Find the original assignment for the project in [Project_Description.md](Project_Description.md)

### Matching SBB and Timetable datasets 

_Note : This section summarize what is done in `hdfs_match_datasets.ipynb`_

As we use _timetable_ dataset to build routes and trips, but sbb to compute delays, we need a robust translation between both datasets. What we needed was to translate trip_id and stop_id to be able to compute delay distributions for every pair of `trip_id` x `stop_id`. 

#### Get corresponding stop_id between two datasets 

We first look at the station names in _timetable_ dataset. Stop_id can be given in multiple formats shown below :
- `8502186` : the format defining the stop itself, which matches `bpuic` field in _sbb_ dataset

We will call the 3 next ones __Special cases__ throughout the notebook :
- `8502186:0:1` or `8502186:0:2` : The individual platforms are separated by “:”. A “platform” can also be a platform+sectors (e.g. “8500010:0:7CD”).
- `8502186P` : All the stops have a common “parent” “8500010P”.
- `8502186:0:Bfpl` : if the RBS uses it for rail replacement buses.

source : [timetable cookbook](https://opentransportdata.swiss/en/cookbook/gtfs/), section stops.txt 

In the sbb actual_data we find equivalent to stop_id in its first format defining the station without platform information, in its `bpuic` field. To get from _timetable_ to a _sbb_-compatible format, we used only __first 7 characters__ of _timetable_ stop_id.

#### Get corresponding trip_id between two datasets 

In sbb dataset, the trip ids are defined by `FAHRT_BEZEICHNER` field and in timetable by `trip_id`. To match both datasets, we matched `stop_id` , `departure_time` and `arrival_time` (with a join) to get corresponding trip_id on the same line. The idea is to take every trip_id with more than X matches between the two datasets. We decided to use 2 as a minimum number of matches needed. _Note : with a threshold > 2 we were not able to get InterCity / InterRegio trains, which have very few stops in the 15km perimeter._

These labels will be used to differentiate 3 different ways to delay distributions :
- __One-to-one__ we find a clear match : we use distribution of delays on weekdays for a given trip/station_id based on all past sbb data. 
- __One-to-many__ we find multiple match :
    - Matches are aggregated together in the final distribution table
- __One-to-none__ we find no match for trip_id between datasets : as described later, we will use delay distribution of similar trip (sharing stop_id, transport type and hour) to infer the delay.

### Get Distributions of Delay Times per trip and station

_Note : This summarize `hdfs_get_distributions.ipynb`_

The goal of this chapter is to create a distribution of arrival delays for each station / trip_id pair, to be used later on to compute transfer probabilities. These are then used in McRaptor implementation, to choose the best trip according to their time but also their __probability of success__.

#### Work from translation tables 

We used data generated in `hdfs_match_datasets.ipynb`, that matches trip_id between _timetable_ and _sbb_ dataset. We begin by looking at all trip_id that are found in both dataset with at least 5 stations in common.

Our goal is to find a match in sbb dataset for all _timetable_ trips (and not the other way around). So we will focus on getting this assymetrical correspondance table. 

In order to do that, we need to do multiple join, as we want to join 3 tables : _sbb_ data which contains information about delays, `joined_trip_atL5_3` table which contains translation between trip_id in two datasets, and `stop_time` which contains all the unique stop_id x trip_id used for later steps.
- First, we join _sbb_ data `sbb_filt_forDelays_GeschaetzAndReal_2` with translation table `joined_trip_atL5_3` to get sbb data with information about _timetable_ trip_id. 
- We can then use this _timetable_ trip_id to join this first table with `stop_time` table, using a _left_outer_ join, so that we get an idea of how many matches are found overall.

First we load SBB data. Following cells were ran twice : once for `geschaetz` / `real` delays only, and once for `all` delays. 
- `geschaetz` / `real` : load and use `/user/{}/sbb_filt_forDelays_GeschaetzAndReal_2.orc` table
- `all` : load and use `/user/{}/sbb_filt_forDelays_AllDelays.orc` table

### Compute probability of transfer success from delays distributions

_Note : This summarize `proba_functions.ipynb` and is run in local._

To be able to compute the probability of success of a given transfert, we use the arrival delay distribution compared with the next trip departure. To be able to do that, we need delay distributions for each trip arrival to a given station. We then use a __cumulative distribution function__ to compute $P(X \leq x)$ :

$${\displaystyle F_{X}(x)=\operatorname {P} (T\leq t)=\sum _{t_{i}\leq t}\operatorname {P} (T=t_{i})=\sum _{t_{i}\leq t}p(t_{i}).}$$

The strategy was to rely entirely on past data to compute $p(t_i)$, without the need of building a model which imply making additionnal assumptions. If we have enough data for a given transfer with known trip_id x stop_id, we use the the abovementionned formula to compute each $p(t_i)$ by simply using :

$$p(t_i) = \frac{x_i}{\sum x_i}$$

with $x_i$ being the number of delays at time $t_i$ from SBB dataset.

We make a few __assumptions__ :
- We assume that if we have less than 2 minutes for the transfer, we miss it.
- We assume the next train is on time.

#### Recover missing data 

Whenever we cannot find a clear match for a given `trip_id` x `stop_id`, we use aggregated delay distributions from similar transfer, on which we used the same CDF function abovementionned. 

To recover missing or faulty data, the strategy is the following :

1. If we have more than 100 data points in `real` group, we rely exclusively on its delay distribution to compute probabilities for a given transfer on a `trip_id x stop_id`.

_Note : `real` group corresponds to arrival time with status `geschaetz` or `real`, meaning it comes from actual measurments._

2. If we do not find enough data within `real` group, we use delay distributions in `all` group (contains all delays including `prognose` status), if there is more than 100 data points for a given `trip_id x stop_id`.

3. If `all` group still does not have more than 100 data points, we rely on `recovery tables` to estimate delay distributions. The strategy is the following :
    - As we will always know the `stop_id`, the `time` and the `transport_type`, we rely on arrival delays from aggregated values of similar transfer. 
        - First, we compute a table of distribution with all possible combination of `stop_id`, `time` (round to hours) and `transport_type`, and aggregate all the counts we have to compute cumulative distribution probabilities. 
        - Is there is less than 100 data points in one of these intersections, we use the last possibilities : a table with `transport_type` x `time` aggregate counts.
        - The last values with no match are given the overall average of cumulative distribution probabilities for each `transport_type` with no limit for the minimum number of data points.

Following this approach, we can find cumulative distribution probabilities for every combination of `trip_id x stop_id` as defined in `stop_times_df`. We will make a table with the same row order so that McRaptor can easily find their indexes. 

#### Evaluate / Validate recovery tables

The question is : How precise are these recovery table-derived probabilities ? Which one should be used in priority ?

To add ...