AN IMPROVED ALGORITHM FOR K-TERMINAL PROBABILISTIC NETWORK RELIABILITY ANALYSIS

Authors

  • S. Chatterjee Department of Applied Mathematics Indian Institute of Technology (Indian School of Mines), Dhanbad Jharkhand, INDIA
  • Venkata Ramana B. Department of Applied Mathematics Indian Institute of Technology (Indian School of Mines), Dhanbad Jharkhand, INDIA
  • Gajendra K. Vishwakarma Department of Applied Mathematics Indian Institute of Technology (Indian School of Mines), Dhanbad Jharkhand, INDIA
  • Aman Verma Department of Applied Mathematics Indian Institute of Technology (Indian School of Mines), Dhanbad Jharkhand, INDIA

Keywords:

Minimal Path Set, Binary Decision Diagram, Ordered Binary Decision Diagram, Reduced Ordered Binary Decision Diagram, Variable Ordering Heuristics, Breadth First Search Traversal

Abstract

An optimal variable ordering technique for Reduced Ordered Binary Decision Diagram (ROBDD) has been proposed to solve the network reliability analysis problem for complex communication networks. Several approaches have been proposed in the literature using the static and dynamic variable ordering techniques to solve the terminal network reliability problems. In this paper, the Minimal path set enumeration of the networks using Breadth first search traversal and ROBDD based Sift-reordering technique on manipulating the reliability evaluation is presented. The experimental results are compared with the previous approaches in computational time and number of ROBDD nodes to evaluate the K-terminal network reliability analysis.

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References

Akers, S.B. (1978). Binary decision diagrams, IEEE Transactions on

computers, 100(6), p. 509-516.

Al-Ghanim, A.M. (1999). A heuristic technique for generating minimal path

and cutsets of a 24 general network, Computers & Industrial Engineering, 36

(1), p. 45-55.

Bollig, B. and Wegener, I. (1996). Improving the variable ordering of OBDDs

is NP-complete, IEEE Transactions on computers, 45 (9), p. 993-1002.

Bryant, R.E. (1986). Graph-based algorithms for boolean function

manipulation, IEEE Transactions on Computers, 100 (8), p. 677-691.

Colbourn, C. (1987). The Combinatorics of Network Reliability, Oxford

University Press, New York, USA.

Gertsbakh, I. and Shpungin, Y. (2008). Network reliability importance

measures: combinatorics and monte carlo based computations, WSEAS

Transactions on Computers, 7 (4), p. 216-227.

Hardy, G., Lucet, C. and Limnios, N. (2007). K-terminal network reliability

measures with binary decision diagrams, IEEE Transactions on Reliability, 56

(3), p. 506-515.

Hui, K.P. (2007). Monte Carlo network reliability ranking estimation, IEEE

Transactions on Reliability, 56 (1), p. 50-57.

Kim, Y. and Kang, W.H. (2013). Network reliability analysis of complex

systems using a non-simulation-based method, Reliability Engineering &

System Safety, 110, p. 80-88.

Kobayashi, K. and Yamamoto, H. (1999). A new algorithm in enumerating all

minimal paths in a sparse network, Reliability Engineering & System Safety,

(1), p. 11-15.

Kuo, S.Y., Lu, S.K. and Yeh, F.M. (1999). Determining terminal-pair

reliability based on edge expansion diagrams using OBDD, IEEE Transactions

on Reliability, 48 (3), p. 234-246.

Kuo, S.Y., Yeh, F.M. and Lin, H.Y. (2007). Efficient and exact reliability

evaluation for networks with imperfect vertices, IEEE Transactions on

Reliability, 56 (2), p. 288-300.

Lee, C.Y. (1959). Representation of Switching Circuits by Binary-Decision

Programs, Bell Labs Technical Journal, 38 (4), p. 985-999.

Li, J. and He, J. (2002). A recursive decomposition algorithm for network

seismic reliability evaluation, Earthquake Engineering & Structural

Dynamics, 31 (8), p. 1525-1539.

Mishra, R. and Chaturvedi, S.K. (2009). A cutsets-based unified framework to

evaluate network reliability measures, IEEE Transactions on Reliability, 58

(4), p. 658-666.

Rauzy, A. (2003). A new methodology to handle Boolean models with loops,

IEEE Transactions on Reliability, 52 (1), p. 96-105.

Rudell, R. (1993). Dynamic variable ordering for ordered binary decision

diagrams, Proceeding of the IEEE/ACM International conference on

Computer-aided design, p. 42-47.

Satyanarayana, A. and Chang, M.K. (1983). Network reliability and the

factoring theorem, Networks, 13 (1), p. 107-120.

Sekine, K. (1999). Computational investigations of all-terminal network

reliability via BDDs, IEICE Transactions on Fundamentals of Electronics,

Communications and Computer Sciences, 82 (5), p. 714-721.

Shen, Y. (1995). A new simple algorithm for enumerating all minimal paths

and cuts of a graph, Microelectronics Reliability, 35 (6), p. 973-976.

Soh, S. and Rai, S. (1993). Experimental results on preprocessing of path/cut

terms in sum of disjoint products technique, IEEE Transactions on Reliability,

(1), p. 24-33.

Somenzi, F. (2012). CUDD-2.5.0, http://vlsi.colorado.edu.

Xing, L. (2008). An efficient binary decision diagram based approach for

network reliability and sensitivity analysis, IEEE Transactions on Systems,

Man, and Cybernetics-Part A: Systems and Humans, 38 (1), p. 105-115.

Yeh, F.M., Lu, S.K. and Kuo, S.Y. (2002). OBDD-based evaluation of k-

terminal network reliability, IEEE Transactions on Reliability, 51 (4), p. 443-

Yeh, W.C. (2007). An improved sum of disjoint products technique for the

symbolic network reliability analysis with known minimal paths, Reliability

Engineering & System Safety, 92 (2), p. 260-268.

Yeh, W.C. (2008). A greedy branch and bound inclusion-exclusion algorithm

for calculating the exact multi-state network reliability, IEEE Transactions on

Reliability, 57 (1), p. 88-93.

Zang, X. Sun, N. and Trivedi, K.S. (1999). A BDD-based algorithm for

reliability analysis of phased-mission systems, IEEE Transactions on

Reliability, 48 (1), p. 50-60.

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Published

2017-02-28

How to Cite

Chatterjee, S. ., Venkata Ramana B., Vishwakarma, G. K. ., & Verma, A. . (2017). AN IMPROVED ALGORITHM FOR K-TERMINAL PROBABILISTIC NETWORK RELIABILITY ANALYSIS. Journal of Reliability and Statistical Studies, 10(01), 15–26. Retrieved from https://journals.riverpublishers.com/index.php/JRSS/article/view/20959

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