01-06-2012, 12:36 PM
On A Traffic Control Problem Using Cut-Set of Graph
On A Traffic Control Problem Using Cut-Set.pdf (Size: 240.88 KB / Downloads: 103)
Introduction
One of the main features of modern cities is the
permanent growth of population and every year new
road and highways are built in most of the urban areas to
accommodate the growing number of vehicles [1], [2].
This increase in the number of vehicles in urban cities
has led to the increase in time losses of traffic
participants, the increase of environmental and noise
pollution and also increases in the number of traffic
accidents. Traffic congestion has become one of the
major obstacles for the development of many urban
areas, affecting millions of people. Constructing new
roads may improve the situation, but it is very costly and
in many cases it is impossible due to the existing
structures. The only way to control the traffic flow in
such a situation is to use the current road network more
efficiently. Intelligent Transportation System (ITS) is
used extensively in urban areas to control traffic at an
intersection [3].
Intelligent Transportation System (ITS)
The term Intelligent Transportation System (ITS) refers
to information and communication technology applied to
transport infrastructure and vehicles, that improves
transport outcomes such as transport safety, transport
productivity, transport reliability, informed traveller
choice, environmental performance etc. [6] , [7].
ITS mainly comes from the problems caused by
traffic congestion and synergy of new information
technology for simulation, real time control and
communication networks. Traffic congestion has been
increased world wide as a result of increased
motorization, urbanization, population growth and
changes in population density. Congestion reduces
efficiency of transportation infrastructure and increases
travel time, air pollution and fuel consumption.
Edge Control Set
To study the traffic control problem at an arbitrary
intersection, it has to be modeled mathematically by
using a simple graph for the traffic collection data
problem. The set of edges of the underlying graph will
represent the communication link between the set of
nodes at an intersection. In the graph representing the
traffic control problem, the traffic streams which can
move simultaneously at an intersection without any
conflict will be joined by an edge and the streams which
cannot move together will not be connected by an edge.
In order to define an edge control set of a graph , we
consider the underlying graph G = (V, E) where V(G)
denotes the set of vertices of G and E(G) denotes the set
of edges of G.
Applications
The minimal edge control set has wide application in
traffic control problems at an intersection. The edges of
the minimal edge control set determines the exact
location where the sensors have to be placed which
minimizes the total cost and the complete data of the
traffic problem can be obtain from the minimal edge
control set.
Conclusion
In this paper we have used cut-set as a graph theoretic
tool to study traffic control problem at an intersection.
As the minimal edge control set represents the flow of
traffic at an intersection, the waiting time of the traffic
participants can be minimized by controlling the edge
control set. This can be achieved by placing traffic
sensors on each of the minimal edge control set of the
transportation network