Research project MD/DD/11 (Research action MD)
Objectives
The primary goal is the development of and advice on mathematical models and interactive software tools that should support governments and traffic management organisations in taking appropriate traffic management measures and in the development of short term and long term traffic management strategies. This includes the development of tools to generate optimal control policies for the reduction of traffic congestion and the evaluation of existing or newly developed analysis and simulation tools, and merging them into a multi-functional interactive software package with a graphical user interface (GUI).
The project is concerned with 'dynamic' traffic control measures in order to manage and to control actual traffic flows. This type of traffic control strategies will be implemented by so-called advanced traffic management and information systems.
The project aims at the assessment, development and selection of models and tools that could be used in these advanced traffic management and information systems. A graphical-user-interface-based program will be developed to analyse the current traffic situation and to simulate and visualise the effect of various traffic management measures.
All the algorithms and the software that will be developed will take realistic and feasible boundary conditions into account (such as an economically feasible number of sensors and controllable information panels, etc.).
Methodology
We propose to develop mathematical models and simulation tools to examine the impact of various traffic management measures on traffic congestion. Traffic management systems are prototype examples of so-called hybrid systems: a combination of continuous variable systems i.e., systems that have a continuous state space and an evolution law that is given by a differential or difference equation- and discrete event systems i.e., systems in which the state changes in response to certain events.
The three key components in our model-based control approach are sensors, models and actuators. Sensors are necessary to measure the status of the system and to collect the data that will be used to construct a model and to validate this model. For the input data for our models we shall start from data such as traffic flow densities, lane occupancies, lane changing, headway distribution and average and instantaneous vehicle velocities. We assume that the input data for our model will be supplied by the traffic police or other traffic management organisations. Initially, we will use the existing and planned infrastructure to obtain the necessary data and to design control strategies. In a next phase we shall also make suggestions for the installation of new infrastructure.
Once input and output data are available we develop a model that 'explains' the dynamic relationships between the input and output data. This model can be a mathematical model (expressed by a set of equations), a computer simulation model or a combination of both. A very important issue is the trade-off between the accuracy of the model and the (computational) complexity of the analysis of the given model. A wide range of modelling techniques exists for continuous variable as well as for discrete event systems. Since hybrid systems are a mixture of these, we shall have to use and combine models that originate from both fields to describe the behaviour of a traffic network.
Once a sufficiently accurate model has been obtained, we use mathematical and computational techniques to determine the impact of certain traffic management options or to determine an optimal traffic management (e.g., for reducing the frequency of occurrence of congestion, for maximising the throughput on a given highway, etc.).
Once we have a valid model for our system, we will try to optimise the performance of the system, i.e., we determine the inputs of the system such that the system exhibits a desired behaviour. Actuators are used to provide the desired inputs to the system.
In the traffic context the following 'actuators' could be used: control of traffic light sequencing, providing information to drivers on the length or duration of traffic jams and/or alternative or preferred routes, using variable message signs to re-route traffic or to recommend appropriate speeds, road admission control (ramp metering).
Remark: we will not design neither sensors nor actuators, but focus on models and control.
The key idea in model-based control system design is the following: starting from some specification, to write down an objective function that characterises the performance of the system to be optimised taking into account the (expected) behaviour of the system. This behaviour, which is described by the model of the system, imposes certain constraints. This results in a constrained optimisation problem that can either be solved analytically or numerically (using optimisation algorithms). For traffic situations we can discern various performance measures: avoidance or reduction of congestion occurrences, reduction of the length or duration of traffic jams, minimisation of average or worst-case travel times, either in general or for certain groups of users (public transport, high-occupancy vehicles,...)
Using a virtual engineering framework (computer simulation) one might calculate the limits-of-performance for a certain type of controller or, the other way around: which type of control actions is needed to achieve a certain required performance level? Quantitative answers to these questions result in so-called trade-off level curves and Pareto-optimal control configurations and solutions. The simulation results are also of utmost importance for decision-makers to assess the amounts of investments required for a certain level of performance of the traffic network.
Potential users
Local, regional or federal governments and traffic management organisations (e.g. police road authority).
Link to Sustainable Development
Traffic jams not only lead to a tremendous amount of lost productivity. They also have a negative impact on the environment and correspond to a considerable waste of fuel. Environment issues are increasingly critical, with vehicle emissions in particular posing a growing problem to public health. An adequate transportation management is an important component for the further growth of economic prosperity and the maintenance of the environment and the current quality of life in Belgium.
The model(s) developed will help us in defining optimal control strategies for traffic flows in various (dynamic) conditions and, as a result, in making a more effective and efficient use of the capacity of the existing infrastructure. Furthermore the designed control strategies can be used to change the circulation of traffic (e.g. by homogenising traffic flows or promoting a shift to environment friendly modes) in favour of environment-friendly traffic patterns. This will lead to a significant reduction of environmental, social and economic costs caused by road traffic, and contribute to a sustainable development of our economy and society.
Het fileprobleem in Belgie: wiskundige modellen, analyse, simulatie, regeling en acties: eindverslag
Brussel: DWTC, 2001 (SP0875)
[To download]
Het fileprobleem in Belgie: wiskundige modellen, analyse, simulatie, regeling en acties: synthese
Brussel: DWTC, 2001 (SP0876)
[To download]
Trafic congestion problems in Belgium: mathematical models, analysis, control and actions: synthesis
Brussels: OSTC, 2001 (SP0877)
[To download]
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