System Model 



The system diagram in problem analysis section is used to develop detailed system diagram with causal relations. This point out that, the study assumes causal model (system dynamics) to express the system. For more deep details mathematical equations (mathematical model) will be used to express the relations of various factors in the model.      As from definition a system model or diagram should present the input, output and the system itself. The inputs to system are the external variables and the instrumental variables while system variables are the internal variables and outcomes of interest are the output variables. They are show in the causal model and explained below:

Causal Model

  • External Variables: They have the influence on the behavior of the internal variables of the system but they themselves cannot be influenced by other variables from the model. The external variables are economic development, population, weather, technological advancement price of cars and fuel which can be seen above in the diagram. These variables affect the internal variables of the system like: income, number of cars on the road, driving speed, public transport capacity and car & fuel buying power respectively.
  • Instrumental Variables: These variables cannot be measured empirically, but is determined by the user of the model  They are the policy alternatives or the tactics that are adopted to affect the system i.e. they are the ‘knobs’ that model user can turn to change the output of the system. The instrumental variables are expand A13 highway, increase private car tax, introduce double Decker train and buses, use fuel cell technology, introduce hybrid vehicles, etc. These variables steer the internal variables and would finally affect the output variables. For example if we increase the car tax then the car buying power would decrease and hence the number of cars on the highway would decrease, which would at the end affect the congestion (output variable).
  • Internal Variables: These variables are the inside the system which are affected by external and instrumental variables and they react internally and give the output of the system. The internal variables react with each other to give the output e.g. if the population increase the number of people driving car increases, which would lead to the increase of cars on the highway and this would increase the gaseous emission and finally that would affect the output variable the local pollution. The number of cars also affects the congestion.
  • Output Variables: They are the outcomes of interests. They provide targeted information about the behavior of the modeled system. The output variables are the affect of the external variables, internal variables and the instrumental variables. The output variables are congestion, travel time, accidents and local pollution. The internal variables like number of cars, gaseous emission, waiting time, etc. affect the output variables. For example the congestion is more because of the number of cars on the road is more, this is because the car buying power has increased which is due to the increase in the income which is due to the economic development.
  • System Boundary: By defining the system boundary we will be able to differentiate on variables which we can affect and which we cannot. The variables that we can affect are inside the system boundary and the remaining variables are outside the system.

Scope of the model
For a clear presentation there should be clear relations between factors and to the outputs. The relations besides being shown by the causal relations but for simulation purpose they should be possible to express mathematically.  Using  the causal model following mathematical equations is shown as an example, that how the study will apply the system model to get the information among the variable mathematically:

Note: Before developing the mathematical model each factor of the system has to be operationalized by giving units.

•    Consider the oval with the factor ”emitted gases”(EG) . The factor emitted gases is influenced with four factors namely Number of cars on road (NCR), number of freight trucks (NTR), fuel used (FU) and car fuel efficiency (FE).

The mathematical equation is
EG = FU * FE * NCR  +  FU * FE * NTR
EG = FU * FE * ( NCR + NTR)

Consider the units  to perform the dimensional analysis
Vg/t = Vf * Vg/(Vf *NC)*( NC/t + NC/t)    V= volume, f=fuel, g=gas, NC=cars=trucks
Vg/t = Vg/t

Thus the dimensions are equal so the equation is correct and thus do not need any addition or multiplication of a constant parameter. The equation so is
    EG = FU * FE * NCR  +  FU * FE * NTR

•    Consider the output local pollution (LP) . The factor has only one link thus from emitted gas(EG). The equation will be
EG = c*EG
    Performing dimensional analysis using the units
        M3 = c* M3/time
So to balance the constant c should be measured in time units thus hour or years or days. So the equation will be
    EG=c*EG     where c is a constant

•    Consider the congestion (CG) . The factor has five links that are number of cars on road (NCR), tracks on road (NTR), Number of roads (NR), number of driving lines (NDL) and driving speed. The will be
CG=(NCR + NTR)/(NR * NDR * DS)
Thus performing dimensional analysis using the units.
     NC/km = (NC/t + NC/t)/(R * L/R * km/t/L)
NC/km = NC/km

Thus the dimensions are balanced and so the equation remain
    CG = (NCR + NTR)/(NR * NDL * DS)

Data required and collection

From the analysis the data needed for this study are those related to the factors as presented in the detailed system model with causal relations. The list of the information that the study needs is shown in table below. The data can be obtained by various means. Some few that this study will assume are literature study (TUDelft library), statistical reports (central Bureau of Statistics CBS), observations (surveys and tests with experts), interviews and researches.

However information that will help for the implementation of the tactics might need research such as

  • Effect of the fuel cell technology on the gaseous emissions
  • Effect of use of hybrid cars on the pollution
Data needed Method of collection
Average travel time per person & Literature study
Average number of cars per kilometer Surveys
Average speed of the car  Statistical report
Distribution of traffic over time Statistical report
Number of death due to accidents Statistical report & Literature study
Number of fatalities due to the accidents Statistical report & Literature study
Number of accidents Statistical report & Literature study
Concentration of different poisonous gases in the environment Literature study and measurements
Amount of gaseous emissions per car per kilometer  Literature study and measurements
Percentage of citizens in the different salary slab Statistical report
Employment level Statistical report
Number of people using public transport Surveys and Statistical report
Waiting time Surveys and calculations
Number of people traveling from Rotterdam to the Hague and vice a versa by car and by public transport Surveys and Statistical report
Number of trucks per km length Surveys
Birth and death rate Statistical report


As mentioned in previous section the strategies are developed after the model is build. The model is run using different tactics and the results are noted. The tactics, which help to attain specific outcomes of interest, are combined into a strategy, which would help us to attain our main objective.

The result from running the model for different tactics after screening can be put in the scorecard . The decision maker would then use the scorecard. He would give weights to each criterion and then rank the strategies or tactics. Ranking is given using different methods like even swaps, normalization, by giving weights or by using colour coding.






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