In order to create a model that will respond to real data, it was deemed necessary to introduce into the Vensim software appropriate equations that will indicate with mathematical relationships of the interaction between the variables. This process aims at a more realistic approach to the problem, as in addition to qualitative relationships, it will also provide quantitative results. In order to capture the interrelationships between the variables and to obtain the mathematical relationships of the model, four variables (stocks) were selected, as well as the demographic characteristics, as mentioned above. These variables are the population of the case study, the economy, the society, the environment, and the satisfaction of citizens.
2.3.1. Population Variables
In order to be able to carry out the level of satisfaction of the citizens of the Municipality of Patras, regarding the transport sector, it was considered necessary to introduce into the model variables referring to the total number of citizens per year, as well as to the changes that appear in this number.
Table 2 presents the equations and values of the variables used in Vensim.
The birth rate and death rate variables represent the rate of births and deaths, respectively, in Greece and therefore the way in which the population is affected. According to the 2011 census, the population of the Municipality of Patras was about 215,000 (rounded up to facilitate the analysis), while based on ELSTAT, the number of births was 9.6 per 1000 people, while the number of deaths was 10 per 1000 people in Greece in 2021. It was assumed that these percentages also apply to the Municipality of Patras. However, the population in one area is not only affected by births and deaths, but also by the transportation of people from one region to another. For this reason, the variables economy rate, environment rate, and social rate were created, which symbolize the extent to which the population is affected according to the level of satisfaction of citizens by the sectors economy, environment, and society, respectively. At this point, it was assumed that if the satisfaction of citizens at the economical level exceeds the grade 6.5 (rating scale 0–10) then the population growth rate of the Municipality of Patras will increase with a grade/step of 0.01, while if this value falls below 5.5 then the citizens will choose another area with a greater economic satisfaction index and it will decrease at a corresponding rate. Respectively, for the environmental level, if the level of satisfaction is above 7, then there will be an increase in the population growth rate, while if it is below 5, there will be a decrease. Finally, for social level, 6 and 5 were chosen as the limits, respectively. These values are an assumption.
2.3.2. Environmental
At first, certain variables that affect citizens’ satisfaction regarding the environmental level should be calculated in order to define the final equation that will give the level of satisfaction of citizens in this area. More specifically, the variables are:
B1. Energy efficiency
Definition:Total energy use by urban transport (annual average for all modes of transport).
E = Energy consumption [MJ/km]
TVpass = Passenger transport volume [passenger kilometers]
TVfre = Volume of goods transport [million tons km]
Sjk = Fuel type k per vehicle type j
Ijk = Energy intensity per distance travelled for vehicle type j and fuel type k [L/km or MJ/km or Wh/km]
Aij = Activity volume (distance travelled by mode I and vehicle type j) [million km per year]
ECk = Fuel energy content for fuel k [MJ/L or MJ/kg]
k = Fuel type (gasoline, diesel, natural gas, electric, etc.)
i = mode of transport (passenger car, tram, bus, train, motorcycle, freight train, truck, etc.)
j = Euro vehicle category (euro 0, euro 1, euro 2, euro 3, euro 4, euro 5, euro 6)
The values of the above variables used in the energy efficiency equation are derived from the completion of the excel spreadsheet (
Supplementary Materials, Figure S1a,b) based on the analysis of the data obtained from the questionnaire responses.
The numerator of the above equation was calculated as the sum of three sub-variables, which are: energy consumed—car, energy consumed—train/bus, energy consumed—truck.
In particular, for the calculation of the variable energy consumed by car, the kilometers per car, the percentages of fuel types per car, and the percentages of the euro category per car are multiplied by the energy consumption per fuel type and per euro category for cars and by the energy content per fuel type. The final price of the variable energy consumed by car is calculated by summing up the above consumptions for all citizens who use a car. The energy consumption per fuel type and per euro category is automatically calculated from the excel spreadsheet (
Supplementary Materials, Figure S1), while the energy content is constant per fuel type and is 34.2 MJ/L for Gasoline, 38.5 MJ/L foe Diesel and 25.1 for LPG. In the same way, the variables energy consumed—rain/bus, and energy consumed—truck, are calculated. The variables
Tvpass and
Tvfre are logical assumptions.
In order to calculate the change in the variables by vehicle type according to the changes occurring in the population,
Tvpass (Volume of passenger transport) and
Tvfre (Volume of freight transport) were created as an assumption, and they determine at what rate the population growth changes in any decrease.
Appendix A—
Table A1 presents the equations and values of the variables used in Vensim.
B2. Air pollutant emissions
Definition: Emissions of air pollutants from all modes of passenger and freight transport (exhaust and non-exhaust gas for PM2.5) in the urban area.
EHI = Harmful emissions equivalent index [kg PM2.5 equivalent/yearly cap]
Eeqs = Emissions of a substance type PM2.5 equivalent value of health effects
Eijkcs = Pollutant emissions per vkm resulting from transport mode i and vehicle type j for fuel type k, emission class c (g/km)
Aij = Activity volume (distance travelled by mode i and vehicle type j) [million vkm per year]
Sijk = Total fuel type k by vehicle type j and by mode of transport i
Cijkc = Total emission class c by fuel type k by vehicle type j and by mode of transport i
NEsi = Non-exhaust pollutant emissions i per distance travelled [g/km] (=0 for NOx)
cap = Number of inhabitants in the urban area [#]
k = Energy type (gasoline, diesel, natural gas, electricity, etc.)
i = Vehicle type (passenger car, tram, bus, train, motorcycle, inland waterway ship, freight train, truck, etc.)
j = Vehicle category.
s = Substance type limited to NOx and PM2.5
c = Emission class (euro)
The values of the above variables used in the equation of air pollutant emissions are derived from the completion of the excel spreadsheet (
Supplementary Materials, Figure S2a,b) based on the analysis of the data obtained from the questionnaire answers.
The numerator of the above equation is equal to the sum of the variables; NOx emissions, PM2.5 emissions, and non-exhaust PM2.5 emissions multiplied by 1000.
More specifically, the variable NOxemissions is calculated by multiplying the kilometers per mode of transport, the percentages of fuel types per mode of transport, and the percentages of the euro category mode of transport by the constant NOxEijkc referring to pollutant emissions. The final value of the variable NOxemissions is calculated by summing up all the products for all the vehicles of the Municipality of Patras.
To calculate the variable PM2.5 emissions, the variables of mode of transport, the percentages of fuel types per mode of transport, and the percentages of the euro mode of transport are multiplied with the constant PM 2.5
Eijkc. Summing up the above result for all modes of transport, the final value of the variable PM2.5 emissions is calculated. The values of the constants NOx
Eijkc and PM2.5
Eijkc are 0.064 and 1 accordingly (source: TSAP report 15, IIASA
http://ec.europa.eu/environment/air/pdf/TSAP-15.pdf, accessed on 13 January 2023).
To calculate the variable non-exhaust PM2.5 emissions, the variables mode of transport, the percentages of fuel types per mode of transport, and the percentages of the euro mode of transport category are multiplied with the constant PM2.5
NEsi. Summing up the above result for all modes of transport, the final value of the non-exhaust variable PM2.5 emissions is calculated.
Appendix A—
Table A2 presents the equations and values of the variables used in Vensim.
B3. Greenhouse gas emissions (GHG emissions)
Definition: Greenhouse gas emissions from all modes of transport of passengers and goods in the urban area.
G = Greenhouse gas emissions [tons CO2/cap./year]
Tk = CO2 emissions per unit of considered energy type [kg/L or kg/kWh]
Wk = Equivalent CO2 emission per unit of considered energy type
Aij = Activity volume (distance travelled by mode i and vehicle type j) [million vkm per year]
Sijk = Total fuel type k per vehicle type j and per mode of transport i [fraction]
Cijkc = Total emission class c per fuel type k per vehicle type j and per mode of transport i [fraction]
Ijk = Energy intensity per distance travelled for vehicle type j and fuel type k [L/km or MJ/km or kWh/km]
Cap = Resident or number of inhabitants in the urban area [#]
Fijk = GHG correction without CO2 (CO2 equivalent)
k = Energy type (gasoline, diesel, natural gas, electricity, etc.)
i = mode of transport (passenger car, tram, bus, train, motorcycle, inland waterway vessel, freight train, lorry, etc.)
j = Category of vehicle
The values of the above variables used in the equation of greenhouse gas emissions are derived from the completion of the excel spreadsheet (
Supplementary Materials, Figure S3a) based on the analysis of the data obtained from the questionnaire replies.
The numerator of Equation (3) is calculated as the sum of the GHG emissions for all vehicles in the Municipality of Patras multiplied by 1000. For the calculation of the variable GHG emissions, the kilometers, the percentages of fuel types, the percentages of the euro category per car and the energy intensity, with the sum of the CO
2 emissions and the equivalent emission, are multiplied. CO
2 is calculated as the sum of the constant 1 with the correction GHG without CO
2 (
Supplementary Materials, Figure S3b).
Appendix A—
Table A3 presents the equations and values of the variables used in Vensim.
B4. Quality of public spaces
Definition: Citizens’ satisfaction with public spaces.
h being the four replies of the agreement scale:
(strongly agree, somewhat agree, somewhat disagree, strongly disagree)
and
where: C
h = strongly agree = 10, C
h = somewhat agree = 6.66, C
h = somewhat disagree = 3.33, C
h = strongly disagree = 0.
The data collection of this indicator was carried out using the questionnaire (S1). The methodology and analysis are presented in detail in
Supplementary Materials, Figure S4.
More specifically, the variable “satisfied” equals the number of citizens who answered “satisfied” to the questionnaire divided by the sum of the citizens who answered “Rather satisfied”, “Rather unsatisfied” and “Not at all satisfied” multiplied by the constant Ch = 10. The variable “Rather satisfied” equals the number of citizens who answered “Rather satisfied” to the questionnaire divided by the sum of the citizens who replied “Satisfied”, “Rather unsatisfied” and “Not at all satisfied’ multiplied by the constant Ch = 6.66. The variable “Rather unsatisfied” equals the number of citizens who answered “Rather unsatisfied” to the questionnaire divided by the sum of citizens who replied “Satisfied”, “Rather satisfied” and “Not at all satisfied” multiplied by the constant Ch = 3.33. The variable “Not at all satisfied” equals the number of citizens who answered “Not at all satisfied” to the questionnaire divided by the sum of the citizens who answered “Satisfied”, “Rather satisfied” and “Rather unsatisfied” multiplied by the constant Ch = 0.
Finally, the sum of all the above values gives the value of the final satisfaction for the variable public spaces. Following the same methodology, the variable green spaces is calculated.
Appendix A,
Table A4 presents the equations and values of the variables used in Vensim.
In the field of the environment, it is assumed that all the individual variables have the same weight in terms of citizens’ satisfaction. Hence, the equation of Environmental Satisfaction is:
2.3.3. Social Variables
In this subsection, the variables referring to the satisfaction of citizens with society are calculated. Through the determination of these variables, the corresponding equation of overall satisfaction in the field of society will also be developed.
C1. Security
Definition: The perceived crime risk and passenger safety in urban transport.
where:
, h being the four replies on the perception of crime related security: (Very safe, safe, unsafe and very unsafe)
and:
where: C
h = Very safe = 10, C
h = safe = 6.66, C
h = unsafe = 3.33, C
h = Very unsafe = 0
The values of the above variables used in the equation of the security variable are derived from the completion of the excel auxiliary spreadsheet (
Supplementary Materials, Figure S5) based on the analysis of the data obtained from the questionnaire answers.
The variable “Very safe” is equal to the number of citizens who answered “Very safe” to the questionnaire, divided by the sum of the citizens who replied “Safe”, “Unsafe”, and “Very unsafe”, multiplied by the constant Ch = 10. The variable “Safe” is equal to the number of citizens who answered “Safe” to the questionnaire, divided by the sum of the citizens who answered “Very safe”, “Unsafe” and “Very unsafe”, multiplied by the constant Ch = 6.66. The variable “Unsafe” is equal to the number of citizens who replied “Unsafe” to the questionnaire, divided by the sum of the citizens who replied “Very safe”, “Safe” and “Very unsafe”, and multiplied by the constant Ch = 3.33. The variable “Very unsafe” is equal to the number of citizens who replied “Very unsafe” to the questionnaire, divided by the sum of the citizens who replied “Very safe”, “Safe” and “Unsafe”, multiplied by the constant Ch = 0.
Finally, the average value of the sum of all the above values gives the final satisfaction for the variable car. (Feeling safe regarding the use of the car). In the same way, the variables public transport, pedestrian safe, motorcycle, and bicycle are calculated (Feeling safe regarding each mode of transport).
Appendix A,
Table A5 presents the equations and values of the variables used in Vensim.
C2. Traffic safety active modes
Definition: Deaths of users of active modes of mobility in urban traffic accidents in relation to their exposure to traffic.
RFi = Risk factor for mode i
Ki = Number of people killed within 30 days after the road accident as a consequence of the incident in a pedestrian mode (motorcycles) [# simple average over the last 3 years for which data are available]
Expi = Report, defined as number of trips (in millions) [# per year]
i = Mode of transport (pedestrian, bicycle)
The values of the above variables used in the equation of the security variable are derived from the completion of the excel auxiliary spreadsheet (
Supplementary Materials, Figure S6) based on the analysis of the data obtained from the questionnaire answers.
Appendix A—
Table A6 presents the equations and values of the variables used in Vensim.
C3. Road deaths
Definition: Road deaths in the urban area on an annual basis.
FR = Mortality rate [# per 100,000 inhabitants of the region per year]
Ki = Number of people killed per mode of transportation I (Pedestrian, Bicycle, Moped, Motorcycles, Cars, HGV—Trucks, LGV, Bus) [# per year]
Cap = Number of urban area inhabitants [#]
i = mode of transport
The values of the above variables used in the equation of the road deaths variable are derived from the completion of the excel spreadsheet (
Supplementary Materials, Figure S7) based on statistical data of ELSTAT.
Appendix A,
Table A7 presents the equations and values of the variables used in Vensim.
With the change in population growth rate in the region, road deaths per mode of transportation will be affected accordingly. For this reason, rate variables (ri) have been created to show the rate of change in deaths by mode of transportation. The rates are an assumption of this research.
C4. Satisfaction with Public Transportation (PT)
Definition: The perceived satisfaction with the use of public transportation.
, h being the four replies of the agreement scale:
(strongly agree, somewhat agree, somewhat disagree, strongly disagree)
where: C
h = strongly agree = 10, C
h = somewhat agree = 6.66, C
h = somewhat disagree = 3.33, C
h = strongly disagree = 0
The values of the above variables used in the equation of the variable “Satisfaction with PT” are derived from the completion of the excel spreadsheet (
Supplementary Materials, Figure S8) based on the analysis of the data obtained from the questionnaire responses. The variable “strongly agree” is equal to the number of citizens who answered “strongly agree” to the questionnaire, divided by the sum of the citizens who answered “somewhat agree”, “somewhat disagree” and “strongly disagree”, multiplied by the constant C
h = 10. The variable “somewhat agree” equals the number of citizens who answered, “somewhat agree” to the questionnaire, divided by the sum of the citizens who answered “strongly agree”, “somewhat disagree” and “strongly disagree”, multiplied by the constant C
h = 6.66. The variable “somewhat disagree” equals the number of citizens who answered “somewhat disagree” to the questionnaire, divided by the sum of the citizens who answered “strongly agree”, “somewhat agree” and “strongly disagree”, multiplied by the constant C
h = 3.33. The variable “strongly disagree” is equal to the number of citizens who answered “strongly disagree” to the questionnaire, divided by the sum of the citizens who answered “strongly agree”, “somewhat agree” and “somewhat disagree”, multiplied by the constant C
h = 0.
Finally, the sum of all the above values gives the final satisfaction for the variable General Satisfaction. In the same way, the variables General Satisfaction, Affordable, Reliable, Easy to Get, Frequent, and Safe are calculated. The variable “Satisfaction with PT” is calculated as the average value of the sum of the variables General Satisfaction, Affordable, Reliable, Easy to Get, Frequent, as well as Safe.
Appendix A,
Table A8 presents the equations and values of the variables used in Vensim.
C5. Commuting travel time
Definition: Duration of commuting to and from work or an educational institution, using any mode of transportation.
Tcom = Average commute time [minutes/day]
Touti = Commute time at work/school per person I [minutes/day]
Treturni = Commute time at home per person i [minutes/day]
n = number of people in the survey
The values of the above variables used in the equation of the “Commuting travel time” variable are derived from the completion of the excel spreadsheet (
Supplementary Materials, Figure S9).
Appendix A,
Table A9 presents the equations and values of the variables used in Vensim.
With the change in population growth rate in the region, travel time will be affected accordingly. For this reason, “rate to home” and “rate to work” variables were created, which show the rate of change. The equations as well as the initial values of these variables are an assumption of the research.
C6. Congestion and delays
Definition: Delays in road traffic and public transportation during peak hours compared to non-peak hours travel (private road traffic) and optimal travel time on public transportation (public transport).
CDij = Congestion and delay index (percentage of delay during peak hours)
CTi = Number of car trips during peak hours on the main road corridor i
PHTi = Travel time by car during peak hours on the main road corridor i [minutes]
FFTi = Off-peak travel time by car on main road corridor i [minutes]
PTj = Number of journeys by public transport to travel during peak hours on the transit corridor j [#]
PTPHTj = Travel time on public transport during peak hours on the main road corridor i [minutes]
PTOTj = Optimal travel time on public transport on the main road corridor i [minutes]
MSroad = Road traffic share [%]
MSpt = Share of public transport [%]
The values of the above variables used in the equation of the variable “Congestion and delays” are derived from the completion of the excel spreadsheet (
Supplementary Materials, Figure S10) based on the analysis of the data obtained from the questionnaire answers, as well as from reasonable assumptions made for traffic on 10 roads of the city of Patras at peak and non-peak hours.
Appendix A,
Table A10 presents the equations and values of the variables used in Vensim. The variables rate MSpt and rate MSroad were created as an assumption and are used to show the change in the respective variables in relation to the population.
It is assumed that all the individual variables have the same weight in terms of citizens’ satisfaction in the field of society. The final equation concerning the social satisfaction of citizens is defined as:
2.3.4. Economic Variables
In a similar way, in the third area of the research, which concerns the satisfaction of citizens in the field of the economy, the calculation of the individual variables is first conducted so that the final equation can be determined.
D1. Access to mobility services
Definition: Total population with appropriate access to mobility services (public transport).
Accl = Appropriate Access Index
PRi = Number of people living in the access typology zone i, determined by the combination of the level of accessibility PT (public transport).
Wi = Weight to determine if accessibility to mobility services is appropriate/good (depending on the combination of the PT accessibility level).
Supplementary Materials, Figure S11 contains the calculation of the indicator. The weight varies for small (i.e., less than 100,000 inhabitants) or large urban areas. The Municipality of Patras is classified as a large urban area.
The Wi weight is preset and determines if accessibility is appropriate (or good) as follows:
i = 1 where absolutely appropriate
i = 0.5 where not fully appropriate
i = 0 where not appropriate
Cap = A number of inhabitants in the urban area [#]
For the calculation of the above indicator, an analysis of the answers to the questionnaire has already been made. More specifically, the calculation of the variable “people with no access” is calculated as the product of people without any access multiplied by the weight w1. The calculation of the variable “people with low access” is calculated as the product of people with low access multiplied by weight w1. The variable “people with medium access” is calculated as the product of people with moderate access multiplied by weight w2. The variable “people with high access” is calculated as the product of people with high access multiplied by weight w3. Similarly, the variable “people with very high access” is calculated as the product of people with very high access multiplied by the weight of w3.
Finally, the variable “parameter value of access to mobility services” is calculated as the sum of all the above, divided by the total population.
Appendix A,
Table A11 presents the equations and values of the variables used in Vensim.
D2. Public transport affordability
Definition: Share of the population using public transport cards (PTCs) (unlimited monthly trips or equivalent) in the urban area.
D3. Quality of public spaces
This indicator, apart from the field of the environment, was also chosen in the field of economy, as the development of public and green spaces requires infrastructure, the cost of which is borne by the municipality.
D4. Active Mobility
Definition: Infrastructure for active mobility, in particular walking and cycling.
Ram = Share of road length adapted for active mobility [n]
Lpv = Length of road network with sidewalks (not if on a pedestrian street) [km]
Lbl = Length of road network with cycle paths (not if in a zone of 30 km/h) [km]
Lz 30 = Length of road network in a zone of 30 km/h [km]
Lpz = Length of pedestrian zone [km]
Lrn = Total length of city road network (excluding motorways) [km]
For the calculation of this indicator, data were collected from GOOGLE EARTH, while at the same time, some reasonable assumptions were made.
Supplementary Materials, Figure S12 details the calculation of the indicator.
Appendix A,
Table A13 presents the equations and values of the variables used in Vensim.
After calculating the above variables, it follows that: