# Phase Diagram Distortion from Traffic Parameter Averaging

## Phase Diagram Distortion from Traffic Parameter Averaging

### Authors

H Stipdonk, SWOV, NL; J van Toorenburg, NL; M Postema, University of Hull, UK

### Description

Traffic flow is visualized by plotting flow as a function of density. In such a diagram, congested traffic data and theories disagree. Our simulations show that this paradox can be overcome by using an unconventional speed averaging method.

### Abstract

Motorway traffic congestion is a major bottleneck for economic growth. Therefore, research of traffic behaviour is carried out in many countries. Although well describing the undersaturated free flow phase as an almost straight line in a (k,q)-phase diagram, congested traffic observations and theories disagree in the oversaturated, forced flow state. In this paper we investigate the relation between traffic observations and the structure of the phase diagram. We focus on the way speed observations are averaged, and how this influences the location of the averaged observations in the phase diagram. Theoretical analysis suggests a phase diagram where the oversaturated phase consists of a straight line. This straight right branch corresponds to upstream moving speed wave regions, called speed waves. The right branch connects the top of the free flow phase line with a point of maximum k and zero q. Its slope corresponds to the speed of the speed wave, with a value of ?18±1 km/h. In practice, however, average traffic states are normally observed below this line, introducing a paradox.

We compare the most commonly used models and theories, and treat the paradoxical results, using both single location traffic data, and data gathered from consecutive locations along a road segment (multi-location data). These data consist of one minute arithmetic averaged speed flow observations. From mean speed v and flow q the mean density k is derived, to obtain observations in the (k,q)- phase diagram. We propose a triangular phase diagram based on a simple car following theory by Newell and demonstrate its agreement with multi-location observations.
Furthermore, we present data from Dutch motorways, and show that they are paradoxical. Multi-location data agree with the triangular model, but single location data do not. By simulating single location average speed flow data, generated from traffic flow that follows the triangular phase diagram, we show that single location averages strongly depend on the speed averaging method. As a consequence, traffic observations based on averaged speeds may give rise to far higher mean speeds, and lower densities than car drivers' experience.

#### Publisher

Association for European Transport