Traffic congestion reconstruction with Kerner's three-phase theory

In particular, common features of traffic congestion are independent on weather, road conditions and road infrastructure, vehicular technology, driver characteristics, day time, etc.

Kerner's definitions [S] and [J], respectively, for the synchronized flow and wide moving jam phases in congested traffic[6][7][8] are examples of common spatiotemporal empirical features of traffic congestion.

We denote the mean value of this time delay in vehicle acceleration at the downstream jam front by

When traffic parameters (percentage of long vehicles, weather, driver characteristics, etc.)

(1) is the characteristic parameter that does not depend on the flow rates and densities upstream and downstream of the jam.

This is the common feature of synchronized flow that is one of the two phases of traffic congestion.

This pinning of the downstream front of synchronized flow at the bottleneck is called the catch effect.

Thus Kerner's definitions [J] and [S] for the wide moving jam and synchronized flow phases of his three-phase traffic theory[6][7][8] are indeed associated with common empirical features of traffic congestion.

Vehicle speeds measured with road detectors (1 min averaged data) illustrate Kerner's definitions [J] and [S] (Fig.

There are two spatiotemporal patterns of congested traffic with low vehicle speeds in Fig.

In contrast, the downstream front of the other pattern of the congested traffic is fixed at the bottleneck.

The FOTO (Forecasting of traffic objects) model reconstructs and tracks regions of synchronized flow in space and time.

Firstly, the ASDA/FOTO models identify the synchronized flow and wide moving jam phases in measured data of congested traffic.

One of the empirical features the synchronized flow and wide moving jam phases used in the ASDA/FOTO models for traffic phase identification is as follows: Within a wide moving jam, both the speed and flow rate are very small (Fig.

Secondly, based on the abovementioned common features of wide moving jams and synchronized flow, the FOTO model tracks the downstream and upstream fronts of synchronized flow denoted by

The ASDA model tracks the downstream and upstream fronts of wide moving jams denoted by

This tracking is carried out between road locations at which the traffic phases have initially been identified in measured data, i.e., when synchronized flow and wide moving jams cannot be measured.

In other words, the tracking of synchronized flow by the FOTO model and wide moving jams by the ASDA model is performed at road locations at which no traffic measurements are available, i.e., the ASDA/FOTO models make the forecasting of the front locations of the traffic phases in time.

The ASDA/FOTO models enable us to predict the merging and/or the dissolution of one or more initially different synchronized flow regions and of one or more initially different wide moving jams that occur between measurement locations.

A good correspondence with empirical data is achieved, if a time-dependence of the location of the synchronized flow front is calculated by the FOTO model with the use of a so-called cumulative flow approach:

There are two main approaches for the tracking of wide moving jams with the ASDA model: The current velocity

of a front of a wide moving jam is calculated though the use of the shock-wave formula derived by Stokes in 1848:[9]

the flow rate and density upstream of the jam front that velocity should be found;

This means that after the downstream front of a wide moving jam has been identified at a time instant

Two wide moving jams propagate upstream while maintaining the mean velocity of their downstream fronts.

Therefore, in a general case the use of formula (5) can lead to a great error by the estimation of the mean velocity of the upstream jam front.

found in different data measured over years of observations varies approximately within the range

Reconstruction and tracking of spatiotemporal congested patterns with the ASDA/FOTO models is done today online permanently in the traffic control centre of the federal state Hessen (Germany) for 1200 km of freeway network.

The raw traffic data are transferred to WDR, the major public radio broadcasting station from North Rhine-Westphalia in Cologne, who offers traffic messages to the end customer (e. g., radio listener or driver) via broadcast channel RDS.

After the transition points have been found, the ASDA/FOTO models reconstruct regions of synchronized flow and wide moving jams in space and time with the use of empirical features of these traffic phases discussed above (see Figs.