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Table 2 Accessibility measures used in this study and their definition

From: Accessibility and territorial cohesion in a case of transport infrastructure improvements with changing population distributions

Indicator Definition Remarks
Location access \( {L}_i={\displaystyle \sum_{j=1}^n{c}_{ij}{P}_j{S}_j}/{\displaystyle \sum_{j=1}^n{P}_j{S}_j} \) \( {S}_j=\left\{\begin{array}{c}\hfill 1\; if\kern0.1em j\; is\; in\;a\; capital\; or\; large\; city\hfill \\ {}\hfill 0\; if\; not\hfill \end{array}\right. \)
For this study only national capitals, Düsseldorf, Hamburg and Munich are selected through S.
Network efficiency \( {E}_i={\displaystyle \sum_{j=1}^n\frac{c_{ij}}{{\acute{c}}_{ij}}}/{\displaystyle \sum_{j=1}^n{P}_j} \) Ideal traveltimes \( {\overset{\acute{\mkern6mu}}{c}}_{ij} \) are based on Euclidean distances between i and j and the fastest maximum speed (130 km/h) recorded in the road network data
Potential accessibility \( Po{t}_i={\displaystyle \sum_{j=1}^n{P}_jf\left({c}_{ij}\right)} \) f(c ij ) = c ij -1.5
Daily accessibility \( {D}_i={\displaystyle \sum_{j=1}^n{P}_j}{\overset{\wedge }{c}}_{ij} \) \( {\widehat{c}}_{ij}=\left\{\begin{array}{c}1\ \mathrm{if}\ {c}_{ij}\le 240 \min .\\ {}0\ \mathrm{if}\ {c}_{ij}>240 \min .\end{array}\right. \)