# A histogram of departures on the Frankfurt airport

Frankfurt's airport is one of the biggest in Europe. There are so many flights and passengers on a given day that we could easily be overwhelmed by all this information if we try to make sense of it at the moment. It is interesting to observe whether there are some patterns in the data—which destinations are served most frequently on a given day and how the flights are distributed over time. This is what we will try to understand from the data about the departuring flights scheduled for 26.10.2016 (as originally planned).

We can count the number of occurences of each destination and then find the most frequent ones:

Destination# flights
Berlin-Tegel23
Hamburg18
London-Heathrow17
München17
Paris Ch. de Gaulle12
Wien12
Amsterdam12
Zürich10
Köln Hbf10

The total number of flights is 217, so slightly more than 10% of them go to the first destination on the list. It is not surprising to see that 4 out of the 10 most frequent destinations are within Germany itself (Berlin, Hamburg, Munich, Cologne). In addition to the 17 flights to London-Heathrow, there are 8 more to London-City, so London comes to 25 flights in total for that day. New York, which is also a very large city, but far away from Frankfurt, gets only six flights in total—four are to the J.F.Kennedy and two to the Newark airports. This shows that short-distance flights are more common.

A minor detail is that there is a relatively large gap in the number of flights between the first four destinations and the ones that follow. For instance, the number of flights to Munich are 17, while those to Paris, Vienna or Amsterdam fall to 12. But this might be valid only on that day.

Here is a distribution of the flights over time given as a histogram. Since they are executed mostly in a five-minute tact, this is what will be used here (to reduce the number of bins, so they can be bigger). A flight, scheduled for 19:44 would appear in the bin corresponding to the time 19:45.

This diagram shows the numbers of departuring flights in the time interval 04:45-22:25 on 26.10.2016. We can see that there are some hours when no flights are scheduled (not only very early in the morning, but also during the day) and some hours when a lot of flights are scheduled. You can see these hours in the tables below.

• Hours with no flights
• 04:55
• 05:05
• 05:15
• 05:25
• 05:30
• 05:40
• 05:50
• 05:55
• 06:00
• 06:10
• 06:15
• 06:20
• 06:25
• 06:30
• 06:35
• 09:55
• 11:55
• 15:05
• 15:20
• 15:40
• 16:35
• 18:30
• 19:05
• 19:25
• 19:35
• 20:50
Hour# flights
10:0011
20:4510
07:009
22:159
09:508
20:558
21:458

We notice that some of the hours with the most flights, for instance 10:00 are very close to some of the hours with no flights, for instance 09:55. If it wouldn't be a problem to schedule half of the flights five minutes earlier, then the airport could keep its utilization more even. But this goal oftentimes stays in conflict with the plans of the individual travelers, who don't want to miss any other connections they might have.

The availability of personnel is also an important factor for a timely service. A flight could get late if only few people are allocated to a gate where lots of travelers have gathered. If the planned times can't be kept, then it could happen that at a given time a lot more flights than initially planned need to be served, which in turn increases the stress for everyone.

Serving destinations that are geographically close together in a short time may prove to be useful in reducing the costs for the airport. This way travelers who have similar requirements/questions can be served together without having to attach extra resources to them on an ongoing basis.