Complex algorithm results in simpler pricing structure

State-wide pricing structure in North Rhine-Westphalia

Complex algorithm results in simpler pricing structure

03/2016 - Many roads - or routes - lead to your destination wherever it might be in North Rhine-Westphalia. In the past, however, there was no uniform fare system or ticketing process for the range of regional and local transport options available. Now, a complex mathematical algorithm makes the system a lot easier for travellers, and that's not the only advantage it confers.

Until the most recent timetable changeover last December, using regional and local transport wasn’t always the most appealing mobility choice in North Rhine-Westphalia (NRW). If you remained within one of the state’s original nine transport associations’ networks, you could use its specific ticketing system to get from A to Z. If, however, your route crossed a border between two associations, a whole host of restrictions concerning pricing structures came into play, which had a detrimental impact on the flexibility of the available fare models.

Once you bought a ticket, you had to take a specific route. It was almost impossible to use alternatives, which led to all kinds of frustrations for season ticket holders and people affected by delays. There were even restrictions on the sequence in which travellers could use different modes of transport. For example, buses and trams services were an option only in the municipalities at the start and end of a journey when getting to and from the nearest train station. If you wanted a break in your trip, you might well have to buy additional tickets.

But now, since December, that’s all a thing of the past. The revised NRW pricing structure functions as a fare system for the entire state, comprising each and every mode of transport. “The state government in Düsseldorf asked DB Regio for the changes,” says Dr. Reinhard Pfaffenbach, IT consultant at DB Systel, when he thinks back about the origins of the project. “If you go from one transport association to another, the new flexible NRW pricing structure comes into play. It’s one ticket for every connection, even if you take a break on the way.” This new, customer-friendly simplicity is rooted in a complex algorithm.

One terabyte of data

The first step was to take the timetable and analyse it, thereby coming up with a mathematical model for simplifying the fare calculation system. “The network included 400 municipalities with 50,000 stops and over 10 billion possible connections,” Pfaffenbach says. The final algorithm combines all of the possible connections and rates them in terms of distance and likelihood of use. This information is used to create a fare system that automatically factors in all possible routes and distance-based pricing variables and which ultimately comprises some 80,000 tickets.

The project’s total data volume came to one terabyte of raw information, and a cloud server with 24 CPUs needed about 100 days to crunch all of the numbers. DB Systel broke new ground with this algorithm developed in-house. “By developing the new pricing structure, we brought two worlds together that had long been separate,” says Pfaffenbach. The innovative algorithm fuses the honeycomb system underpinning the transport associations fares with the distance-based ticketing prices used at DB. The result is the first regional and local transport fare system valid for an entire state but which also has the flexibility of a transport association’s ticket prices. The model also managed to leave fares unchanged for 88% passengers, and some users even saw a reduction in travel costs.

With the new NRW pricing structure, a single ticket from start to destination (green) is valid for all three reasonable routes (red) via selected municipalities (blueish).

DB Systel GmbH

Handling the negotiations between all of the participating transport associations was another challenge for the people behind the project, which affected scores of interest groups alongside DB Regio. When it came to price calculations, having large fare zones clashed with what is known as “fare undercutting”, which arises when someone travels 100 km but only pays for 90 km. There is no way of completely resolving these conflicts using mathematics alone, so all of the parties involved had to sit down with each other for extremely detailed talks. Only then was it possible to arrive at the best possible compromise and develop the right algorithm.

Travellers come up trumps in all kinds of ways

The new system confers a whole host of advantages on customers. Travellers now face a far less arduous task when trying to buy the right ticket: they don’t have to worry about the route they take or what form of transport they use, and this gives them far more flexibility. They can also interrupt a journey as often as they want. The new system covers every sales channel – internet, machines, travel centres, ticket purchases on trains and subscription tickets.

The NRW pricing structure complements transport associations’ fare systems on a state-wide level. However, the associations’ own pricing systems continue to apply within their own zones. In other words, when buying a ticket, a traveller needs to know if they are staying within a specific association’s catchment area or if they are crossing the border to a different association. At present, this information is not automatically available at ticket machines. “It would be nice if customers didn’t have to pick a pricing structure any more when using a machine. Our project has laid the technological foundations for this,” Pfaffenbach says. He adds that it is at present merely a vision: making it a reality would require further negotiations and in-depth planning between the transport associations and state of NRW.

He has another vision too: using the algorithm in other German states. “Our achievements can be applied to as many regions and fare systems as required,” Pfaffenbach says. “The basic function remains the same and can be expanded to other areas, provided you take their specific factors into account.” He continues by saying that the algorithm can be modified to suit point-to-point fares from a specific timetable. This move would radically simplify pricing systems and be far closer to what customers need. In the end, travellers outside of North Rhine-Westphalia would benefit from flexible tickets and a very appealing local and regional transport network.