Volume 2

Treating Inadequate Headway's on a High Flow Freeway

Authors: D. Lierkamp
Keywords: Tailgating; Headway; Following; Safety; Accident

The effects of altering headways on a high flow freeway are multifarious. Inadequate headways cause flow instability and accidents. Increasing headways can reduce flow and induce jamming, making determining the optimum headway difficult. Using a micro-simulation this article determines the costs of implementing various headway treatment regimes and compares these to the likely benefits resulting from accident reduction. The most beneficial headway regime is then put forward. In order to implement this treatment regime a roadside Intelligent Transport System (ITS) following-distance advisory and enforcement system is suggested. The system takes varying flow and weather conditions into consideration before modifying the headways of drivers.

A Dynamic Side-Constrained User Equilibrium Problem

Authors: H.-K. Chen, S.-H. Lui, and C.-W. Chang
Keywords: Variational Inequality; Link Capacity Constraint; First-in-first-out Requirement; Dynamic User Equilibrium; Augmented Lagrangian Method

This paper incorporates two side constraints, namely, the link capacity and first-in-first-out (FIFO) constraints, into the dynamic user equilibrium (DUE) problem. Although the link capacity constraint has been addressed in the literature, its implications for the associated multiple-valued dual variables have not been properly drawn out and, thus, the matter is still subject to controversy. Since the dual variables associated with any side constraint can hardly be realized as true link queuing delays on the physical links, it is more appropriate to regard them as shadow costs (or link toll levies) for avoiding traffic congestion. Interpreting the dual variables as shadow costs (or minimum tolls) reconciles, to a great extent, the arguments that might accrue due to the multiple-valued dual variables. Moreover, this approach implies that the feasible time-space networks used in the first loop operations of the proposed nested diagonalization (ND) method can only be constructed/updated according to the actual link travel times, rather than by the generalized actual link travel times. On the other hand, the FIFO constraint is unusual because it can be activated only when the same physical links in two different time intervals have positive flows. This unusual FIFO constraint is tactically treated by introducing a set of new indicator variables to identify the incidence relationships. The new indicator variables have been incorporated into the equivalence proof between the equilibrium conditions and the VI model, as well as the proposed ND method. The ND method, embedding the augmented Lagrangian method (ALM), which is in turn coupled with the path-based gradient projection (GP) algorithm, is then demonstrated with a numerical example. The results show that the corresponding dynamic generalized equilibrium conditions are satisfied, since for each origin-destination pair and time interval, the generalized route travel times incurred by the travelers on all used paths are equal and minimal. Although the two side constraints have been incorporated into the DUE problem and their physical meanings have been interpreted in a more plausible way, the interactive effects between these two side constraints are still unknown and, therefore, require more in-depth sensitivity analysis in the future.

Perfect Equilibria of Network Flows

Authors: V. Sever and M. Sever
Keywords: Network Flows; Systems Dynamics; Transportation; Game Theory; Economics

In the paper, we enhance the notion of user equilibrium of network flows in a way to take account of group behaviour of network users. We present some initial existence results for the enhanced equilibrium notion and their implications for the equilibrium economics and dynamics of transport markets.

     Volume 1

Reconstructing the Spatio-Temporal Traffic Dynamics from Stationary Detector Data

We present a new method to obtain spatio-temporal information from aggregated data of stationary traffic detectors, the ``adaptive smoothing method''. In essential, a nonlinear spatio-temporal lowpass filter is applied to the input detector data. This filter exploits the fact that, in congested traffic, perturbations travel upstream at a near-constant speed, while in free traffic, information propagates downstream. As a result, one obtains velocity, flow, or other traffic variables as smooth functions of space and time. Applications include traffic-state visualization, reconstruction of traffic situations from incomplete information, fast identification of traffic breakdowns (e.g., in incident detection), and experimental verification of traffic models, and even a short-term traffic forecast.

We apply the adaptive smoothing method to observed congestion patterns on several German freeways. It manages to make sense out of data where conventional visualization techniques fail. By ignoring up to 65 % of the detectors and applying the method to the reduced data set, we show that the results are robust. The method works well if the distances between neighbouring detector cross sections do not exceed 3 km.

Critical Discussion of "Synchronized Flow"

We critically discuss the concept of "synchronized flow" from a historical, empirical, and theoretical perspective. Problems related to the measurement of vehicle data are highlighted, and questionable interpretations are identified. Moreover, we propose a quantitative and consistent theory of the empirical findings based on a phase diagram of congested traffic states, which is universal for all conventional traffic models having the same instability diagram and a fundamental diagram. New empirical and simulation data supporting this approach are presented as well.

Fingerprinting Traffic from Static Freeway Sensors

An extension of the Cassidy-Windower diagrams of rescaled cumulative counts is proposed. This new tool allows an even more detailed analysis of traffic data. With it, one can identify individual vehicle groups and even detect and diagnose unusual disturbances. An example based on real data is presented.