## 2 Place- and Person-Based Accessibility Measures
### Limits of STA in Describing the Role of the Transport System
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{1}{c}{**Accessibility Measure**} & \multicolumn{1}{c}{**General Definition**} & \multicolumn{1}{c}{**Mathematical Formulation *} & \multicolumn{1}{c}{**Conceptual/**} & \multicolumn{1}{c}{**Conceptual/**} & \multicolumn{1}{c}{**Competional/**} & \multicolumn{1}{c}{**Sample References**} \\ \hline \multirow{8}{*}{_Cognitive opportunity_} & Set of opportunities & \multirow{2}{*}{\(A_{i}=\sum_{j=1}^{i-m}O_{j}f(TC_{ij})\)} & \multirow{2}{*}{English} & Opportunities have & \multirow{2}{*}{} \\  & reachable from a & & location within a & \(f(TC_{ij})=\left\{\begin{array}{ll}1\ for\ TC_{ij}\leq T\\ 0\ otherwise\end{array}\right.\) & & understandable and & the same & \\  & & & & \(0\) & _otherwise_ & applicable & regardless of their \\ \cline{3-6}  & & time or cost & & & & & \\  & Set of opportunities & & & & & \\  & reachable at & & & & & \\  & destination & & & & & \\  & weighed by the & & & & & \\  & travel effort needed & & & & & \\  & to reach them & & & & & \\  & & Gravity-based & & & & & \\  & & measure including & & & & \\  & _Adapted_ & competition effects & & & & \\  & gravity-based & between demand & & & & & \\  & for and supply of & & & & & \\  & opportunities & & & & & \\ \hline \multirow{8}{*}{_Utility-based_} & Maximal economic & \multirow{8}{*}{\(A_{u}=\frac{1}{1}\ln\sum_{c\in C_{u}}\exp(\lambda V_{u})\)} & Utility is measured & Temporal & \multirow{8}{*}{} \\  & & utility individuals & & at individual level & & & \\  & can get from the & & access to spatially & & & & \\  & distributed & & & & & \\  & opportunities & & & & & \\  & Gravity-based & & & & & & \\  & measure adapted to & & & & & \\  & analysis individual & & & & & \\  & _Integrial_ & accessibility & & & & & \\  & through & & & & & \\  & disaggregation or & & & & & & \\  & point-based & & & & & & \\  & approach & & & & & \\  & Set of opportunities & & & & & \\  & reachable by an & & & & & \\  & individual & & & & & \\  & according to & & & & & \\  & his/her daily & & & & & \\  & activity programme & & & & & & \\  & and constraints & & & & & \\ \hline \hline \end{tabular}  
* **Where: Cumulative opportunity:**_i_ is an origin location; \(j\) is a destination location; _O_j_ are the opportunities available at destination; _TC_ij_ is the cost of travelling from \(i\) to \(j\); \(f\) (_TC_ij_) is the travel cost function, which may assume different forms such as linear, Gaussian, logistic or negative exponential; \(T\) is the travel cost threshold set in the analysis. **Gravity-based:**_i_, \(j\), _O_j_, _TC_ij_ and _f_(TC_ij_) are defined above. **Adapted gravity-based:**_i_, \(j\), _O_j_, _TC_ij_ and _f_(TC_ij_) are defined above; **_a_ is the balancing factor for demand in location; \(b\) is the balancing factor for supply in location \(j\); \(D\) is the demand for opportunities in \(i\). **Utility-based:**_a_ is a user for whom accessibility is calculated; \(A\) is the travel cost coefficient; \(z\) is one of the choices that \(u\) can make; \(C\) is the set of choices \(z\) that \(u\) can make; _V_u_ is the systematic utility of the choice \(z\) for \(u\). **Individual integral:**_u_, \(i\), \(j\), _O_j_ and _f_(TC_ij_) are defined above; _TC_ij_,_\(u^{k}\) is the travel cost for \(u\) from \(i\) to \(j\) by transport mode \(k\). **Space-time:**_u_ is defined above; \(w\)1_\({}_{-}\)_are the locations of discretionary opportunities; _O_u_ are the discretionary opportunities \(O\) are the discretionary opportunities \(O\) are the travel cost threshold set in the analysis. **Gravity-based:**_i_, \(j\), _O_j_, _TC_ij_ and _f_(TC_ij_) are defined above. **Adapted gravity-based:**_i_, \(j\), _O_j_, _TC_ij_ and _f_(TC_ij_) are defined above; \(a\) is the balancing factor for demand in location; \(b\) is the balancing factor for supply in location \(j\); \(D\) is the balance factor for supply in location \(j\); \(D\) is the demand for opportunities in \(i\). **Utility-based:**_a_ is a user for whom accessibility is calculated; \(A\) is the travel cost coefficient; \(z\) is one of the choices that \(u\) can make; \(C\) is the set of choices \(z\) that \(u\) can make; _V_u_ is the systematic utility of the choice \(z\) for \(u\). **Individual integral:**_u_, \(i\), \(j\), _O_j_ and _f_(TC_ij_) are defined above; _TC_ij_,_\(u^{k}\) is the travel cost for \(u\) from \(i\) to \(j\) by transport mode \(k\). **Space-time:**_u_ is defined above; \(w\)1_\({}_{-}\)_are the locations of discretionary opportunities; \(O\) are the discretionary opportunities \(O\) are available in \(w\)1_\({}_{-}\)_; _D_**TPA_ is the Daily Potential Path Area; \(t\) is the time needed to participate in a discretionary opportunity _O_n_; _t_\({}_{a}\) is the ending time of a fixed activity \(a\); _t_\({}_{a+}\)_is the starting time of the following fixed activity _a_\({}_{+}\)_; _d_\({}_{a,w}\) is the physical distance between \(a\) and \(w\); _d_\({}_{a,w+1}\) is the physical distance between \(w\) and _a_\({}_{+}\)_; \(r\) is the average speed on the transport network.  
\end{table}