---
# System prepended metadata

title: Public Transport Service Level

---

# Public Transport Service Level

The indicator Public Transport Service Level ($ptsl$) describes the service for a given location based on following subindicators:
* travel distance (Isochrone) $pt_{iso}$ [km²]
* service duration $pt_{dur}$ [min/d]
* service frequency $pt_{frq}$ [trips/d]
* service ratio weekday to weekend $pt_{rat}$ [%] 
* barrier liberty $pt_{bl}$ [%]

The indicator is calculated as:

\begin{equation}
ptsl_i = \frac{pt_{iso_i} + pt_{dur_i} + pt_{frq} + pt_{rat} + pt_{bl_i}}{n} 
\end{equation}

where $n$ denotes the number of subindicators. 
All mentioned subindicators are described below. 
### Isochrone area

To evaluate the possible travel distance $pt_{iso}$ for a given location within every 15 min during service hours of a weekday, a 30 min public transport isochrone $pti$ (including the modes walking and public transport) is computed.
The mean area of $pti$ within service hours is calculated from all observations of $PTI = (pti_1, pti_2, ... ,pti_{n-1}, pti_{n})$ as follows:

\begin{equation}
pt_{iso} = \frac{1}{n} \cdot \sum_{i=1}^{n} pti_i 
\end{equation}


### Service Duration 

The public transport service duration $pt_{dur}$ [min/d] is computed as the mean time between the first and last trip for all stations within walking distance:

\begin{equation}
pt_{dur} = \frac{1}{n} \cdot \sum_{i=1}^{n} t_i 
\end{equation}

where $t$ denotes the service time of an individual public transport station.


### Service Frequency

The service frequency $pt_{frq}$ [trips/d] is calculated as the mean no. of trips of all stations within walking distance of a given location:

\begin{equation}
pt_{frq} = \frac{1}{n} \cdot \sum_{i=1}^{n} trips_i 
\end{equation}

where $trips$ denotes the number of trips of an individual public transport station on a given day.

### Service ratio weekday to weekend

Service ration of weekday to weekend is computed as mean ratio between the isochrone area for weekday to weekend, service duration for weekday to weekend and service frequency for weekday to weekend.




### Barrier liberty

A barrier-free station is defined as a station which is accessible to wheelchair users without outside help, i.e. has no steps or steep climbs. Stations with small steps, less than 7.5 cm, are defined as restricted barrier-free (information on source from wheelmap.org is pending). Stations that do not meet these criteria are defined as not barrier-free.

The Accessibility indicator is calculated as the proportion of Accessible Stations, whereby the restricted Accessibility Stations are given a weaker weighting. Accessibility for mobility impaired ($pt_{bl}$) is calculated as follows: 

\begin{equation}
pt_{bl} = \frac{1}{n} \cdot \sum_{i=1}^{n} s_i \cdot w_i 
\end{equation}

With each station $s_i$ (default value = 1) and its weighting $w_i$, which is 1 for fully barrier free stations, 0.5 for restricted barrier free stations and 0 otherwise (not barrier free). Stations for which the barrier liberty is unknown are not considered in the analysis.
