Calculating the reliability of motorways
RUB engineers contribute to a calculation model
by Julia Weiler
March 26, 2015
Drivers are familiar with the tiresome problem: yesterday, getting to work via the motorway was easy, today they are stuck in a traffic jam. In Germany, North Rhine-Westphalia in particular has many notoriously congested routes, where drivers cannot rely on reaching their destination in time. Would it help to add more lanes in those bottlenecks or perhaps to build new motorways? More space for all cars sounds like a good solution; but neither do unlimited monies for that purpose exist, nor can roads be made as wide as one likes everywhere. The Federal Government decides which investments in the federal road network are the most urgent ones and are to be implemented first. In order to draw up the so-called Federal Transport Infrastructure Plan (Bundesverkehrswegeplan), a complex model is deployed. It helps to determine which projects make most sense from the economic point of view. A portion of the assessment model for the Federal Transport Infrastructure Plan 2015 has been developed by the RUB team headed by Prof Dr Justin Geistefeldt.
For the purpose of the analysis, Germany is subdivided into traffic cells. Then, it is determined how many journeys take place between which cells and which routes the drivers take. In order to assess investment measures in the road construction industry, the model is used to calculate to what extent the average travel time would change on a certain route following an extension or construction of a new road. A building project is generally rated more useful if it would ensure that road users reach their destination more quickly. Other parameters are factored in in the assessment as well: costs, environmental stress, impact on accident occurrence and on settlements and ecoregions. “It would be problematic to only consider the average travel times,” says Justin Geistefeldt, Head of the Institute for Traffic Engineering and Management. It is also important to incorporate the reliability of travel time into the model. For this purpose, the team from Bochum has developed a function.
“If you calculate with nothing but the average travel time, only time losses caused by actually occurring traffic jams are considered,” explains the RUB engineer. But there is another phenomenon that can cost a driver a lot of time, namely the unpredictability of traffic conditions. Geistefeldt illustrates it with an example: “Let’s assume you’ve got to keep an appointment in Duisburg at 4:30 pm. Going via the motorway A 40 from Bochum, it will take you 40 minutes on average. But you will probably be setting off sooner than 3:50 pm, because you know that the A 40 is frequently congested. And so you’ll set off at 3:30 pm. If the appointment is extremely important, you may even set off at 3:00 pm.” But perhaps there is no traffic jam at all on the route on that particular day, and you’ll arrive much too early. “Then, you’ll be in Duisburg by 3:40 pm, almost an hour too early, and you’re probably forced to simply kill time,” adds Geistefeldt. “Thus, you will lose time, even though there was no traffic jam at all.” Such time losses occur due to the variability of travel times from day to day. In mathematical terms, that variability can be described by the standard deviation. It is factored in as an assessment parameter in the Federal Transport Infrastructure Plan 2015.
In order to determine how the reliability of a route is influenced by a road widening project, the standard deviation has to be considered in connection with other parameters of traffic infrastructure, for example the number of lanes, gradient, percentage of heavy vehicles and location of the route. The so-called volume-to-capacity ratio contains all these parameters. It is defined as the ratio of traffic demand volume and capacity. Capacity, in turn, is determined by the factors listed above. “The relation between the standard deviation of travel time and the volume-to-capacity ratio is described by a function that is not very complicated,” says Justin Geistefeldt. Reliability could in fact be rendered even more detailed than with the standard deviation. But then, the model would become too complex. After all, the function made in Bochum is only one component of a larger model which assesses potential construction projects with regard to their economic feasibility. It does so for billions of journeys between the individual traffic cells. In order to generate a result, the computers carry out calculations for several days.
Including reliability into the assessment of potential investment measures in the federal road network is an important step, according to Geistefeldt. It would mean that, on the whole, extension projects in frequently congested bottlenecks would be rated more important than new construction projects. An example: if a new motorway is built in a rural region as an alternative to an already existing federal highway, the average travel time on that route will be reduced. However, the reliability of travel time barely changes, unless the federal highway is frequently congested. This is not the case on routes where road users get stuck in a traffic jam on a regular basis and have to set off sooner, because they cannot rely on arriving on time. According to Geistefeldt, defusing such bottlenecks should be prioritised over new construction projects in rural regions. The enhanced calculation method for the Federal Transport Infrastructure Plan 2015 contributes to this goal.