## Realistic Congestion Indicators For Long Periods

### Authors

P Danzanvilliers, F Leurent, S Tram, SETRA, FR

### Description

### Abstract

In the road traffic-engineering sector, it is well known how to characterise the traffic condi-tions on a road over a short period, ranging from one minute to one hour. There are two steps in this method:

* If the traffic flow is stable over this short period, then the average speed (or occupancy rate) indicates whether the flow regime is free or imposed, in other words whether or not the traffic is saturated. Saturation means the existence of a queue over the entire period.

* In saturation situations, the flow rate is equal to the capacity rate, itself dictated by the downstream flow movement conditions: traffic signals or average speed. The capacity decreases in function of the speed.

* In other situations, in the absence of saturation, the flow rate determines the speed. The speed decreases as the flow rate increases, but remains greater than the maximum speed in saturation conditions.

However, this analysis based on the fundamental diagram, cannot be applied over a long period (i.e. a year) that incorporates considerable flow rate and speed variations because, in this case, there is no simple relationship between the average flow rate and the average speed.

The aim of the article is to propose a synthetic measurement method and a forecasting model to analyse congestion on a road over a long period.

The article is structured into three parts.

I- Measuring congestion over a long period

* It is first necessary to define short periods within the long period (for example: hours of the year in an interurban environment).

* Disaggregated indicators for each short period: number of vehicles inconvenienced, average delay, lost capacity (in case of saturation and in relation to the maximum capacity).

* Aggregation of indicators over all the short periods, with proposition of thresholds for a qualitative overall appreciation.

II- Application to the A7-A9 motorway in France (Lyons-Montpellier)

* This site is equipped with electromagnetic sensors every 10 km. The flow rates of long and short vehicles, the speed and occupation rate are constantly measured and archived for all hours of the year.

* We shall be looking at two complete years: 1997 and 2002.

* The results show that saturation effects a relatively small proportion of hours (depend-ing on the section, from 30 to 200 hours out of the 8,760 in the year).

However, a large number of vehicles are inconvenienced and much time is lost.

III- A statistical forecasting model

* The aim, through the use of analytical formulas, is to link the average time and the variance time to the average flow rate and the variance flow rate. The model is applied to forecasting as follows: in accordance with the trend hypotheses for the average flow rates and the variance flow rates over the short periods, one obtains the average time and the variance time.

* In a non-saturated situation, the flow rates for the short periods are modelled using a lognormal distribution. The average time is linked to the flow rate by a BPR function. It can be deduced that the average times per period comply with a lognormal distribution. Similarly, with respect to the vehicle population, the flow rates and times encountered comply with lognormal distributions. Thus we obtain relatively simple analytical formulas to estimate averages and individual time variances, as well as for the total amount of time lost.

* We apply this model to a section of the A7 motorway: to respect the lognormal hy-pothesis, it is simply necessary to split the yearly set of hours in two parts, first the daytime hours (7h00 to 19h00) and second the nighttime hours (19h00 to 7h00).

* We then propose a method to take the saturation into account, using a function that measures the saturation probability according to the flow rate.

To conclude, we discuss the question of the user?s appreciation of the congestion. We indicate possibilities for measuring the acceptability of congestion levels by users.

#### Publisher

Association for European Transport