the context of a transport planning model the task can be described as follows. Based on a
given demand matrix (trip table) with separated information for HGV and LDV traffic the
existing network model has to be extended such that the various through traffic prohibitions
are represented in the network model. Within the traffic assignment the through traffic
1
Professor, Universität Stuttgart, Department for Transport Planning and Traffic Engineering,
Stuttgart, Germany, email: [email protected]
2
Dipl. –Ing., Universität Stuttgart, Department for Transport Planning and Traffic Engineering,
Stuttgart, Germany, email: [email protected]
3
Dipl. –Ing., Universität Stuttgart, Department for Transport Planning and Traffic Engineering,
Stuttgart, Germany, email: [email protected]
1
prohibitions then need to be considered in the route search and choice process. Therefore the
impedance for the route search and choice may not merely be a function of the travel time but
must also include a penalty for certain demand classes on prohibited network elements
independent of congestion. Modelling through traffic prohibition therefore results in demand
class specific traffic flows, which are the basis for more advanced pollution and noise models.
In the first part of the paper various methods of modelling through traffic prohibition are
analyzed. In the second part different assignment procedures are examined on their
performance concerning simultaneous assignment of the different demand classes.
CLASSIFYING DIFFERENT TYPES OF THROUGH TRAFFIC PROHIBITION
The paper classifies four general types of through traffic prohibition. All types can be
combined to a complex through traffic prohibition scheme for a city.
Prohibited Vehicle Classes
Through traffic prohibition may concern all vehicle classes or only particular classes, e.g.
HGV exceeding a certain weight. If restrictions only apply to a particular vehicle class this
class needs to be represented as a demand class of its own within the transport model in order
to achieve a different behaviour in route choice as a reaction to the through traffic prohibition.
Prohibited Areas
Through traffic prohibition for a single area permits only trips that are origin or destination
traffic to enter the closed cordon. Through traffic needs to be rerouted around the prohibited
area. This route choice behaviour needs to be modelled without influencing route choice of
the internal traffic. Figure 1 shows a simplified network. The area, for which through traffic
prohibition is valid, is indicated with the grey area. All network elements prohibited for HGV
traffic are displayed in dashed lines.
Prohibited Areas with Exceptions on Selected Main Roads
The situation explained above changes if selected main roads within a prohibited area are
opened for through traffic. Through traffic is now allowed to travel through the prohibited
area by using those selected main roads, yet is not allowed to use any other road within the
prohibited area. This must be modelled in a way that the selected main roads have no
influence on route choice of internal traffic, for which no roads are prohibited. Figure 2 shows
such exceptional main roads within the prohibited area.
2
Figure 1. Example of prohibited area
Figure 2. Example of prohibited area with exceptions on main roads
3
Multiple Prohibited Areas
In large networks not only the greater city area but also districts within the city may have
additional through traffic prohibition in order to prevent the cities internal traffic to drive
through highly populated neighbourhoods. This influences route choice of the city’s origin,
destination and also internal traffic. Traffic with its destination in the city, for example, is
allowed to enter the city area. Yet it is not allowed to drive through district A to get there.
Only traffic with its origin or destination in district A is allowed to enter the district area.
Figure 3 shows two prohibited city districts.
In case of exceptions for selected main roads, not only on city level, but also within the
districts themselves, the complexity of the problem rises with the number of prohibited
districts as route choice for internal district traffic must remain unaffected.
Figure 3. Example of multiple prohibited areas
APPROACHES TO MODELLING THROUGH TRAFFIC PROHIBTION
In order to meet the requirements of all types of through traffic prohibition introduced above,
four modelling methods are now discussed and evaluated on a small sample network:
• Additional impedance on links within prohibited area,
• Additional impedance on all turns entering prohibited area,
• Splitting trip tables in prohibition relevant segments,
• Combination of splitting trip tables and turn based approach.
The four methods are discussed in this order for didactical reasons. The approach that the
authors recommend is discussed last and represents a general modelling solution for any kind
of through traffic prohibition scheme.
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Additional impedance on links within prohibited area
By introducing a Boolean link attribute for all links within a through traffic prohibition area
the link’s impedance function will consist of the travel time as well as an additional penalty z
if the attribute is set true. This is done by adding the additional penalty z and multiplying it
with the Boolean attribute. If the link is outside the prohibited area the Boolean value is zero,
yet if the link is within the prohibited area the Boolean value is one and the additional penalty
amounts to z seconds. The value of z needs to be chosen such that the link becomes
effectively unattractive as an alternative, e.g. z being 3600s. This approach is a simple
solution and follows the same concept as modelling an additional road toll. The solution
meets the requirement that all through traffic drives around instead of through the city. This is
illustrated in Figure 4.
The shortest path search, with impedance = time, finds the direct route through the city area.
However the shortest path search, with impedance = time + link penalty, determines another
route avoiding the city area which uses only the permitted main roads within the city. This
approach is therefore suitable for modelling route choice of external through traffic. Figure 5
shows the distribution of a demand matrix containing only external zones highlighted in
shaded grey. There are no link flows on prohibited links within the city area. However, links
outside the prohibition area or urban links excluded from the prohibition contain traffic flow.
The simplicity of the approach is its greatest benefit. Very few specific link attributes are
needed to include through traffic prohibition in the model. The prohibited links can easily be
selected by intersecting the nodes with the prohibited zones or territories. Links between two
nodes within such a territory are then selected. Excluded main roads need to be selected
manually or filtered by road number.
5
impedance = time
Destination
Origin
impedance = time + link penalty
Destination
Origin
Figure 4. Route choice of external traffic without prohibition (above)
and with prohibition (below)
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Figure 5. Volumes of external through traffic
If the link penalty for prohibited links is also considered in the route search for origin,
destination or even internal traffic this approach will lead to unrealistic results. Routes will
prefer links outside of the prohibited area, as the additional impedance adds up with each
internal link. Figure 6 illustrates this issue and shows the route choice for internal traffic when
applying a shortest path search with impedance = time + link penalty and with impedance =
time. Obviously the second result displays the desired route choice behaviour.
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impedance = time + link penalty
Destination
Origin
impedance = time
Destination
Origin
Figure 6. Shortest path search for internal traffic in the link based approach
8
Additional impedance on all turns entering prohibited area
To overcome this deficit the link-based solution is extended to a turn based approach.
Therefore, a Boolean turn attribute is introduced. As explained in the link-based concept
above, the impedance function will consist of the travel time as well as an additional penalty
z if the attribute is set true. In contrast to the link based solution now the impedance function
of the turn is critical for route choice. The attribute is set true if the turn is entering the
prohibited area. Technically that means, if the turn’s From-Link is not prohibited and its ToLink is prohibited the Boolean value is one. For all turns between two links both prohibited or
both not prohibited the Boolean value is zero. Figure 7 shows the prohibited turns marked by
the bold arrows.
Figure 7. Turns entering prohibited area
This approach solves the problem of the link-based approach for single prohibited areas
because the additional penalty occurs only once when entering the city and therefore it does
not make any difference how many network elements within the prohibited area are traversed.
However, if the prohibited areas are no closed cordons but have exceptions for some main
roads this turn based approach will again lead to unrealistic routing of the internal city traffic
by biasing minor roads within the prohibited area. This is due to the fact, that an additional
penalty is always added when making a prohibited turn. Internal traffic will therefore not use
excluded main roads within the city area as the additional penalty occurs when leaving the
main road. Figure 8 shows an example of such an inner city relation.
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impedance =
time + turn penalty
Destination
Origin
impedance = time
Destination
Origin
Figure 8. Shortest path search for internal traffic in the turn based approach
10
Splitting trip tables in prohibition relevant segments
The impact of the shortcomings of both modelling approaches increases when including
prohibited districts within the city area. For network elements within a prohibited district an
additional penalty needs to be added in order to prohibit all district through traffic, which
includes origin, destination and internal traffic of the city as well as of external zones. The
link based approach can be extended to meet those needs by adding a Boolean attribute for
each prohibited district area, stating whether a network element is prohibited for district
through traffic or not. Including these Boolean attributes in the impedance function, likewise
to the Boolean attribute for the city, will lead to a penalty z = z city + z district which is twice as
high, e.g. 7200 seconds, if a link is both prohibited for city as well as district through traffic.
This makes clear that the problematic route choice behaviour, shown in Figure 6, will affect
some network parts even more crucially. Thus, modelling a complex through traffic
prohibition scheme, as for example implemented in the City of Stuttgart, merely by adding
network attributes is not possible but needs to include information on the origin and
destination of a trip in order to model correct route choice behaviour.
Splitting the original trip table of the prohibited demand class (e.g. the HGV trip table) in
subsets, so that one subset is only subject to interdependent through traffic prohibition areas,
provides a situation where only those Boolean link attributes are valid for a subset trip table
that influence the route choice behaviour in the same way. This approach reduces the
complexity of the problem by eliminating the interdependence between different prohibition
area levels (city level and district level) to a definite constraint for each trip table. For an
explicit allocation between trip table and valid Boolean link attributes the following subsets
need to be derived from the original demand matrix:
• One subset of external traffic, containing all trips with origin and destination outside of the
city area. For these trips all links within the city area are prohibited, with the exception of
the excluded main roads.
• One subset of origin, destination and internal traffic of the city area. For these trips only
links on the district level are prohibited while all other links are permitted.
• One subset for each prohibited district containing origin and destination traffic of this
particular district. For these trips only links within other districts are prohibited.
• One subset of internal traffic of all districts. For these trips no links are prohibited.
Now an impedance functions is defined for each demand class respectively each trip table.
Each impedance function contains additional penalties z i , of e.g. 3600s, which are
individually activated by the Boolean link attribute of the prohibited areas i that are relevant
for the respective subset.
Using subsets of the trip table together with the link based approach meets all requirements
for route choice as the internal city traffic is now unaffected. Yet with a growing number of
prohibited city districts the number of required trip tables grows linearly. The small sample
network with two prohibited districts already requires a number of five trip tables for each
prohibited demand class. A major concern in this context is that the calculation time of an
assignment depends highly on the number of demand classes in the network. Therefore, this
solution is not recommendable for modelling complex through traffic prohibition schemes as
implemented in the City of Stuttgart with a total of four prohibited districts.
11
Combination of splitting trip tables and turn based approach
In order to meet all route choice requirements for modelling complex through traffic
prohibition schemes but also providing practical calculation times, a combination of splitting
the trip table and the turn based approach is suggested. This approach makes use of the fact,
that in the turn based approach the additional impedance occurs only once when entering a
prohibited area and does not increase while travelling on network elements within. The
combined approach requires only the three following subset trip tables and is independent of
the number of prohibited districts:
1. One subset of external traffic, containing all trips with origin and destination outside of
the city area. These trips consider the turn penalties when leaving the permitted urban
road network and entering the prohibited network in the city area.
2. One subset of internal traffic of all districts. These trips do not consider any turn penalties.
3. One subset for the rest of the traffic, i.e. the city’s origin, destination and internal traffic as
well as the origin and destination traffic of the districts. These trips consider the turn
penalties when leaving the permitted road network inside the districts and entering the
prohibited network in the district area.
The problem that occurs when using this reduced set of trip tables with a link based approach
is displayed in Figure 9. The first picture shows the route choice behaviour for district origin
trips (subset three) combined with the turn-based approach. The second picture shows the
route choice behaviour for the same subset combined with the link based approach. In the turn
based approach the additional penalty occurs only when traversing an entering turn, whereas
in the link based approach the additional penalty occurs whenever using links within the
prohibited district. That is the reason why the link based approach would need an additional
subset matrix for each prohibited district.
Combining the splitting of trip tables with the turn based approach is therefore a general
solution for modelling complex through traffic prohibition schemes and is applicable to the
requirements of different cities.
12
turn based approach
Destination
Origin
link based approach
Destination
Origin
Figure 9. Route choice behaviour with turn and link based approach
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ASSIGNMENT PROCEDURES
A traffic assignment allocates the trips of all origin-destination pairs to routes (paths) in the
network, resulting in volumes on links. The resulting volumes for a given network and a
given travel demand depend mainly on four factors:
• Volume-delay function:
It describes the relationship between the volume-capacity ratio (saturation) and the speed
or travel time on a network element. A typical volume-delay function is the BPR-Function
from the Traffic Assignment Manual of the American Bureau of Public Roads (1964).
• Impedance function:
It determines the impedance of a network element which is used as input for the route
search. The impedance often includes only time, but can also consider length, road tolls,
road type and penalties for specific purposes as described above.
• Assignment procedure:
The most commonly used assignment procedure in transport modelling is the deterministic
user equilibrium assignment. But other procedures, for example a stochastic user
equilibrium, may also provide an adequate approach.
• Level of convergence:
Experiences of transport modellers show that minor changes in the network (with / without
scenario) can lead to unrealistic changes in link volumes in the entire network, if the level
of convergence (relative gap, changes of volumes or times on links or entire routes
between two iteration steps) is too low. Studies by BOYCE et al (2004) confirm that a
better stability of volumes does require better convergence.
In the calibration and validation process of modelling through traffic prohibitions for the City
of Stuttgart especially the impacts of the impedance function and of the assignment procedure
were examined.
Analysis of Assignment Procedures
In the analysis three assignment procedures were examined using the transport planning
software VISUM (PTV AG, 2005):
• Deterministic user equilibrium (DUE),
• Stochastic user equilibrium (SUE),
• Learning Procedure or Lohse user equilibrium (LUE).
In VISUM all three assignment procedures are implemented as route-based procedures, i.e. all
routes of all iteration steps are stored and can be used for analysis of convergence (e.g.
difference in impedance between routes of the same origin-destination pair) or for the
procedure itself (e.g. route choice set in a stochastic assignment).
To analyze the assignment procedures and to gain a better understanding of the general effects
of through traffic prohibition a simple sample network is used (Figure 10, first picture). All
eight links in the sample network have the same characteristics (length, speed, capacity). No
additional time is added for turning at the junction in the net middle. There are four routes
connecting the origin O1 and four routes connecting the origin O2 with destination D. All
routes have the same impedance. The travel demand between O1 and D is 1000 LDV and 200
HGV. Between O2 and D it is only half as high. It is assumed that one HGV loads the
network with two passenger car units (PCU). The expected solution for a multi-class
assignment of two demand classes is that LDV and HGV are equally distributed on all
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network links (Figure 10, second picture). On the route level it is likewise expected that each
route carries the same volume of LDV and HGV. For example, each of the four routes
connecting O1 and D should have 250 LDV and 50 HGV.
Figure 10. Symmetrical sample network and expected solution
In an equilibrium assignment the travel demand of a demand class is distributed in the
network according to Wardrop’s first principle (1952), such that all routes of one origin
destination relation have the same impedance. If several demand classes, e.g. HGV and LDV,
are assigned simultaneously in a multi-class assignment the equilibrium assignment produces
correct traffic volumes on each link as a total over all demand classes (in passenger car units).
However, it does not guarantee a unique solution for the share of trips assigned for each
demand class. Figure 11, first picture, shows one of many possible solutions for equilibrium
assignment. Because every link is loaded with a total of 1.050 PCU the load-dependant
impedance is the same on all links and therefore also on all routes in the network. The
convergence criteria for user equilibrium, which says all routes of a relation need to have the
same impedance, is therefore met. For the split between LDV and HGV on the several links
many combinations are possible. A split of 750 LDV and 150 HGV results in the same total
traffic volume of 1.050 PCU as a split of 675 LDV and 188 HGV. In the symmetrical sample
network the route-based equilibrium and the link-based equilibrium usually produce the
expected solution shown in Figure 10, but in real networks this may not be the case. On the
route level the number of routes and the route volumes in VISUM depend on the starting
solution, which usually is a three or four step incremental assignment. The common result is
two routes for each od-pair which are equally loaded.
Stochastic assignment, as it is described by CASCETTA (2001), is based on the concept of
random utility models and considers that not all travellers take the objective shortest route
15
but, with a certain probability, choose other longer routes due to insufficient knowledge or
personal evaluation. In contrast to the equilibrium assignment it explicitly uses all existing
routes as choice set when distributing the demand of an od-pair. For this reason a stochastic
assignment will produce the expected results on the level of links and routes for the sample
network.
The learning assignment procedure developed by LOHSE (1997) models the learning effect
of the traveller by slowly converging the estimated travel time to the actual travel time. The
procedure is very similar to an equilibrium assignment algorithm using the method of
successive averages. Compared to the standard user equilibrium it generates more reasonable
routes and produces better splits of LDV and HGV on routes. This advantage is normally
linked with an increase in calculation time. If the number of iterations and the level of
convergence is high the learning procedure produces the desired result and distributes the
total traffic volumes as well as the individual demand classes as expected. Thus the link
volumes are in an equilibrium state and traffic volumes in the sample network match the
expected results on the level of links and routes.
prohibited
for HGV
Figure 11. Possible solution with equilibrium assignment (left) and
effects of a through traffic prohibition (right)
Analysis of impedance function
For modelling through traffic prohibition by using the combined approach of splitting the trip
table together with turn penalties as suggested by the authors on page 12, an impedance
function including through traffic penalties has the following general form for links and turns:
16
wL = α LinkType ⋅ t L + β ⋅ lL
wT = t T + z ⋅ p1 ⋅ bCity +
(1)
NumDistricts
where
wL
impedance of a link [s]
wT
impedance of a turn [s]
tL
travel time on a link [s]
tT
travel time on a turn [s]
lL
length of a link [m]
∑ (z ⋅ p
d =1
2
⋅ bd )
(2)
α LinkType link-type specific parameter [s]
β
parameter length [s/m], e.g. 0.02
bCity
Boolean turn attribute (1, if turn enters the prohibited city network)
bd
Boolean turn attribute (1, if turn enters the prohibited district network)
p1
Boolean attribute for demand class (1, if demand class = city through traffic)
p2
z
Boolean attribute for demand class (1, if demand class = district through traffic)
additional penalty, e.g. 3600 seconds
The link-type specific parameter α aims at prioritising main roads. Initially this parameter was
0.8 for motorways, 0.9 for federal roads and 1.0 for other roads.
Validation of assignment results
For the validation process observations from 32 road side count locations were available. The
comparison of modelled and observed volumes showed a good match (GEH value < 15) for
most of the count locations in the case of the DUE and LUE assignment. The SUE
assignment, however, produced results with higher GEH values for most of the count
locations. Nevertheless it was observed that in some parts of the urban network the HGV
volume of the through traffic was unrealistically high in the base scenario without through
traffic prohibition independently of the assignment procedure. This was due to through traffic
which took a shortcut through the secondary urban network in order to avoid the highly
congested motorways around Stuttgart City. In order to overcome this shortcoming two
alternative settings were tested:
• Preference of HGV for main roads:
For HGV the link-type specific parameter α was reduced to 0.5 for motorways and 0.8 for
federal roads thus significantly favouring main roads as more adequate roads for heavy
vehicles. The tested assignment method was a multi-class Lohse user equilibrium
(M_LUE).
• Low sensitivity of HGV concerning congestion:
The multi-class assignment was replaced by a sequential deterministic user equilibrium
assignment (S_DUE), which first assigned the HGV to the uncongested network and then
the LDV. This resulted in an equilibrium state for the LDV while the HGV was not in
equilibrium.
Both approaches solved the problem of the unrealistic through traffic in the urban network.
The GEH values were slightly better for the M_LUE. Considering computation time the
17
M_LUE required a time approximately twice as high as the S_DUE. The M_LUE produced
almost 10 times as many routes as the S_DUE (7.2 million compared to 0.9 million routes).
Results concerning the traffic volumes can be found below in Figure 12.
General effects of through traffic prohibition
In general there are two main effects of through traffic prohibition:
• HGV traffic reroutes onto non prohibited links.
• Due to the reduced volume of HGV traffic, LDV traffic and urban HGV traffic partly
reroutes onto prohibited links.
These effects can also be illustrated in the sample network. Without through traffic
prohibition the learning procedure distributes the LDV as well as the HGV traffic equally on
to the network links. Yet by introducing through traffic prohibition on the lower left link
(Figure 11, second picture) for HGV traffic, all HGV are rerouted onto the lower right link.
The cleared capacity on the prohibited link leads to a reduction of impedance. The left net
loop becomes more attractive to LDV traffic because the impedance is lower than on the
alternative right loop. This leads consequently to rerouting of LDV traffic onto the lower left
link. For these considerations it is important to distinguish between vehicle units and
passenger car units. PCU are the relevant value within an assignment. If, for example, one
HGV vehicle reroutes from a prohibited link onto a non-prohibited link, this equals a shift of
two PCU. The impedance is reduced accordingly and two PCU can fill the cleared capacity.
RESULTS FOR THROUGH TRAFFIC PROHIBITION IN STUTTGART
The network model of the greater Stuttgart area includes through traffic prohibition for the
city area as well as for four city districts. The network model is fairly large with 1171 zones
and contains all discussed strategies for modelling through traffic prohibition. The following
results only compare the base scenario 0 with a scenario 1, where the through traffic
prohibition is implemented on the city level but not on the district level. Figure 12 shows the
changes in vehicle-kilometres in the prohibited and in the entire road network for scenario 1
in comparison with scenario 0. It distinguishes the results calculated for two assignment
methods:
• Multi-class Lohse user equilibrium,
• Sequential deterministic user equilibrium.
The main results concerning the traffic volumes can be summarized as follows:
• The vehicle-kilometres of HGV decrease in the prohibited network, but slightly increase in
the entire network as the HGV have to accept detours.
• The vehicle-kilometres of LDV increase in the prohibited network as LDV partly reroutes
onto prohibited links.
• The decrease in HGV vehicle-kilometres is higher when using the multi-class Lohse user
equilibrium (M_LUE). The reason for this is the route choice behaviour of the HGV
through traffic in scenario 0 without through traffic prohibition. Here a share of HGV
avoids congested roads outside the city. This traffic is rerouted in scenario 1 leading to a
decrease. In the sequential deterministic user equilibrium the HGV mainly chose the
shortest route and do not react to congestion.
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Entire Network
M_LUE S_DUE
LDV
0,0%
0,0%
HGV
+0,3% +0,3%
Prohibited Network
M_LUE S_DUE
LDV
+0,3% +0,1%
HGV
-5,1% -2,3%
motorway
main roads open for
through traffic
main roads with through
traffic prohibition
M_LUE:
S_DUE
multi-class Lohse user equilibrium
sequential deterministic user equilibrium
Figure 12. Changes in vehicle-kilometres for the prohibited and the entire road
network for scenario 1 in comparison with scenario 0
CONCLUSIONS
The work introduces a general solution for including through traffic prohibition within a
network model. The suggested approach is very suitable for modelling future scenarios of
through traffic prohibition as new prohibited areas can easily be added. It also minimizes the
number of demand classes. This is important as each demand class requires an additional
route search and therefore increases the computation time.
The discussion of the assignment methods illustrates the problem of the DUE with providing
unique link flows in the specific case of a multi-class assignment. This problem is similar to
the problem of non-unique route flows in the DUE as it is described by several authors. BARGERA (2007) suggests a solution for finding a maximum entropy user equilibrium (MEUE).
As tools for providing such an unique solution are not yet available, it seems appropriate to
either use the LUE or the SUE. Both methods produce significantly more routes than the DUE
and therefore require more computation time. In the case of the Stuttgart model the LUE
produced the better results on the link level. Despite the fact that the examined assignment
results match the measured link volumes at 32 count locations the quality of the results
remains to a certain extend unknown. The comparison of the calculated volumes with the link
counts did not show a significant difference between the two assignment methods analysed
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above. The decrease in vehicle-kilometres for HGV, however, varies significantly between
multi-class Lohse user equilibrium (-5.1%) and sequential deterministic user equilibrium (2.3%). The difference occurs mainly in the secondary urban road network, where no link
counts are available.
This uncertainty indicates a general dilemma in route choice modelling. Compared to mode
choice little is actually known about route choice in private transport. This is even more the
case when distinguishing the route choice behaviour of car and truck drivers and when
looking at route choice in dense networks with many alternatives. In general, transport
modellers can only rely on data from link counts in the calibration and validation process.
Here it would be beneficial to have more surveys observing the actual route choice of drives
in various situation.
From the perspective of a transport planer the example of Stuttgart shows that a through
traffic prohibition has the desired impact. All counts at locations in the prohibited network
show a decrease of HGV after the introduction of the prohibition scheme. Nevertheless, such
a scheme should not be considered a general remedy against high traffic and resulting noise
and air pollution. If many neighbouring cities or many urban districts implement the same
scheme it will lead to confusion and undesired detours of HGV. Here a hierarchically
organized road network with priority routes for HGV could provide a more appropriate
solution.
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