# Analyzing Demand with Respect to Offer of Mobility
## 4 Model and Analyzer
### Beginning and Final Stops' Analysis  
We focus on some parameters when analyzing beginning \(s_{beg}\) and final \(s_{fin}\) stops of trips: household density, parking density and service provider density which are formal defined as follows. **Household density. ** Since the residential buildings density near a stop increases, then a higher number of pick-ups (drop-offs) could be considered at the stop in the morning (afternoon). More precisely, it is more expected that the commuters/city-user begin (end) their H2W (W2H) trips at the given stop in the morning (afternoon). Figure 6 shows the residential building density at the stops A and B using the Overpass Turbo tool [45]. **Parking density. ** As above-discussed, commuters study or work places in restricted traffic zones, typically park their private vehicles in public parking spaces, and then use public transport systems to reach their destination in the morning (see Figure 3). Moreover, in the afternoon, the public transport system is used to reach the parking spaces to reach home by private vehicles. Therefore, like residential buildings, in the morning (afternoon), when the density of public parking spaces around a stop increases, more commuters can use the given stop. Since a considerable number of commuters use public parking spaces to park their private vehicles, stops around public parking spaces, compared to those around residential buildings, usually could produce and attract more commuters. To consider this point, we define \(pr\) (parking-residential) weight vector \(W_{pr}[parking,residential]\), where a higher weight for a place (e.g., \(W_{pr}\)\([parking]=0.95\)), compared to others (e.g., \(W_{pr}\)\([residential]=0.05\)), indicates that a higher number of commuters could start (or end) their H2W (or W2H) trips at a nearby stop. Formally, we have:  
**Definition 3**. : _Let \(P_{bg}(s,mgg)\big{(}P_{fin}(s,aft)\big{)}\) denote the probability that stop \(s\) is a beginning \(s_{bgg}\) (final \(s_{fin}\)) one in the morning (afternoon). It is then calculated as in (10)._  
\[P_{bgg}(s,mng)=P_{fin}(s,aft)=e^{(-\frac{1}{spr(s)})} \tag{10}\]  
_It is noted that \(\alpha_{pr}(s)\) is the parking-residential level of stop \(s\), which indicates the normalized weighted sum of the number of public parking spaces and residential buildings in circle \(c(s,r)\), and calculated as in (11)._  
\[\alpha_{pr}(s)=\frac{u_{pr}(s)-u_{pr}(min)}{u_{pr}(max)-u_{pr}(min)} \tag{11}\]  
_where, \(u_{sp}(s)\) is the \(pr\) weighted sum of stop \(s\) and calculated as in (12)._  
\[ \begin{array}{l}u_{sp}(s)=N_{pr}(s,parking).W_{pr}[parking]\\ +N_{pr}(s,residential).W_{pr}[residential]\end{array}  \tag{12}\]  
Figure 6: Density of residential buildings around stops **A** and **B**. \(N_{pr}(\text{parking})\) and \(N_{pr}(\text{residential})\) are respectively the number of public parking spaces and residential buildings in circle \(c(s,r)\). Furthermore, \(u_{sp}(\text{min})\) and \(u_{sp}(\text{max})\) respectively denote the minimum and maximum pr weighted sums, considering all stops._  
**Service provider density. ** There are several categories of service providers including work (e.g., offices, shopping malls) and study (e.g., schools, universities) places. As mentioned, in the morning, the city-users are supposed to go to work/study (H2W trips) and return in the afternoon (W2H trips). Therefore, when the service provider places' density is higher near a stop \(s\), then the probability that \(s\) is a final stop \(s_{fin}\) (beginning stop \(s_{bgg}\)) is higher since more commuters can terminate (start) the related trips in the morning (afternoon). In Figure 7. Density of services around stops A and B. Since the service density is higher in B, then we can expect that the city-users would select stop B as their final \(s_{fin}\) (beginning \(s_{bgg}\)) one in the morning (afternoon). Please note that not all services \(\mathbb{P}\) have the same attraction. For example, a shopping mall or a public university may attract more people, compared to small private offices.