$$\text{Accessibility} = \text{PoI quality} \times \text{Distance}$$

• PoIs - Stops

$$\text{Accessibility} = \overbrace{ \text{PoI quality} }^{\text{Public Transport quality}} \times \text{Distance}$$

• PoIs - Stops

• Stop quality

$$\text{Accessibility} = \overbrace{ \text{headway} \cdot \text{speed}\cdot \text{mode} }^{\text{Public Transport quality}} \times \text{Distance}$$

• PoIs - Stops

• Stop quality

• Normalization $[0,1]$

$$\underbrace{\text{Accessibility}}_{[0, 1]} = \overbrace{ \underbrace{\text{headway}}_{[0, 1]} \cdot \underbrace{\text{speed}}_{[0, 1]} \cdot \underbrace{\text{mode}}_{[0, 1]} }^{\text{public transport quality}} \times \underbrace{\text{distance}}_{[0, 1]}$$

$$\text{Distance} \to [0,1]$$

Exponential decay function - Elasticity:

$$e = \frac{\%\text{ change in Demand } (\approx \text{ Quality})}{\%\text{ change in Distance}}$$

$$\text{Accessibility} = \overbrace{ \color{red}{\fbox{$\text{headway} \;\cdot\; \text{speed} \;\cdot\; \text{mode}$}} }^{\text{Public Transport quality}} \times \text{Distance}$$

Contribution of multiple routes?

Harmonic mean
$\text{HM} = 1/\left[\text{mean}\left(\frac{1}{\text{headway}_i}\right)\right]$

Elasticity:

Theoretical value:
0.5 (Mohring's Law)

Empirical:
< 30 min: e = 0.3 to 0.5
> 60 min: e = 0.6 to 1

Most influencial factors for Massachussets

• Population density

• Car ownership

• Race

• But not income

PyGTFSHandler

• Tutorial Download GTFS and compute speed and headway

UrbanAccessAnalyzer

• Schools Basic example and download of PoIs from OpenStreetMap


• Parks Simple tutorial introducing PoI quality


• Public Transport Complete example of our accessibility to public transport indicator including isochrone computation and GTFS processing