A group multicriteria decision aid and system dynamics approach to
study the influence of an urban toll and flexible working hours on the
congestion problem.
Johan Springael, Pierre Kunsch and J ean-Pierre Brans.
CSOO-Vuije Universiteit Brussel
Pleinlaan 2, B-1050 Brussels, Belgium
Tel.: +32-2-629.20.47 Fax: +32-2-629.21.86
email: jspringa@ mach.vub.ac.be
Abstract
The effect of an urban toll and flexible working hours on traffic crowding in cities is analysed by means of a
framework based on a methodology in which system dynamics and group multicriteria decision aid are
combined. The basic model, which extends a congestion model described by K. Small, examines the
behaviour of driving car commuters with respect to their home departure times to office during the morning
tush hours. Several strategies for urban toll combined with working time flexibility are investigated as well
as the possible use of the benefits induced by the toll for transforming the vicious circle of crowding into
virtuous circles, e.g. promoting alternate transport means.
1, Introduction.
A major problem nowadays in Westem countries is the so called congestion problem. It is clear that the road
network is no longer sufficient to handle the traffic. Especially the traffic crowding in the cities resulting in
large traffic jams in the moming and the evening have reached a level far above the acceptable limits.
In this paper we try to understand potential solutions for this problem through the combination of several
techniques of operational research such as system dynamics and multicriteria analysis. Our starting point is
a simple congestion model introduced by K. Small (1992) based on the trade-off between two cost-
functions: the time people spent on road when driving to the office, and the pressure of the schedule people
are “suffering” to get at time at the office (9 am. in our model). The major supposition in this model is that
every car commuter from the suburbs defines his personal strategy for leaving home by calculating this
trade-off.
With our model we try to apply Small’s theory and to extend it in such a way that it would enable us to
propose possible solutions allowing an influencing on the trade-off made by the car commuters.
In the next section we briefly explain the techniques used in the model. In the third section the basic
assumptions of the model are discussed. Finally, the last section consist of a first model which has still to be
validated and which is partially under construction.
2. Multicriteria decision making and system dynamics.
Our everyday experience leams us that tackling socio-economic and environmental problems is a very hard
thing to do. System dynamics with its focus on structuring a problem seems an appropriate technique to help
us to understand the basic mechanisms of these complex problems. However, most “analysts” use system
dynamics only to understand the problem and to make a long term forecast. Afterwards the model is never
used again. Some of the authors: J.P. Brans et al. (1998) proposed to go beyond what most system dynamic
users do by introducing a method to control this socio-economic or environmental system based on control
theory and multicriteria analysis.
Important questions in the construction of a system dynamic model are: for who is the model intended,
which policies should be examined, etc. (see e.g. G.P. Richardson and A.L. Pugh (1981)). In relation to
these two question Brans et al. proposed to use a multicriteria analysis with the following purpose: the
decision maker (i.e. the person using the results of the model) will have to make a choice between several
policies simulated by the model. Most of the time this choice will depend on the outcome of different
variables, which may not all have the required value or behaviour. Hence, a choice must be made between
different policies which are validated on several, possibly conflicting, criteria. It is at this stage that the
multicriteria techniques can help the decision maker. Which multicriteria method is used, is not essential at
this stage, in principle any method can be used.
Once the decision maker has determined its policy, this policy is implemented as well in the model as in
reality. It is now that the control and monitoring phase starts. A constant interaction between the real data
and the expectations of the model takes place. Though if the behaviour of the variables in the real world are
diverging too much from those expected in the model a waming signal occurs, meaning that the policy was
not the appropriate one or that the model was too restrictive. In this way they were able to construct a
decision support system for complex socio-economic problems.
However, an important lack in the structure of their method, which was later on remarked by C. Macharis
(1999), is that the system itself can incorporate choices (ie. the system itself is making choices between
several options) and that these choices are goveming the system and its behaviour. In our model we will
incorporate such a “decision-motor” based on the multicriteria method PROMETHEE introduced by J.P.
Brans and P. Vincke (1985), which we have transformed in such a manner that it could be used in our
model. However, we are not working with one decision maker within the system but with a large number
since the decision makers in the system are nothing but the car commuters. Hence, we must introduce some
kind of statistical decision making which would lead to a distribution of choices or percentages of decision
makers choosing a particular option.
The transformation of the PROMETHEE method is necessary since this gives a ranking of the several
choices and not a percentage or a distribution. If we now suppose that the car commuters are all alike and all
think more or less in the same way, one can transform the Promethee-I ranking into a distribution by means
of the following expression:
probability of choice A=9*(A)(1-9~(A)) (2.1)
where g*(A) and g (A) respectively stand for the power and the weakness of the choice A (for more
explanation and detail on the Promethee method we refer to J.P. Brans and B. Mareschal (1994)).
3. Basic assumptions of the model.
A first assumption we made is that of an idealised city, in which the car commuters get immediately from
their house on the highway and from the highway to their job. In a much more advanced stadium of the
model the bottleneck effects rising up at the entrance and exit of the highway should of course be
incorporated in the model. We also suppose that there is only one highway to this city, and that every car
commuter must take this highway. Although this is a large simplification it seems to be good approximation
of the reality.
In this model we are only interested in the moming traffic jams. Hence the model is constructed in such a
way that it leads to an iteration process (by resetting the levels and certain crucial variables on their initial
value), each iteration representing a day from 6 am. till 12 am. Of course if we want to fully implement
flexible working hours without any limit on the time to start 24 hours should be modelled, including also the
traffic jams in the evening. The integration step of the model represents 6 minutes, which implies that in our
model every 6 minutes a bunch of people are leaving from their home. Hence, the distribution of departures
is known every 6 minutes. The iteration interval (360 minutes) and the time step (6 minutes) can easily be
adapted in the model such that extending the length of the iterations to 24 hours should not be to difficult.
After each iteration we make the hypothesis that every decision maker asks himself the question in the
evening at what time he will leave in the moming, taking into account the past situations and traffic jams the
days before, and making the balance between the several criteria through the use of the cost-functions.
A final and more technical assumption is the one with respect to the “decision-motor’. In the model we
suppose that the “decision-motor” generates the statistical decision making process in an appropriate
manner. Presently it is too early at this stage of the model to confirm this. Validation tests should be
performed in order to calibrate this “decision-motor’” and its inclusion in the system dynamic model.
4. The iterative system dynamic model.
As already mentioned the model is constructed in such a way that it generates an iterative process. In fact if
one considers a single day the main process of people leaving home, getting on the highway and then
arriving at their job is a so called open loop problem (blue part of fig.1). However, in reality the car
commuters take into account what the traffic jams would be, using there daily experience, in their decision-
process on leaving home. Of course they are making a guess, expecting that the situation would be the same
as yesterday and the day before, etc. This leads to the creation of certain habits which is translated into a
kind of optimal departure distribution. This effect can easily be verified experimentally: the day after a long
holiday, traffic on highways becomes chaotic; after a week or so the distribution of departures has
converyed towards its optimal shape. Hence, the study of this departure distribution through an iterative
process could leam us something about this convergence.
It is clear that if we can influence the departure distribution in such a way that the number of people on the
road at the same time decreases, a part of the traffic jams will dissolve and the congestion will also diminish.
So the question remains: how can we influence the distribution of departures in an appropriate way ?
A first approach is to try to modify the cost-functions by implementing several strategies. To modify the
time spent on road directly it would be a hard task, since this can only be done by investing in infrastructure
(such as enlarging and adding highways). Moreover this solution would not be sustainable in the sense that
after a while the same problem would arise again. A real sustainable solution can in our opinion only be
generated by changing people's habits.
toll,
people at
er oe
anivals office cost ee:
cost time on road
people on s
ng Siggy (2%! leaving igvay
moving way ae, .
% time on road
Yo es \ distribution of decisions
minimal time on road
congestion on highway”
people home} Ee x
maximal road capacity
Figure 1: Sketch of the model.
The people's habits with respect to the departure time are in fact imposed and restrained by the second cost-
function namely the pressure of the schedule: people must be at time at their job or they are penalised and
can even lose there job. By giving them some freedom with respect to the working schedule through the
introduction of flexible working hours the fear of being too late at their job will disappear. Hence, the weight
of the cost-function pressure of schedule in the decision-process will decrease, which determines the
distribution of departures as can be seen in the above figure.
However, by only allowing flexible working hours, the effect on the moming jams would probably be
marginal since habits of people are very inelastic by definition. Hence, an incentive should be created in
such a way that affects them deeply, namely their wallet. This can be done by adding a new cost-function
namely a toll when entering the city depending on the degree of congestion at that time starting from a given
threshold (in pink in fig. 1).
The introduction of this third cost-function corresponds to the introduction of a control loop, the intensity of
which can be regulated. In this way we are able to control the system and to guide it to a desired level. If this
toll is well chosen (i.e. if the intensity of the control loop is well determined) the people will get the incentive
to leave earlier or later in the moming. However, it is an absolutely necessity that this toll is combined with
flexible working hours, otherwise the effect of the toll will be practically nonexisting. The taxes collected
through the toll can then be used to increase the investments for a better public transportation network which
on its tum would create an incentive for people to leave their car home. However, the influence of the public
transportation has not been included in this model, because it is beyond the scope of this model.
5. Conclusions.
In this paper we have tried to demonstrate on the traffic problem the necessity to combine several techniques
with system dynamics modelling. This necessity is imposed by the nature of the problem itself since there
are different time scales. Although we were not able to present simulation results here, due to the fact that
several parts of the model need to be validated, the basic structure of the model is clear and allows us to
understand the process which cause the traffic jams in the moming.
One may conclude that if one wants to “solve” (partially) the traffic problem, it is the departure distribution,
created by some statistical decision process of the car commuters from the suburhs, which should be spread
out by introducing new cost-functions for these decision makers.
References.
Brans, J.P., Macharis, C., Kunsch, P.L., Chevalier, A. and Schwaninger, M. (1998) Combining multicriteria
decision aid and system dynamics for the control of socio-economic processes. An iterative
real-time procedure European J ournal of Operational Research 109, 428-441.
Brans, J.P. and Mareschal, B. (1994) The PROMCALC & GAIA decision support system for multicriteria
decision aid Decision support systems 12, 297-310.
Brans, J.P. and Vincke, P. (1985) A preference ranking organisation method. The PROMETHEE method
for MCDM Management science 31, 647-656.
Macharis, C. (1999) Hybrid Modeling: System Dynamics combined with Multi-criteria Analysis, submitted
for publication.
Richardson, G.P. and Pugh, A.L. (1981) Introduction to system dynamics modeling, MIT Press, Cambridge,
Massachusetts.
Small, K. (1992) Urban transportation economics, Harwood Academic Publishers.
CC BY-NC-SA 4.0