Proceedings of the Second International Conference on Computer and Communication Technologies pp 463-470 | Cite as

# 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.

## Keywords

RT-graphs TBL LS LSC TBN RN Fuzzy shortest path estimate RT fuzzy relaxation## References

- 1.Abbasbandy, S.: Ranking of fuzzy numbers, some recent and new formulas. IFSA-EUSFLAT
**2009**, 642–646 (2009)Google Scholar - 2.Allahviranloo, T., Abbasbandy, S., Saneifard, R.: A method for ranking of fuzzy numbers using new weighted distance. Math. Comput. Appl.
**16**(2), 359–369 (2011)Google Scholar - 3.Sujatha, L., Elizabeth, : Fuzzy shortest path problem based on similarity degree. Appl. Math. Sci.
**5**(66), 3263–3276 (2011)MATHMathSciNetGoogle Scholar - 4.Biswas, S.S., Alam, B., Doja, M.N.: A theoretical characterization of the data structure ‘multigraphs’. J. Contemp. Appl. Math.
**2**(2), 88–106 (2012)Google Scholar - 5.Biswas, S.S., Alam, B., Doja, M.N.: A GRT-multigraphs for communication networks : a fuzzy theoretical model. In: International Symposium on System Engineering and Computer Simulation (SECS-2013). Advanced in Computer Science and its Applications, pp. 633–641. Danang, Vietnam, 18–21 Dec 2013. Print ISBN: 978-3-642-41673-6Google Scholar
- 6.Dat, L.Q., Yu, V.F., Chou, S.-Y.: An improved ranking method for fuzzy numbers using left and right indices. In: 2nd International Conference on Computer Design and Engineering, IPCSIT, vol. 49, pp 89–94 (2012). doi: 10.7763/IPCSIT.2012.V49.17
- 7.Biswas, R.: Fuzzy numbers redefined. Information
**15**(4), 1369–1380 (2012)Google Scholar - 8.Parandin, N, Araghi, M.A.F.: Ranking of fuzzy numbers by distance method. J. Appl. Math.
**5**(19), 47–55 (2008) (Islamic Azad University of Lahijan)Google Scholar - 9.Zadeh, L.A.: Fuzzy sets. Inform. Control
**8**, 338–353 (1965)MATHMathSciNetCrossRefGoogle Scholar