Traffic Shifts in a Comprehensive Truck Toll System
A Real-World Multi-Agent Based Simulation Case Study
Dr. Heinz Schild
Bonn - Bad Godesberg, Germany
Summary
As part of a project which deals with comprehensive free-flow toll systems for trucks
and buses, a multi-agent based simulation model was developed. This model is used
here to discuss the general development process for multi-agent based simulations
which map real-world situations and whose results are the foundation for real-world
decisions. It will be demonstrated that developing such models is a demanding task,
requiring detailed understanding of the relevant reality and meticulous work.
Goals
Based on a case study this paper aims to
‘ describe the approach when developing a multi-agent based simulation model of a real-
world problem
‘ spell out the issues requiring special consideration in the course of the development and
implementation process of the case study
& explain conclusions derived from the simulation results for real-world problems.
The case study is part of a project in which a concept for a comprehensive free-flow toll system
for trucks and buses in central and eastern European countries is explored. In this concept ! all
trucks and buses with a gross weight of 3.5 t or more are to be eligible for tolls on every public
road of a country. Rebates are granted for kilometres driven on higher-ranking roads as an incen-
tive to transfer traffic to these roads. Higher-ranking roads permit higher speeds, normally give
rise to fewer accidents and have better noise protection facilities; their externality costs are nor-
mally below those of lower-ranking roads. Free-flow operations require that onboard units be
installed in all the toll-eligible vehicles wanting to apply for a rebate on the standard toll charge.
1 Schild, Heinz: Umfassendes Lkw-Mautkonzept, Begriindung, Gestaltung und Beschaffung, Bonn, Oktober 2005,
www.caselab. info
? Onboard units are needed to register the kilometres driven on the different road types. Two techniques are common
nowadays. With the DSRC technique, data abon the road segments which have been passed are collected with the help
of gantries which communicate via microwaves with the onboard unit in the vehicle. With the GPS technique, the road
segments passed are located using GPS (in future Galileo) and data are transmitted to the central system using GSM.
1
Only GPS-based onboard units are considered in this study. They give toll system operators
greater freedom in determining the roads on which rebates will be granted.
Fig. | shows the main actors and processes of the relevant real-world segment as a UML Use-
Case diagram >.
Overview
——
Owners ~ hes
Dispatcher =~
1
A
Other Vehicles
1 '
‘\<einclude at << include >>,
<< include >> %
OBU Decision
ons no include >> —
Standard Route Toll-eligible i 1 K
Vehicles :
‘ 9
1
'
pee Weather
? \
Freight Commission acest
Toll System Operator
Client
Toll and OBU
Fees
Roads
Fig. 1: Actors and processes
A client assigns a freight commission to the operator of a toll-eligible vehicle. The operator’s dis-
patcher plans the route in such a way that his business goals can be optimally fulfilled. Planning of
the route depends on whether an onboard unit is installed in the vehicle or not. The operator will
only install an onboard unit in a vehicle if he expects that during the lifetime of this vehicle the toll
savings made by taking advantage of the rebates on higher-ranking roads will be greater than the
costs for the onboard unit. The planned route may deviate from the standard route to take account of
both the rebates on the standard toll charges and the expected delays due to congestion on the
higher-ranking roads. Traffic conditions during the journey mainly depend on the amount of traffic
on the roads used and their capacity. These traffic conditions may cause substantial delays which
the dispatcher of the vehicle will bear in mind when he plans future routes for the vehicle.
> UML stands for unified modeling language. Here version 2 was used as implemented in “Poseidon for UML Standard
Edition from www.Gentleware.com, 2005
It is the intention of the case study to analyse and quantify the deviation of optimised routes from
standard ones when traffic transfers from lower- to higher-ranking roads depend on the amount of
rebate on the standard toll charges. The findings are important for toll system operators, as they can
help them to estimate the amount of revenue they may lose due to rebates and to recognise the
amount of traffic transferring to the higher-ranking roads which may subsequently generate political
pressure to upgrade these roads.
It will be shown later that a multi-agent based simulation model seems to be the appropriate means
to support this study.
Design and implementation
Characteristics and problems of multi-agent models
A multi-agent simulation model maps explicitly the behavior of every agent as influenced by its
own attributes and the behaviour of other agents into a computer program which calculates the in-
teractions of all agents over some period of time. Agents can be autonomous, proactive, reactive
and interactive +. In our case agents are vehicles and road segments.
Multi-agent models sometimes have advantages over models which use global or aggregated enti-
ties. The agents, their attributes, behaviour and interactions may be directly observable in the real
world. However, the modelling of their behaviour should be based on a relevant and broadly ac-
cepted behaviour theory and not on episodic and subjective impressions only. Models based on
global or aggregated entities are highly abstract and depend on theoretical concepts and statistical
data. The behaviour of their entities is not directly observable but deduced using statistical means,
mostly regression analysis.
Nevertheless, the mapping of agents, their attributes and behaviour is normally not a straightfor-
ward task. Often constraints exist concerning the available development time, the expressive power
of the simulation language and the know-how of the developer. Multi-agent simulations normally
need much more computer power than global simulations and may be handicapped by the available
computer systems. These constraints often do not allow all aspects of the real world to be mapped
in their original scales. For instance in the real world modelled here, 40,000 toll-eligible vehicles
drive on the roads simultaneously. For reasons discussed later, the model has to make do with 500
vehicles, meaning a scale of | : 80 has to be applied.
4 See also Wooldridge and Jenning (1995) quoted in Gilbert, Nigel, Troitzsch, Klaus G.: Simulation for the Social Sci-
entist, Second Edition, Maidenhead, 2005, Chapter 8
In order to extract behaviour procedures directly from observations and pass them on into the
model, scales must be chosen in such a way that their combination maps those states for which the
behaviour is relevant on a | : | scale.
Even if the design of the scale follows this rule, mapping errors are unavoidable. They are caused
by simplifications and by formulating behaviour relationships or selecting values for attributes
which only approximate reality. Using a multi-step validation and calibration process, the effects of
the mapping errors must be reduced enough to allow conclusions to be drawn from the model re-
sults which have relevance for the real world.
Graphical representations showing the agents and their states during a simulation run are very help-
ful in debugging a multi-agent simulation program and validating behaviour relationships. They are
an essential part of a multi-agent simulation.
Overview of the design and implementation process
The design and implementation process of a multi-agent simulation model and program, though
broadly similar to that of common simulation models, is in some respects quite different. It consists
of a set of tasks which must be performed at least once >. The process is not always linear and may
loop back.
The tasks are:
1. Describe the problem which is to be solved by a model in a comprehensive and clear way.
2. Select the appropriate modelling method and the computer tool for implementing it.
The following tasks are relevant if the multi-agent simulation method and a computer tool specially
provided for this method are being used.
3. Identify the actors and use cases which cover the reality to be modelled and which appear
relevant to the problem at hand. Select those processes which will build the core of the model,
those actors which will become the agent classes and finally designate the processes and ac-
tors which affect the model via input parameters.
4. Determine the main output variables of the model and the main parameters of the alternative
scenarios to be investigated with the model.
5. Specify the agent classes and subclasses of the model and their specific attributes.
5 See Gilbert, Nigel, Troitzsch, Klaus G.: Simulation for the Social Scientist, Second Edition, Maidenhead, 2005, Chap-
ter9
Determine the number of instances of the agent classes and the size of the simulation interval,
bearing in mind the limits of the “simulation view window” ° which can be programmed with
the chosen tool.
Design the possible movements of the dynamic agents in the simulation view window and
their states.
Map the endogenous and interactive behaviour of the agents using programmable behaviour
functions and applying approved behaviour theories, published observations of relevant spe-
cialists or own experiences and intelligent guesses.
Determine the time regime of the simulation in such a way that the output variables are not
unduly disturbed by start-up abnormalities and oscillations.
Implement the simulation program and debug the code; search for mapping errors and im-
plausibilities by studying the simulation view window and other ad-hoc charts and improve
the program until its results no longer contradict relevant information about the real world.
Perform simulation runs by systematically varying parameter settings to explore the behav-
iour space of the model. Select one scenario whose results correspond reasonably with the
real world. Fine-tune it by calibrating the behaviour equations of the agents until progress in
the simulation and the final results sufficiently map the real world.
Perform simulation runs with the fine-tuned model and alternative scenarios to generate the
behaviour space for the problem. The behaviour space should allow one to draw conclusions
as to how, and how sensitively, the real world will react to exogenous decisions or events.
Document the model and its implementation and the evaluated scenarios with their inputs and
results to substantiate the findings.
Step 1: Problem description
The problem which is to be dealt with in this case study has already been outlined above (see Fig.
1). It is always good practice to apply UML and its visualisation tools.
In this study the operator of a comprehensive truck toll system wants to examine how rebates on the
standard toll charges which are granted for the kilometres driven on higher-ranking roads may af-
fect the traffic flow and toll revenues. A computer model is to be developed to provide further in-
sights.
© In the “simulation view window” the agents and their moves during a simulation run are visualised. Agents are de-
picted as icons. Colours may be used to show different states of the agents.
5
A metric must be applied which is compatible with the real situation of a central European country
in 2002. In this country there existed 2,000 km of motorways and 10,000 km of through roads.
About 40,000 toll-eligible vehicles on average travelled on these roads during main traffic hours.
Step 2: Method and tools
The movement of vehicles and their interactions while on a journey will be simulated with the
computer model. The traffic situations depend on the characteristics of the instances of the road
classes and the different behaviour patterns of the vehicles. It seems obvious to apply the multi-
agent based simulation method for the computer model and not one based on aggregated entities.
Several software packages are available for the implementation of multi-agent simulation models.
Because of previous knowledge ’ and positive experiences with it *, NetLogo for Mac OS X 10.4 on
an Apple PowerBook G4 with a 1024 x 768 12” screen was selected. This constrains the maximum
number of agents and the maximum number of simulation periods and simulation runs. The con-
straints must be considered when designing and implementing the model.
The statistics language R ° was used for the preparation of some of the input data and the behaviour
equations needed in the simulation model. The analysis of the results of the simulation runs was
done with Quantrix Modeller !°, a multi-dimensional spreadsheet software.
Step 3: Core process and agent classes
The core process of the simulation model covers the four use cases which are shown in violet in
Fig. 1. The main use case is “Journey”. It includes “Route optimising”, “Traffic” and “Delays en
route”. From among the actors directly associated with the core use cases, only those actors who
interact in a way relevant to the problem form the agent classes. They are the “Toll-eligible
vehicles”, the “Other vehicles” and the “Roads”.
The other actors and use cases affect the model through parameters which either are direct inputs to
the simulation or are attributes of the agents or parameters of behaviour equations. Examples of the
first type are the standard toll charges and the costs for onboard units. Other parameters are the spe-
cific mean journey length for every toll-eligible vehicle or the mean percentage of vehicles using a
7 Schild, Heinz: Enforcement in Free-Flow Systems: a Case Study, System Dynamics Society Proceedings of the 22nd
International Conference, Oxford, 2004
8 Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-
Based Modeling, Northwestern University, Evanston, IL
®R : Copyright 2005, The R Foundation for Statistical Computing, Version 2.1.1 (2005-06-20), ISBN 3-900051-07-0,
http://cran.r-project.org/
10 Quantrix Modeler, Professional Edition, Version 2.000.3, www.quantrix.com
6
specific instance of a road class. Further parameters are needed for the weights with which current
and historical information or rumours about delays are combined to estimate the risk of a delay dur-
ing the next journey.
Step 4: Result variables and alternative scenarios
During the design and implementation process of a multi-agent model one can easily be led astray.
This can happen if one investigates too many interesting-looking details or concentrates primarily
on those features which are easy to implement using a subset of the tool one is most familiar with.
To prevent getting caught in a dead end, the variables for which the simulation must produce values
should be defined before implementation work is started. These variables should be reporter vari-
ables, as they are called in NetLogo. Reporter variables do not have equivalents in reality but com-
bine values from other variables for reporting purposes.
Here we are interested in the transfer of traffic from lower to higher-ranking roads as a result of re-
bates on the standard toll charges. Therefore the simulation model should deliver values for the fol-
lowing reporter variables:
. proportion of toll-eligible vehicles with onboard units installed
. mean relative saving of toll fees by taking advantage of rebates and transferring parts of the
route to higher-ranking roads
. mean proportion of toll-eligible vehicles for which their dispatchers notice delays and take
these into consideration when planning the next journey
. mean proportion of kilometres driven by toll-eligible vehicles which were transferred to
motorways compared with all kilometres driven on motorways by these vehicles
. mean proportion of kilometres driven by toll-eligible vehicles which were transferred to
through roads compared with all kilometres driven on through roads by these vehicles,
. mean proportion of toll-eligible vehicles driving on motorways.
In order to solve this problem, values of the reporter variables are needed for a set of alternative
scenarios. The scenario parameters which define the behaviour space of the problem should be
. rebate schema (combination of the rebates for through roads and motorways)
. number of toll-eligible vehicles
° number of other vehicles.
Step 5: Agent classes and their instances
As already mentioned, three agent classes should be sufficient. They are
. the toll-eligible vehicles (trucks)
. the other vehicles (cars)
. the roads.
The next question is whether these classes should be split up into subclasses and if so, how. When
answering this question, one should bear in mind that subclasses can be substituted by additional
attributes of the instances. On the other hand, it is easier to visualise subclasses or their instances
than attributes. Visualisation helps one to understand the behaviour of the model and makes debug-
ging quicker but normally demands more computer resources.
Splitting up the class of toll-eligible vehicles into subclasses would be reasonable if the rebates de-
pended on the weight or number of axles of the vehicles. But this is not an assumption in this study
(although in reality it may be the case). Here different rebates are granted according to road type
only. The instances of the class of toll-eligible vehicles are depicted in the simulation view window
as small icons with a shape like a truck. They own static and dynamic attributes. For example, the
attribute “mean journey length” is static because it does not change during a simulation run whereas
the attribute “current speed” is dynamic. The attribute “OBU”, which may have the value “yes” or
no”, is set after the start-up period and then remains static. The icons of vehicles with an onboard
unit are red, those without an onboard unit are blue. The distribution of the values of the static at-
tributes of all instances should be sufficiently similar to that observable in the real world.
The role of the other vehicles in the model is to generate realistic congestion situations like those
found during holiday periods. Therefore no subclasses are needed. The instances of the class of
other vehicles are depicted as small yellow icons with a shape like a car. They also have static and
dynamic attributes.
The class of roads must definitely be split up into subclasses. Following the practice in traffic engi-
neering, three subclasses should be used !!:
. motorways (and dual carriageways) or limited-access facilities (US)
. through roads (often called A roads) or arterials (US)
. local roads (all other roads including secondary urban roads) or collectors and local streets
(US)
The standard toll fee is charged for every kilometre driven on every road subclass. Toll-eligible
vehicles with onboard units installed get rebates for the kilometres driven on motorways and
11 US terms: see Roess, Roger P. et.al.: Traffic Engineering, Third Edition, N.J, 2004
8
through roads. The level of rebate may differ for motorways and through roads. The instances of the
road subclasses are depicted as tracks and are distinguished by the mean traffic which they carry.
Does the topology of the road system have a significant influence on the interactive behaviour of
the toll-eligible vehicles? Experience shows that in segments where roads join or where the width of
a road is reduced congestion is more frequent. Unfortunately no comprehensive data about these
congestion sources exist for the relevant real world. Therefore it seems prudent to do without them
in the model. The tracks of the road subclasses are implemented in the simulation view window as
simple ribbons of equal width without interchanges and arranged parallel to the x-axis , coloured in
different shades of grey. Each ribbon is divided into equal-sized patches.
The instances of the vehicle classes move along the ribbons from left to right. Because the simula-
tion view window uses the wrap-around feature, vehicles leaving at the right edge reappear on the
left.
[Model Objects
‘Agent classes
Vehicles Roads
A ay
fToll-eligible Vehicles Motorways:
Other Vehicles Through roads
Fig. 2: Agent classes
Step 6: Scales
In the preceding section the agent classes and subclasses and their instances were defined at least in
principle. In a next step the cardinality of the instances must be decided upon. For this the granular-
ity of the simulation view window is crucial. Tests show that a 12” screen with a resolution of 1024
x 786 patches consisting of 9.5 pixels allows one to see sufficient detail. With patches of this size a
simulation view window of 101 columns and 41 rows is reasonable and leaves enough space on the
screen for other necessary input and output fields.
Each of the 41 rows of the simulation view window is an instance of a subclass of road. In this
model the local roads are only feeders for the higher-ranking roads. It is assumed that congestion on
them will not influence the transfer of traffic between road subclasses. All toll-eligible vehicles
have their home and goal locations in patches which are an instance of local roads. As will be ex-
plained later, 500 or 600 instances of toll-eligible vehicles will be used. To visualise these in the set-
up phase and later during the simulation, 11 rows are sufficient for the instances of the local roads.
Every instance of road “owns” 101 columns or patches. It proved useful to interpret a patch as a
stretch of road which a vehicle driving at 50 km/h passes in one minute. The length of a patch is
equivalent to 833 m in the real world. The length of an instance is about 85 km, but due to the wrap-
around effect it is equivalent to about 100 km in the real world.
To prevent mapping errors in congestion behaviour the same scale must be applied for the cardinal-
ity of the motorway and the instances of the through-road subclass. As stated earlier, in that part of
the real world which is relevant to this study there are 10,000 km of through roads with 20,000 lane
kilometres and 2,000 km of motorways with 4,000 lane kilometres !?. There are 30 rows available
in the simulation view window to depict these. That means 25 rows can be assigned to the through
road instances and 5 to the motorway instances. The scale for the kilometres is approximately 1 :
10.
Finally one must determine the number of instances of toll-eligible vehicles. As said earlier, 500
vehicle icons can be recognised sufficiently well in the simulation view window. With 500 instances
to be represented, the scale of toll-eligible vehicle instances is 1 : 80.
Real-world observations can best be applied in a modelled state when they are not distorted by
scale. This would mean that the scale should be | : 1. In our model this situation occurs when a toll-
eligible vehicle gets caught in congestion or drives in a queue. Its behaviour depends on the dis-
tance to the vehicle ahead when this vehicle starts breaking or accelerating. This distance is about
50 m. The scale for this distance in the model, denoted X , in combination with the other scales
must be | : 1, as formulated as a rule at the beginning of this chapter. Thus:
Xx (1:10) / (1: 80) > (1: 1).
The scale 8 : 1 fulfils the condition. This means that in the model a vehicle starts to react when its
distance to the next vehicle ahead is 50 x 8 or about half the length of a patch, which is 416 m.
!2 It is assumed for purpose of the model that the toll-eligible vehicles drive only on one lane of the motorways.
10
Step 7: Movements and states
NetLogo, like most other multi-agent simulation packages, is a discreet simulation software, not an
event-driven one. Every simulation run consists of equally long time steps. In this model one step
is equivalent to one minute in reality.
At the start of a simulation the subclasses of the roads are created in the simulation view window.
Next the icons for the instances of the other vehicles are put on the tracks of the through-road and
motorway subclasses. The density distribution of the vehicles over the tracks must be similar to that
observed in reality, as explained in greater detail later. The tracks of the through roads are placed in
ascending order of vehicle density in the simulation view window, the tracks of the motorways in
descending order. This makes visual analysis of congestion on the through roads and motorways
easier. The distribution of the instances of the other vehicles in the tracks is uniform random. Fi-
nally the icons for the instances of the toll-eligible vehicles are put on the tracks of the local roads
in a uniform random fashion. The icons are still blue because the decision as to which vehicle will
have an onboard unit installed will be made later. Fig. 3 shows the simulation view window after
set-up.
« « - aa GS « « &
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* Se Cy ada ‘* ane eas a ‘ae we
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a ane ave a «
aa = ee aa
oe oe « .
* ry « aa
om o
. ae *
« rn 2
a * *
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Fig. 3: Simulation view window immediately after set-up
At every simulation time-step every vehicle performs one of the moves described as follows:
First every vehicle checks whether its current speed has already reached the maximum speed al-
lowed in the current track for that vehicle type; if not, it increases its speed. After this the vehicle
moves along its track to the right for as many parts of a patch as it can drive in one minute, depend-
ing on its current speed. If it overshoots the length of route segment planned for the current road
class, the vehicle immediately moves vertically up or down to the next track, as defined in its route
plan. There it checks its speed and eventually adapts it.
11
If the vehicle is in a track on a through road or motorway, it also checks whether any other vehicles
are within its reaction distance. If this is the case, it slows down its speed to that of the slowest ve-
hicle and thereby starts a queue or adds itself to an already existing queue. A vehicle in a queue
moves at the same speed as its predecessor. A queue starts disbanding when the leading vehicle has
covered the length of route segment planned for the current road class and has moved to a track in
another road class.
A toll-eligible vehicle which has come to the end of its current journey receives new values for its
route-related attributes and starts its next journey at the next simulation step.
Fig. 4 shows the states a toll-eligible vehicle can be in and the transitions between states.
TallEligible Vehicle States,
Generate tricks wih attributes Finished on
Congested ve
through road Commesied Ne Firished Congested ave
Thome Tocaion — cemetery
nthe local road
No vehicle wain 7
reaction distance
eect No vehicle wah
tev longe Siowvehide poem
start nest tip veftin the Priel
reaction distance
Toloca road Weclrocds
Finished
es oat on motorvey
Bac to hame postion a iN Slow vehicle within
\ reaction dstence
Totheloca road \.
Tothe through road
Drive an the
local road
Finished on the
through road \
~~
Unabaructed arive Unobatructed erive
onthe motorway
onthe through road
To Broad
Tometorvay
Finished on local road
Nest segment?
Fig. 4: The states of a toll-eligible vehicle
The role of the other vehicles is to help model realistic congestion situations. Therefore no specific
journeys need be generated for them. They move along in their tracks and only carry out the follow-
ing manoeuvres if they encounter a queue.
At the beginning of every simulation step the vehicle checks if any other vehicles are within its re-
action distance in its current track or in the immediately neighbouring tracks to the left or right. If
not and if not yet driving at its permitted maximum speed, the vehicle increases speed and moves
on. If yes, it lowers its speed to that of the slowest vehicle ahead and moves on. If there is no other
vehicle in one of the immediately neighbouring tracks within its reaction distance, it jumps to that
track, adapts it speed appropriately and moves on. This means vehicles can overtake other vehicles.
12
At the start of a simulation step vehicles which are not in their home track jump to that track unless
hindered by other vehicles there.
Fig. 5 shows the states which an instance of the class of other vehicles can be in and the transitions
between states.
(Gther Vehicle States
No vehicle in my postion
‘on the home track lobstructed drive but not on
whom e track on thraugh raed
No dow/vehide wahin reaction
distance any longer
Slowvehicte wahin
reaction distance
a Cangeded drive on my home
(Gnobetructed drive on my track on the through road
Ihome track on the through road]
_______J stowvehicte within
50 % of cars on home reaction clstance
‘rack on through road
Generate COFS 59 % of cars on home
track on motorway
he inobstructed drive onmy) Slowvehicle within (Congested drive on my home
home track on motorway | reaction distance | track on the motorway
Slow vehicle wahin
reaction distance
indbstructed dive but not On my)
No vehicle in my postion home track on the motorway
‘on the home track
No slow'vehicle within reaction
distance any longer
Fig. 5: The states of other vehicles (cars).
Fig. 6 shows an example snapshot of the simulation view window after about 1000 simulation steps
with some queues on the motorway tracks and also some on the through road tracks.
Fig. 6: Example of the simulation view window after about 1000 simulation steps
13
Step 8: Behaviour functions
In this simulation model three groups of behaviour functions are applied:
. at the set-up of a simulation run: functions to generate the instances of the agent classes and
the values of their static attributes,
. at the start of a new journey of a toll-eligible vehicle: a function which determines the values
of the attributes characterising the route of the next journey and the behaviour during the
journey when specific states are encountered,
. during the simulation run: functions which govern the interaction between instances depend-
ing on their current states.
At the set-up of a simulation run the values of global attributes like the standard toll fee or the price
of an onboard-unit including installation costs are determined. Then the tracks of the road sub-
classes (co-ordinates and colours) and the maximum speed allowed on them are generated. In addi-
tion distribution functions are activated which assign to every track on the through roads and
motorways the percentage of vehicles starting there. This reverse J-shaped function is derived from
the relevant data of the real world. For example it defines that 22 % of the vehicles will start on the
first track of the motorway and only 7 % on the fifth. Fig. 7 shows the distribution for through
roads.
%
5 10 15 20 25
track number
Fig. 7: Distribution of vehicles over the tracks of the through roads
14
After this the instances of other vehicles and their attributes are generated. The number of instances
depends on the scenario being investigated. Half of the instances are randomly distributed over the
through roads and the other half over the motorways. The vehicle distribution over the tracks of the
road classes is the same as described above. These tracks are the vehicles’ home tracks.
Next the instances of the toll-eligible vehicles with their attributes are generated and in a uniformly
random distribution placed on the patches of the tracks of the local roads. The number of instances
depends on the scenario being investigated. A very important attribute of the vehicles is their mean
journey length. The journey length distribution is derived from the relevant data of the real world
and has a monomodal shape which is skewed to the right with a mean value of 60 km. Another im-
portant attribute indicates whether the vehicle has an onboard unit installed or not. The decision
whether to install an onboard unit or not takes into account the values of rebates, the price of the
onboard unit and other realistic factors concerning the journey pattern of the toll-eligible vehicle, as
is explained below. The decision is postponed to the end of the start-up phase of the simulation run.
At the start of every journey of a toll-eligible vehicle the total length of the standard journey and the
lengths of its route segments on the three road subclasses must be generated. The total journey
length is calculated by means of a stochastically distributed J-shaped function with a mean equal to
the value of the vehicle’s mean journey length as generated earlier. Using uniformly random num-
bers and with the maximum values for the segment lengths set as global attributes, the segment
lengths on the local and through roads of the standard route are then generated. The segment length
remaining for the motorways is simply the difference between the total length of the journey and
the sum of the segments on the local and the through roads.
For vehicles which have an onboard unit installed a check is performed to find out if the standard
route can be optimised by taking advantage of rebates. This must take into account the possible sav-
ings from driving on an optimised route as well as the delays due to congestion which may be en-
countered on this route. As many kilometres as possible are transferred to higher-ranking roads to
optimise the route. Minor detours which make the optimised route slightly longer than the standard
route are accepted. Intelligent guesses are used to set the minimum segment length for the road sub-
classes.
If many other vehicles optimise their routes, the probability of congestion on the higher-ranking
roads will increase. This is related to problems which are the domain of the Minority Game !3. Con-
trary to the approach of the Minority Game, there is a predefined solution tactic in this case. Model-
ling the behaviour procedure which maps the dispatcher’s estimation of the risk of delays due to
13 A NetLogo version of the Minority Game is implemented by Daniel Stouffer; see Wilensky, U. (2004). NetLogo Mi-
nority Game. http://ccl.northwestern.edu/netlogo/models/MinorityGame. Center for Connected Learning and Computer-
Based Modeling, Northwestern University, Evanston, IL
15
congestion depends largely on episodic observations and the transfer of experiences '+ from other
traffic situations. The decisive quantity is the standardised relative time advantage between driving
on the motorway vs. on the through road '5. Its expected value for the next journey is calculated by
weighting and combining the experience which the vehicle gathered from its last journey, the expo-
nentially smoothed experiences from all other journeys of the vehicle, information about the current
situation on the motorways and through roads, and the exponentially smoothed information from
past periods about the motorways and through roads. The weights are one of the means to calibrate
and fine-tune the model, as will be discussed later.
Looking at experiences with the truck toll system in Germany, one can assume that dispatchers base
their decision to deviate from the standard route mainly on the possible savings in toll charges. Only
if these do not seem worthwhile, do they consider the consequences of delays and change the stan-
dard route by transferring kilometres from the motorways to the through roads or even onto the lo-
cal roads. This behaviour is modelled by defining a threshold value for the savings, which is then
applied to the rebates and which must be surpassed before the dispatcher deems it cost-effective to
optimise the journey route.
The route which will be stored in the vehicle attributes is defined by five values: km on local roads
“up”, km on through roads “up”, km on motorways , km on through roads “down” and km on local
roads “down”. If the total journey length is very small, then segments on the through roads or the
motorways may become zero.
Step 9: Time regime of the simulation
Progress during the simulation and the states at the end of a run may be disturbed by singular start-
up behaviour and later by strong oscillations. These effects can mask the real results or produce dis-
torted findings. A properly designed time regime for the simulation runs will eliminate or at least
attenuate them.
This model shows a distinct start-up regime due to the simultaneous generation of all toll-eligible
vehicles in their home locations. Trial runs demonstrate that the start-up behaviour subsides when
each vehicle has finished on average 10 journeys. At this point the decision will be made in which
vehicle an onboard-unit is to be installed.
Vehicles with onboard units may optimise rebate payments by transferring traffic to the higher-
ranking road classes. But then the probability of congestion and delays increases, which makes op-
14 See Underwood, Geoffrey(Ed): Traffic and Transport Psychology: Theory and Applications, Amsterdam, 2005
'5 standardised relative time advantage between driving on the motorway vs. on the through road =
(speed on motorway / speed on through road ) / (effective top speed on motorway / effective top speed on through road)
16
timising less attractive. The oscillation caused by this feed-back loop never ceases but its amplitude
becomes relatively stable after a certain number of simulation steps. Only then should the sampling
of simulation results start. In this case-study sampling starts after each vehicle has finished 30 jour-
neys on average. To limit computer power run time, the simulation is stopped after each toll-eligible
vehicle has finished 50 journeys on average.
Simulation models apply random number generators. To eliminate the effect of their seed values, 10
runs are performed in this model for each scenario and the results registered. These are condensed
using standard statistical methods and their spread visualised.
Step 10: Debugging and validation
The model was implemented with NetLogo. Although debugging is supported by NetLogo features,
for instance by the possibility to single out one agent, put a spotlight on it and follow its movement
in the simulation view window during a simulation run, it is still a demanding exercise. Software
tools for multi-agent simulation on personal computers do not handle the activities of the agent in
parallel but transform them into sequences, sometimes in an idiosyncratic way. Debugging needs a
thorough understanding of what the code really does. The best way to gain this insight is to take
some time “playing” with the program until one really knows how the agents behave and interact
and which piece of code triggers what. All the while one should aim to improve the code by simpli-
fying or amending it until it is parsimonious and perfectly transparent.
The bug-free functioning of a multi-agent simulation program does not automatically mean that it
maps the relevant part of the real world correctly. It must be validated. The standard validation pro-
cedure would be to compare the results from the simulation program with known data about the real
world. This does not really work with multi-agent models because at best only global data are avail-
able for the real world and not at all, or not in sufficient detail, for a sufficient number of agents.
What is known about the behaviour of real agents is often only episodic, biased and not representa-
tive. As a surrogate for the missing real data a plausible scenario about the behaviour of agents and
the whole system was created. This scenario is based on information from professionals working
with freight companies, toll operators and the authority in charge of monitoring freight traffic on
roads. Missing aspects were supplemented with “intelligent” predictions and guesses.
The program was walked through, executed and adapted until it was recognisably no longer false or
implausible; i.e., the agents behaved as expected in all their possible states and the relationships of
the result variables showed correct signs and magnitudes.
17
Step 11: Calibrating
Before a validated multi-agent simulation program can be applied to produce quantitative predic-
tions for alternative scenarios it must be calibrated. Here calibrating means finding through a trial-
and-error process values for parameters which are not directly observable and measurable in the
real world. In this case-study two sets of parameters are used. One set consists of the weights in the
behaviour procedure which estimates the standardised relative time advantage between driving on
the motorway as opposed to on the through road. The other is the threshold which allows the dis-
patcher to decide if the route for the next journey of a toll-eligible vehicle should be optimised or
not.
To calibrate the weights they must be varied until a calibration benchmark is satisfied. Here the
proportion of drivers of toll-eligible vehicles who, before the launch of the toll system, perceived
serious delays on motorways due to congestion outside main holiday weeks was used as a calibra-
tion benchmark. The benchmark value is 5 %. To find the combination of values for the calibration
parameters which best satisfies the benchmark, their behaviour space !° with the weights as dimen-
sions was generated and evaluated.
When calibrating a multi-agent simulation model sometimes no meaningful combination of values
for the parameters can be found which will satisfy the benchmark. Normally the problem can be
solved with an adaptation of the behaviour procedure of which the parameters are a part. Sometimes
more far-reaching changes are required.
In this case-study the calibration process uncovered a minor error in the program. After its correc-
tion and re-validation of the model, values for the parameters were found which give a reasonably
close approximation to the benchmark value even when the parameter values were varied slightly.
Step 12: Alternative scenarios and behaviour space
A series of alternative scenarios was executed with the validated and calibrated simulation program.
As input data those explained above under 4) were used:
. Rebate schemata:
Schema |: through roads 0 %, motorways 0 %
Schema 2: through roads 5 %, motorways 5 %
Schema 3: through roads 5 %, motorways 10 %
. Number of toll-eligible vehicles:
500
16 NetLogo has a feature called “BehaviorSpace”. It allows the alternatives and the number of runs to be defined and
executes them in batch mode. After each run the input data and the result data are collected in a matrix.
18
600
. Number of other vehicles:
100
200
Each of the 18 combinations of input data was run 10 times.
Findings of the case study
Results
About 10 hours of computer time were needed to execute the runs for the alternatives. The resulting
matrix with the input and result data for the alternatives was further processed. Fig. 8 shows a selec-
tion of the result variables in condensed form.
Rebate Toll eligible Other Mean % km added Mean % km added | Mean % vehicles on
schema vehicles | vehicles to motorways to through roads motorway
100 -3.0 3.4 31.3
500
200 -13.9 13.9 30.5
1
100 -7.0 78 31.5
600
200 -20.7 19.6 30.2
100 11 2.6 33.9
500
200 -6.2 10.8 33.5
2
100 -2.1 6.4 34.3
600
200 -16.1 19.8 31.9
100 17.2 -8.8 43.6
500
200 7A 5.2 414
3
100 10.0 0.5 43.0
600
200 0.2 12.0 39.1
Fig. 8: Results of the simulation
The values are the arithmetical means of the data collected by the BehaviourSpace feature of Net-
Logo during the simulation steps between the point when on average every toll-eligible vehicle fin-
ishes 30 journeys to the point when on average every vehicle finishes 50 journeys. Because 10 runs
19
were evaluated for every result variable, the arithmetical mean of these 10 values then had to be
calculated.
The effect of the random numbers on the mean percentage of toll vehicles driving on motorways is
shown as “box and whisker plots” !7 (see Fig. 9). The boxes in the middle indicate quartiles and
medians. The lines show the largest/smallest observations that fall within a distance of 1.5 times
the box sizes. The x-axis is composed of the alternatives. The first 4 columns stand for the alterna-
tive where no rebates on the standard toll fee are considered, the next 4 for the alternative with 5 %
rebate for all kilometres driven on through roads and motorways, the last 4 for the alternative with 5
% rebate for all kilometres driven on through roads and 10 % for all kilometres driven on motor-
ways.
Mean % of toll-
igible vehicles on motoways
t
eam f
& H =
; i 7 i ; i ; i ; i ; i
100.500.1 100.600.1 100.500.2 100.600.2 100.5003 100.6003
‘Scenarios: 1st: Other vehicles, 2nd: Toll eligible vehicles, 3rd: Rebate schema
Fig. 9: Box plot based on 10 simulation runs
Fig. 10 shows in one column the minimum and maximum mean values of the rebates effectively
gained by the vehicles with installed onboard units for the 3 rebate schemata. These rebates are
slightly smaller than the possible maximum, which would be 5 % for the second rebate schema and
about 7.5 % for the third rebate schema. The deviations are caused by the detour kilometres and the
transfer of traffic to lower-ranking roads to avoid congestion.
The other column shows the percentage of onboard units installed in the toll-eligible vehicles. As
long as rebates are small, as in the second rebate schema, onboard units make sense from an eco-
nomic point of view, and under the assumptions made here, only for those vehicles which on aver-
age drive long journeys.
'” Dalgaard, Peter: Introductory Statistics with R, New York, 2002, p. 65
20
Rebate schema Mean effective rebates % Onboard units installed %
1 0 0
2 42-44 28-31
3 67-68 94 - 95
Fig. 10: Rebates and onboard units.
Conclusions
The values of the result variables look reasonable in their tendency and magnitude. The higher the
rebates, the more traffic is transferred to the higher-ranking roads. Increasing the number of
vehicles halts this trend but only to a small extent.
Before quantitative conclusions can be drawn from the results the influences of the simplifications
which have been made in the simulation model must be discussed. In the model a toll-eligible vehi-
cle starts its next journey immediately after the previous one has ended. In reality the start of the
next journey is always delayed and follows a pattern over the hours of the day, days of the week and
over the weeks of a year. As a consequence of these patterns the traffic load and the probability of
congestion change over time. When the peak traffic hours are over, congestion usually dissolves
quickly if not caused by accidents. These effects are not included in the model. Therefore the
congestion-related results are to some extent distorted, as discussed later.
Including the start pattern of the vehicles in the model would have increased the complexity of the
code and the number of periods per simulation run. As it is, the model uses about 1500 steps in a
run to collect values for the result variables. To map the daily traffic pattern 1440 steps would be
needed for one day (in the model one simulation step equals one minute in real time). To achieve
statistically stable results a simulation run would have to cover at least 10 days. Hence, about 10
times more simulation steps then used in the study now would be needed. This is beyond the capa-
bility of the available computer.
The percentage of toll-eligible vehicles driving on motorways increases more than linearly when the
rebates are increased. While in the second rebate schema the proportion of vehicles on motorways
increases only 0.6 percentage points for 1 percentage point of rebate increase compared to the sce-
nario without rebates, for the third rebate schema the increase is 1.8 percentage points. In reality
this number will be slightly higher because the model overestimates the delays caused by conges-
tion. On the other hand congestion caused by accidents or bad weather conditions are not included.
21
The proportion of vehicles driving on motorways is not very sensitive to a change in the number of
vehicles. A 20 % increase in toll-eligible vehicles combined with a 100 % increase in other vehicles
reduces the proportion of vehicles driving on motorways by 3 percentage points for the second re-
bate schema and by 3.7 percentage points for the third. Hence, an increase in other vehicles, for
instance during holidays, has a greater effect than an increase in toll-eligible vehicles. Due to the
simplifications in the model the reduction in the proportion of vehicles driving on motorways is
overestimated.
The results of the multi-agent simulation model allow the road owners to draw helpful conclusions
when considering the introduction of a comprehensive truck toll system. Nevertheless, road owners
should bear in mind that the model results are slightly negatively biased due to the simplifications
discussed above. Negative here means that the results look less advantageous for the road owners
than they would be in reality. A few of the conclusions derived from the results presented above are
spelled out as follows:
< Only when the rebates offered are higher than 5 % and strongly differentiated between
through roads and motorways will there be a considerable traffic shift. Rebates below 5 %
have too small an impact on the traffic structure, do not reduce the externality costs signifi-
cantly and therefore are not worth the effort. To find the rebate schema with the best cost/
benefit ratio the externality costs and other relevant influences must be assessed and
weighted, which is beyond this study.
. Those bottlenecks on the motorways which are especially sensitive to the number of other
vehicles should be eliminated before the launch of the toll system. Otherwise delays caused
by congestion and experienced by the dispatchers may unduly hinder the shift of toll-eligible
vehicles to the motorways.
. The shift of traffic to the motorways is not very sensitive to changes in the number of toll-
eligible vehicles. An increase in the number of toll-eligible vehicles over the next years will
not substantially increase pressure on the road owners to expand the capacity of their motor-
ways.
A global corporate model was developed for the comprehensive toll system. There the traffic shifts
between through roads and motorways are modelled by behaviour equations. To find appropriate
mathematical functions for these behaviour equations and their parameters, econometric methods
were used which evaluated the data generated by runs of the multi-agent simulation model.
It is hoped that this study has demonstrated that multi-agent simulation models are a useful device
for dealing with real-world problems and has shown how to proceed in such circumstances. Some-
22
times, as in this case, it would seem that multi-agent simulation is the best approach available. But
the study should also have demonstrated that developing such models is a demanding task, requir-
ing detailed understanding of the relevant reality and meticulous work. Models based on global or
aggregated variables definitely take less time to implement. Maybe this is the reason why in recent
years many agent-based demonstration models have been announced and offered for downloading
on the internet but real-world based ones have rarely become widely known.
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