GRAPH APPLICATIONS IN TRAFFIC CONTROL

PROBLEMS

BY

ISAH SANI BIRNIN GWARI

A graph G consists of a finite set of ordered pairs, called edges E, of certain entities called vertices V. Edges are also called as arcs or links. Vertices are also called as nodes or points.

G=(V,E)

A graph is a set of vertices and edges. A vertex may represent a state or a condition while the edge may represent a relation between two vertices.

Directed Graph Directed Graphs or DIGRAPHS make

reference to edges which are directed (i.e.) edges which are ordered pairs of vertices.

Undirected Graph A graph whose definition makes reference to

unordered pairs of vertices as edges is known as an undirected graph

INTRODUCTION

APPLICATIONS OF GRAPH Amazon use graphs to make suggestions for

future shopping Graph is use in solving Travelling Salesman

Problem (TSP) Branch and bound algorithmso Logistics of delivering goodso Sport Tournamento Drilling holes in circuit boardso Programming space telescopes like Hubble

The seven bridges of Konigsberg Social Networks (Facebook) use graph for finding

friends, etc. Solving Traffic Control Problems

GRAPH APPLICATIONS IN TRAFFIC CONTROL PROBLEMS

The Traffic control problem at a four leg intersection, with five streams and the corresponding compatibility graph as shown below:

The traffic control problem is to minimize the waiting time of the public transportation while maintaining the individual traffic flow optimally.

Vehicles approaching an intersection prepare themselves to perform a certain maneuver i.e. to drive through, turn left, or turn right at an intersection.

The resulting compatibility graph of the intersection and its connectivity is used to study the most efficient route or the traffic control system to direct the traffic flow to its maximum capacity using the minimum number of edges or the minimum number of vertices.

DISCUSSION..

DISCUSSION..

As the edges of the edge connectivity represents the flow of traffic at an intersection, the waiting time of the traffic participants can be minimized by controlling the edges of the edge connectivity .

The traffic sensors can be placed on each edge in a cut-set of G determined by its edge connectivity as well as on each vertex of G determined by its vertex connectivity. These sensors will provide complete traffic information for the control system.