# Analyzing Demand with Respect to Offer of Mobility
## 4 Model and Analyzer
### Modelling Public Transport Service Offer
\begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Description** \\ \hline \(s\) & A given bus stop \\ \hline \(M\) & Mobility modality set (e.g., \(M=\{bus,\ tran,train\}\)) \\ \hline \(\mathbb{O}\) & Mobility operator set (e.g., \(\mathbb{O}=\{ATAF,GEST,TRENTALIA\}\)) \\ \hline \(T=\{mng,aft\}\) & Time set \\ \hline \(t\) & A given time in \(T\) \\ \hline \(k\) & The \(k\)-th time interval in \(t\in T\) \\ \hline \(\mathds{t}_{ij}(t,\ m,\ \mathfrak{o})\) & Number of vehicle trips in time \(t\in T\) with mobility modality \(m\in M\) \\ \hline \(c(m,\ \mathfrak{o})\) & Vehicle capacity with modality \(m\) and mobility operator \(\mathfrak{o}\) \\ \hline \(\mathbb{P}\) & Service provider set (e.g., \(\mathbb{P}=\{Office,Public\ university,\ Shopping\ mall\}\)) \\ \hline \(O(t)\) & Offer by means ODMs \\ \hline \(D(t)\) & Demand by means ODMs \\ \hline \(L\) & Set of locations in the region \(R\) \\ \hline \(L^{\prime}\subset L\) & Set of locations in the area \(A\) \\ \hline \(In(t)\) and \(Out(t)\) & Number of inbound and outbound individual trips \\ \hline \(pick(mng)\)_and_\(pick(aft)\) & Total morning and afternoon pick-ups in the studied area \(A\) \\ \hline \(drp(mng)\)_and_\(drp(aft)\) & Total morning and afternoon drop-offs in the studied area \(A\) \\ \hline \(s_{beg}\)_,_\(s_{tra}\)_, and_\(s_{fin}\) & Beginning, Transfer and Final stops in a commuter trip \\ \hline \(c(s,r)\) & Circle with stop \(s\) in its center and related radius \(r\) \\ \hline \(W_{md}\) & Modality weight vector \\ \hline \(W_{pr}\) & _pr_ (parking, residential buildings) _weight vector_ \\ \hline \(W_{sp}\) & Service provider weight vector \\ \hline \(H(t)\) & Time interval vector for \(t\in T\) \\ \hline \(W(t)\) & Weight vector associated with time \(t\in T\) \\ \hline \(a_{slp}(s,t,k)\) & Stop level of stop \(s\) in interval time \(H(t)[k]\) \\ \hline \(a_{lin}(s,t,k)\) & Line level of stop \(s\) in interval time \(H(t)[k]\) \\ \hline \(a_{pr}(s)\) & _pr_ (parking, residential buildings) level of stop \(s\) \\ \hline \(a_{sp}(s)\) & _Service provider_ level of stop \(s\) \\ \hline \(u_{tra}^{(sp)}(s,t,k)\) & stop weighted sum of stop \(s\) in interval time \(H(t)[k]\) \\ \hline \(u_{pr}(s)\) & _pr_ (parking, residential buildings) weighted sum of stop \(s\) \\ \hline \(u_{sp}(s)\) & _Service provider_ weighted sum of stop \(s\) \\ \hline \(P_{tra}^{(spl)}(s,t,k)\) & Probability that stop \(s\) is a transfer one by choosing other stops in circle \(c(s,r)\) in interval time \(H(t)[k]\) \\ \hline \(P_{tra}^{(lin)}(s,t,k)\) & Transfer Probability of the stop \(s\) by choosing other lines of \(s\) in interval time \(H(t)[k]\) \\ \hline \(P_{tra}(s,t,k)\) & Transfer Probability of the stop \(s\) in interval time \(H(t)[k]\) \\ \hline \(P_{beg}(s,t)\) & Beginning Probability of the stop \(s\) in \(t\in T\) \\ \hline \(P_{fin}(s,t)\) & Final Probability of the stop \(s\) in \(t\in T\) \\ \hline \(P_{tra\cup beg}(s,t,k)\) & Probability of \(a\) transfer \(s_{tra}\) or \(a\) beginning \(s_{beg}\) stop in interval time \(H(t)[k]\) \\ \hline \(P_{tra\cup fin}(s,t,k)\) & Probability of \(a\) transfer \(s_{tra}\) or \(a\) final \(s_{fin}\) stop in interval time \(H(t)[k]\) \\ \hline \(drp(s,t,k)\) and \(pck(s,t,k)\) & Drop-offs and pick-ups at stop \(s\) in interval time \(H(t)[k]\) \\ \hline \(\mathds{t}(s,t,k)\) & Number of vehicle arrivals at stop \(s\) in time interval \(H(t)[k]\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Main formal notations.