Traffic safety and forecasts

© Ö Hallberg, Hallberg Independent Research 2009.

Most traffic safety models use regression analysis to find mathematical expressions linking traffic properties to the number of killed people per year. It may be the traffic intensity, average speed, age of the car park, annual driving time or kilometers etc.

But, so far, very few reports have brought up the simple fact that you will become a better driver as your driving experience accumulates over time. The annual reports about traffic injuries and deaths from Statistics Sweden always present a graph showing how the risk of being injured declines by age. An example is given below together with an analysis of reported and calculated traffic deaths in 1987.

This model was further developed using better computers and was presented in Lisbon 1997.

The tool was used to extract characteristic functions describing failure rates for electronics over field use time or as an other example death risk functions for drivers over accumulated driving time.

Today, this tool has been developed and specialized for different purposes. One is being used for the analysis of global warming, where the temperature response function to increasing levels of CO2 is found. Another application is the analysis of cancer statistics to find models of predictive value for future trends.

And the application has also become fine tuned as a tool for traffic death analysis and projections. This application will be described in more detail in the following.

Basic principles

1. We assume that when the total amount of cars in traffic is increased by a number X in one year, there will also be a need , or room, for X number of new, inexperienced car drivers in the traffic.
2. These new drivers will cause traffic deaths at a risk that will decrease by their driving experience the forthcoming years
3. The total number of deaths will then be the sum of all drivers' contribution according to the matrix below. Since people don't live for ever and many do not drive that much we defined 25 years as the death generating time period of a drivers life.

The table shows how total deaths are calculated by summation vertically in the matrix.

A description of this model is also given here: How to estimate future traffic mortality rates

The latest model development

In cooperation with Swedish Road Administration and Swedish National Road and Transport Research Institute we further fine-tuned this model to also include the fact that during the past 10 years many road kilometers have been rebuilt into motor ways or ways with separated lanes. This seems to have a good life saving capability, and it also appears to be quite predictable.

In this model we used the traffic death statistics reported between 1975-1985 in order to determine the characteristic function for driver experience. This function is a log-normal distribution requiring two parameters, a dispersion and a median time, here transformed to time to 0,1% deaths.

The new thing is that we now multiplied the vertical summations shown above with the fraction of the total road network that still had not separated lanes, taken to the power of another factor, b. If all roads had the same traffic intensity, then b would have been equal to 1, but since motor ways and roads with separated lanes in average transport more cars, the power b will be > 1. After fine-tuning it turned out that b=4.84 gave the best fit to reported data.

So, all in all we have to deal with only three parameters in this model, and this is much less than normally is being used in traditional regression analysis. Below is shown the result of the analysis and prediction for the two cases:

The original two parameter model

The model shows that we apparently today have a better traffic safety than the data from 1975-1985 predicts. Since 1999 we seem to have saved 649 lives thanks to improved roads and other technical actions taken by the authorities.

Including increasing fraction of roads having separated lanes

Conclusions

It looks as we might reach just about 200 deaths in year 2020 assuming the next improvement in economy really shows up. Otherwise we will most probably see even lower numbers.

So, let's hope for the best!

Örjan Hallberg, Hallberg Independent Research
http://hir.nu

Note.
It is interesting to note that the model used gives a risk function vs age that is very similar to the one actually reported by Vägverket (Clic to enlarge).