Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-22T14:00:18.397Z Has data issue: false hasContentIssue false
  • English
  • Français

DECOMPOSITION ALGORITHMS TO COMPUTE THE QUICKEST TIME DISTRIBUTION IN DYNAMIC NETWORKS

Published online by Cambridge University Press:  06 February 2018

Chin-Chia Jane  and
Yih-Wenn Laih
Chin-Chia Jane
Affiliation:
Department of Business Administration, Ling Tung University, Taichung, Taiwan E-mail: [email protected]
Yih-Wenn Laih
Affiliation:
Department of Finance, Ling Tung University, Taichung, Taiwan
Get access Rights & Permissions [Opens in a new window]

Abstract

In dynamic networks, the quickest time is the least possible time required to transmit specified data from the source to the sink. When arcs in dynamic networks are independently subjected to failures, the quickest time is a random variable. Although previous studies have already explored the reliability of the quickest path, this work presents an algorithm that computes the probability distribution of the quickest time from the viewpoint of the quickest flow that contains all possible joint and disjoint paths. For moderate dynamic networks, the proposed algorithm can be easily modified to approximate the quickest time distribution with a trade-off between accuracy and running time. The performance and properties of the exact and modified algorithms are explored through computational experiments, which are conducted on 10 randomly generated networks. The exact algorithm is also compared with the exhaustive method which examines all state vectors.

Keywords

dynamic networkevacuation systemquickest time distributionreliability
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 33 , Issue 1 , January 2019 , pp. 50 - 63
Copyright
Copyright © Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Bang, Y.-C., Choo, H., & Mun, Y. (2003). Reliability problem on all pairs quickest paths. In Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Gorbachev, Y.E., Dongarra, J.J. & Zomaya, A.Y. (eds.), Computational Science—ICCS 2003. Berlin, Heidelberg: Springer, pp. 518–523.Google Scholar
2.Bretschneider, S. & Kimms, A. (2011). A basic mathematical model for evacuation problems in urban areas. Transp. Res. Part A Policy Pract. 45(6): 523–539.Google Scholar
3.Burkard, R.E., Dlaska, K., & Klinz, B. (1993). The quickest flow problem. Z. Oper. Res. 37(1): 31–58.Google Scholar
4.Chen, Y.L., & Chin, Y.H. (1990). The quickest path problem. Comput. Oper. Res. 17(2): 153–161.Google Scholar
5.Fleischer, L. & Skutella, M. (2002). The quickest multicommodity flow problem. In Cook, W.J. & Schulz, A.S. Integer Programming and Combinatorial Optimization. Berlin, Heidelberg: Springer, pp. 36–53.Google Scholar
6.Ford, L.R. & Fulkerson, D.R. (1962). Flows in networks. Princeton: Princeton University Press.Google Scholar
7.Fredman, M.L. & Tarjan, R.E. (1987). Fibonacci heaps and their uses in improved network optimization algorithms. J. ACM 34(3): 596–615.Google Scholar
8.Göttlich, S., Kühn, S., Ohst, J.P., & Ruzika, S. (2016). Evacuation modeling: a case study on linear and nonlinear network flow models. EURO J. Comput. Optim. 4(3–4): 219–239.Google Scholar
9.Hamacher, H.W. & Tjandra, S.A. (2001). Mathematical modelling of evacuation problems: a state of art. Berlin: Springer.Google Scholar
10.Klingman, D., Napier, A., & Stutz, J. (1974). NETGEN: A program for generating large scale capacitated assignment, transportation, and minimum cost flow network problems. Manage. Sci. 20(5): 814–821.Google Scholar
11.Lin, M. & Jaillet, P. (2015). On the quickest flow problem in dynamic networks: a parametric min-cost flow approach. In Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms. 1343–1356. SIAM.Google Scholar
12.Lin, Y.K. (2003). Extend the quickest path problem to the system reliability evaluation for a stochastic-flow network. Comput. Oper. Res. 30(4): 567–575.Google Scholar
13.Lin, Y.K. (2011). Transmission reliability of k minimal paths within time threshold. Comput. Ind. Eng. 61(4): 1160–1165.Google Scholar
14.Locks, M.O. (1982). Recursive disjoint products: a review of three algorithms. IEEE Trans. Reliab. 31(1): 33–35.Google Scholar
15.Ruzika, S. & Thiemann, M. (2011). Reliable and restricted quickest path problems. Lect. Notes Comput. Sci. 6701: 309–314.Google Scholar
16.Tjandra, S. A. (2003). Dynamic network optimization with application to the evacuation problem, PhD thesis, Universität Kaiserslautern, Shaker Verlag, Aachen.Google Scholar
17.Wilkinson, W.L. (1971). An algorithm for universal maximal dynamic flows in a network. Oper. Res. 19(7): 1602–1612.Google Scholar
18.Xue, G. (1998). End-to-end data paths: quickest or most reliable? IEEE Trans. Commun. Lett. 2(6): 156–158.Google Scholar
19.Yeh, W.C. (2015). A fast algorithm for quickest path reliability evaluations in multi-state flow networks. IEEE Trans. Reliab. 64(4): 1175–1184.Google Scholar