Real-Time Graphs for Communication Networks: A Fuzzy Mathematical Model

Abstract

For a given alive network, in many situations, its complete topology may not always be available because of the reason that few of its links may be temporarily disabled. Thus, at any real-time instant, only a subgraph, rather than the complete graph may be available to the system for executing its activities. Besides that, in most of the cases, the cost parameters corresponding to its links are not crisp numbers, rather fuzzy numbers. Under such circumstances, none of the existing algorithms on the shortest path problems or fuzzy shortest path problem can work. In this paper, the authors propose a mathematical model for such types of graphs to be called by real time graphs (RT-graphs) in which all real-time information (updated every q quantum of time) are incorporated so that the network can serve very efficiently with optimal results. Although the style of Dijkstra’s Algorithm is followed, the approach is a completely new in the sense that the SPP is solved with the real-time information of the network.