Stochastic Model to Describe Traffic Dynamics in Time Intervals with Stationary Traffic.

A Ph.D Scholarship.

Further information: Bo Friis Nielsen,

The aim of the proposed project is to establish a dynamic (stochastic) model capable of describing the traffic during peak situations. The project will include the following phases:

1. Data Analysis.

Selected road sections and selected hours within the TRIM system, known to expe rience difficulties are analysed. The analysis is composed of two elements: (a) A macro analysis to develop an understanding of the intertwining relations, and to construct a statistically based short-term forecast model., (b) a more detai led analysis to be used to set up a micro model for the traffic pattern. This m odel is, e.g., to be used as a traffic generator in the simultaneously construct ed simulation model (an ongoing PhD project), and also to be applied to commerci al products.

Macro Analysis.

Experience shows that traffic develops in different ways all dependent on a num ber of macro parameters: weather, day or night, day of the week, time of the ye ar, traffic intensity, etc. etc. The data analysis determines the relevant macro parameters. Such parameters are used to determine fairly homogeneous sets of data, i.e., time intervals where it is presumed that it is the same traffic mechanism (defined by macro parameter s) which has generated the observed pattern.

On the basis of these investigations a model is developed to predict a number of statistical parameters within a time frame of -1 hour. Subsequently, these pa rameters are to be applied to the validation of the micro model. One of the sta tistical parameters used in this context is the travelling time between two loca tions on the road system. This part is concluded with a short-term forecast mod el based on macro parameters.

Micro Analysis.

This analysis is to be used to illuminate behavioural parameters and to establis h a basis for a^M detailed vehicular based model for freeway traffic. In order to estimate behavi oural parameters it may be necessary to carry out additional recording, i..e., video.

To establish a data basis for the traffic model it is necessary to carry out de tailed analyses. One of such analyses is to illustrate how changes in the traff ic pattern are detected. In other words, periods during which the traffic intens ity is increasing or decreasing. Certain elements of this analysis will be the same elements as those of the macro analysis.

In order to establish a reliable model of the traffic of a multi-lane freeway it is necessary to look into the correlation of the traffic, both with respect to time and with respect to lanes and various types of vehicles.

This latter consists of an explorative phase where various graphic ways of illus trating will be used in order to establish major patterns, and of a phase where such patterns are examined quantitatively witht the assistance of statistical mo dels.

2. Identification of Model.

On the basis of the data analyses, fairly homogeneous sets of data are identifi ed - i.e., time intervals during which it may be assumed that the same traffic m echanism has generated the observed pattern.

Among the model classes to be tested as a model for the traffic process are the socalled Markovian Arrival Processes.

These models are of a more general type, and can include more types of occurence s, i.e., several types of vehicles. Likewise, the processes may be used to mode l increasingly correlated phenomena. These models are straightforward to implement as a module to be used by the para llel PhD project or in commercial products.

Furthermore, other types of models may be used, i.e., models which are typically used in time series analysis.

The aim of the project is that the model developed, coupled with the knowledge acquired in connection with the data analysis, should form the basis for the con struction of models to forecast problems in the road system.

3. Implementation of Model in the Simulation Model.

The model or models constructed are to be adjusted for implementation in dedicat ed or third party software.

This point is of vital importantance, but it is expected that it will be less de manding since the model types being investigated all are types with well-known s oftware implementation .

3. Validation of Model.

The validation consists of a number of various parts:

Primarily, the model need to have the same statistical qualities as expressed b y data. This can only be verified for specially selected descriptors, such as i ntensity, correlation, and marginal distributions.

Next, it has to be tested whether this similarity is sufficent so that the model can be used to model real traffic in a realiable way.

It is necessary that such validation is carried out by comparing numerical simul ations of the model with data, a comparison which is complicated because also a ccuracy of the very simulation model plays a role.

Such a comparison has to be statistical.. For that purpose it is necessary to de velop methods to determine whether deviations between model and data may be due to random variation or whether it is a systematic tendency.

Finally, an analysis is carried out to determine to which exent the supposedly different traffic mechanisms - as defined in the data anlaysis - are actually d ifferent. (As an example, it may be that the different traffic patterns of day and night are directly reflected on the micro parameters in such a way that ther e is no need for different models in order to handle this difference).

4. Short-term Forecast Model.

Besides the need to micro model the traffic during a heavy traffic situation, th ere is also a need to forecast travelling times within such a net.

On the basis of a simulation model for a heavy traffic situation it is possible to determine the travelling time from A to B. It is of great importance for a t raffic control center to be able to present a short-term forecast (1/2-1 hour) for travelling time. On the basis of the simulation model, a forecast model is built for travelling times taking those parameters possible to measure dynamically into consideration.

Carrying Out the Project:

The department of Informatics and Mathematical Modelling (IMM) has great expertise within statistical analysis and stochastic modelling.

IMM puts office space, computer and other facilities at the disposal of the cand idate. Furthermore, it is possible to establish good contact to the newly estab lished Centre for Traffic and Transport on the DTU campus. It is intended to in clude a co-supervisor from this Centre in the project.

In order to give a professional input to the project, a steering committee has b een established with representatives from all parties involved, i.e., the Danish Transport Council, Tetraplan, the University of Southern Denmark, Informatics a nd Mathematical Modelling at the Technical University of Denmark, the Danish Roa d Directorate.