Traffic Control Problems using Graph Connectivity

In modern day automobile traffic the problem of traffic congestion calls for the design of efficient control strategies. In this paper it is argued that in order to have efficient and systematic solutions to a traffic control problem at an intersection, graph theoretic models of the problem are quite appropriate for its exploitation. Connectivity of compatibility graph of a traffic intersection can be 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. This result has got application in traffic control problems at an arbitrary intersection so as to minimize the waiting time of the traffic participants and the cost of locating the sensors in order to collect traffic data.