Exact two-terminal reliability of some directed networks

2007 6th International Workshop on Design and Reliable Communication Networks, DRCN 2007

Volumn , Issue , 2007, Pages

  Tanguy, Christian ^a  

^a ORANGE LABS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION ALGORITHMS; STRUCTURAL DESIGN; SYSTEMS ENGINEERING; TELECOMMUNICATION NETWORKS; TRANSFER MATRIX METHOD;

ANALYTICAL SOLUTIONS; BUILDING BLOCKS; COMMUNICATION NETWORKS; COMPLEX ZEROS; CONVENTIONAL APPROACHES; DIRECTED NETWORKS; FAILURE FREQUENCIES; FAILURE RATES; LONG HAULS; MONTE CARLO; NETWORK RELIABILITIES; RELIABILITY POLYNOMIALS; SPECIFIC VALUES; STRUCTURE TRANSITIONS; TRANSFER MATRICES; TWO-TERMINAL RELIABILITIES;

RELIABILITY;

EID: 63249093894     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/DRCN.2007.4762273     Document Type: Conference Paper

References (66)

1. E. F. Moore and C. E. Shannon, "Reliable circuits using less reliable relays, " J. Franklin Institute, vol. 262, pp. 191-208, September 1956; vol. 262, pp. 281-297, October 1956.
2. M. O. Ball, C. J. Colbourn, and J. Scott Provan, "Network reliability, " Handbooks in operations research and management science, volume 7: Network Models, M. O. Ball, T. L. Magnanti, C. L. Monma, and G. L. Nemhauser (Editors), Amsterdam: Elsevier, 1995, pp. 673-762 (with over 400 references).
3. R. E. Barlow, F. Proschan, and L. C. Hunter, Mathematical theory of reliability, New York:Wiley, 1965.
4. C. J. Colbourn, The combinatorics of network reliability, Oxford: Oxford University Press, 1987.
5. D. R. Shier, Network reliability and algebraic structures, Oxford: Clarendon Press, 1991.
6. M. L. Shooman, Probabilistic reliability: an engineering approach, New York: McGraw-Hill, 1968.
7. W. Kuo and M. J. Zuo, Optimal Reliability Modeling: Principles and Applications, Hoboken:Wiley, 2003.
8. C. Singh and R. Billinton, System reliability modelling and evaluation, London: Hutchinson, 1977.
9. H. M. AboElFotoh and C. J. Colbourn, "Computing 2-terminal reliability for radio-broadcast networks, " IEEE Trans. Reliability, vol. 38 (5), pp. 538-555, 1989.
10. J. Graver and M. Sobel, "You may rely on the reliability polynomial for much more than you might think, " Communications in Statistics: Theory and Methods, vol. 34 (6), 1411-1422, 2005.
11. D. J. A. Welsh, "Complexity: Knots, Colourings and Counting, " London Mathematical Society, Lecture Note Series 186, Cambridge: Cambridge University Press, 1993.
12. W. P. Dotson and J. O. Gobien, "A new analysis technique for probabilistic graphs, " IEEE Trans. Circuits and Systems, vol. 26 (10), pp. 855-865, 1979.
13. J. A. Abraham, "An improved algorithm for network reliability, " IEEE Trans. Reliability, vol. 28 (1), pp. 58-61, 1979.
14. A. O. Balan and L. Traldi, "Preprocessing minpaths for sum of disjoint products, " IEEE Trans. Reliability, vol. 52 (3), pp. 289-295, 2003.
15. K. D. Heidtmann, "Smaller sums of disjoint products by subproduct inversion, " IEEE Trans. Reliability, vol. 38, pp. 305-311, 1989.
16. S. Rai, M. Veeraraghavan, and K. S. Trivedi, "A survey of efficient reliability computation using disjoint products approach, " Networks, vol. 25, pp. 147-163, 1995, and references therein.
17. A. Rauzy, E. Châtelet, Y. Dutuit, and C. Bérenguer, "A practical comparison of methods to assess sum-of-products, " Reliability Engineering and System Safety, vol. 79, pp. 33-42, 2003.
18. S. Soh and S. Rai, "Experimental results on preprocessing of path/cut terms in sum of disjoint products technique, " IEEE Trans. Reliability, vol. 42 (1), pp. 24-33, 1993.
19. J. P. Gadani, "System effectiveness evaluation using star and delta transformations, " IEEE Trans. Reliability, vol. 30 (1), pp. 43-47, 1981.
20. A. Rosenthal and D. Frisque, "Transformations for simplifying network reliability calculations, " Networks, vol. 7, pp. 97-111, 1977; errata, Networks, vol. 7, p. 382, 1977.
21. S.-D. Wang and C.-H. Sun, "Transformations of star-delta and delta-star reliability networks, " IEEE Trans. Reliability, vol. 45 (1), pp. 120-126, 1996.
22. R. Kevin Wood, "A factoring algorithm using polygon-to-chain reductions for computing K-terminal network reliability, " Networks, vol. 15, pp. 173-190, 1985.
23. F. Beichelt and L. Spross, "Bounds on the reliability of binary coherent systems, " IEEE Trans. Reliability, vol. 38 (4), pp. 425-427, 1989.
24. T. B. Brecht and C. J. Colbourn, "Improving reliability bounds in computer networks, " Networks, vol. 16, pp. 369-380, 1986.
25. J. Scott Provan, "Bounds on the reliability of networks, " IEEE Trans. Reliability, vol. 35 (3), pp. 260-268, 1986.
26. G. S. Fishman, "A comparison of four Monte Carlo methods for estimating the probability of s-t connectedness, " IEEE Trans. Reliability, vol. 35 (2), pp. 145-155, 1986.
27. D. R. Karger, "A randomized fully polynomial time approximation scheme for the all terminal reliability problem, " SIAM Review, vol. 43 (3), pp. 499-522, 2001.
28. L. D. Nel and C. J. Colbourn, "Combining Monte Carlo estimates and bounds for network reliability, " Networks, vol. 20, pp. 277-298, 1990.
29. S. Kuo, S. Lu, and F. Yeh, "Determining terminal pair reliability based on edge expansion diagrams using OBDD, " IEEE Trans. Reliability, vol. 48 (3), pp. 234-246, 1999.
30. A. Rauzy, "A new methodology to handle Boolean models with loops, " IEEE Trans. Reliability, vol. 52, pp. 96-105, 2003.
31. F. M. Yeh, S. K. Lu, and S. Y. Kuo, "OBDD-based evaluation of kterminal network reliability, " IEEE Trans. Reliability, vol. 51, pp. 443-451, 2002.
32. Fu-Min Yeh, Hung-Yau Lin, and Sy-Yen Kuo, "Analyzing network reliability with imperfect nodes using OBDD, " Proceedings of the 2002 Pacific Rim International Symposium on Dependable Computing (PRDC'02), pp. 89-96.
33. J. Carlier and C. Lucet, "A Decomposition Algorithm for Network Reliability Evaluation, " Discr. Appl. Math., vol. 65, pp. 141-156, 1996.
34. H. L. Bodlaender, "Discovering Treewidth, " technical report UU-CS-2005-018, Utrecht University, 2005, and references therein.
35. J. Galtier, A. Laugier, and P. Pons, "Algorithms to evaluate the reliability of a network, " Proceedings of the Workshop on the Design of Reliable Communication Networks 2005 (DRCN'05), pp. 93-100.
36. M. K. Chari and C. J. Colbourn, "Reliability polynomials: a survey, " J. Combin. Inform. System Sci., vol. 22, pp. 177-193, 1997; August 12, 1998 Web version.
37. C. J. Colbourn, "Some open problems on reliability polynomials, " DIMACS technical report 93-28, April 1993; Congressus Numerantium, vol. 93, pp. 187-202, 1993.
38. J. Oxley and D. Welsh, "Chromatic, flow and reliability polynomials: the complexity of their coefficients, " Combinatorics, Probability and Computing, vol. 11, pp. 403-426, 2002.
39. J. I. Brown and C. J. Colbourn, "Roots of the reliability polynomial, " SIAM J. Disc. Math., vol. 5 (4), pp. 571-585, 1992.
40. E. Hänsler, G. K. McAuliffe, and R. S. Wilkov, "Exact Calculation of Computer Network Reliability, " Networks, vol. 4, pp. 95-112, 1974.
41. W.-J. Ke and S.-D. Wang, "Reliability evaluation for distributed computing networks with imperfect nodes, " IEEE Trans. Reliability, vol. 46 (3), pp. 342-349, 1997.
42. V. A. Netes and B. P. Filin, "Consideration of node failures in networkreliability calculation, " IEEE Trans. Reliability, vol. 45 (1), pp. 127-128, 1996.
43. O. R. Theologou and J. G. Carlier, "Factoring & reductions for networks with imperfect vertices, " IEEE Trans. Reliability, vol. 40 (2), pp. 210-217, 1991.
44. D. Torrieri, "Calculation of node-pair reliability in large networks with unreliable nodes, " IEEE Trans. Reliability, vol. 43 (3), pp. 375-377 and 382, 1994.
45. C. Tanguy, "Exact solutions for the two-and all-terminal reliabilities of a simple ladder network, " unpublished (arXiv:cs.PF/0612143).
46. C. Tanguy, "Exact solutions for the two-and all-terminal reliabilities of the Brecht-Colbourn ladder and the generalized fan, " unpublished (arXiv:cs.PF/0701005).
47. C. Tanguy, "What is the probability of connecting two points?, " unpublished (arXiv:cs.PF/0612142).
48. N. Biggs, Algebraic graph theory, 2nd edition, Cambridge: Cambridge University Press, 1993.
49. R. P. Stanley, Enumerative combinatorics, vol. 1, Cambridge: Cambridge University Press, 1997, chapter 4.
50. C. Singh and R. Billinton, "A new method to determine the failure frequency of a complex system, " IEEE Trans. Reliability, vol. R-23, pp. 231-234, October 1974.
51. C. Singh, "Tie set approach to determine the frequency of system failure, " Microelectron. & Reliab., vol. 14, pp. 293-294, 1975.
52. W. G. Schneeweiss, "Computing failure frequency, MTBF & MTTR via mixed products of availabilities and unavailabilities, " IEEE Trans. Reliability, vol. R-30, pp. 362-363, October 1981.
53. D.-H. Shi, "General formulas for calculating the steady-state frequency of system failure, " IEEE Trans. Reliability, vol. R-30, pp. 444-447, December 1981.
54. S. V. Amari, "Generic rules to evaluate system-failure frequency, " IEEE Trans. Reliability, vol. 49, pp. 85-87, March 2000.
55. Y.-R. Chang, S. V. Amari, and S.-Y. Kuo, "Computing System Failure Frequencies and Reliability Importance Measures Using OBDD, " IEEE Trans. Computers, vol. 53, pp. 54-68, January 2004.
56. W. G. Schneeweiss, "Addendum to: Computing failure frequency via mixed products of availabilities and unavailabilities, " IEEE Trans. Reliability, vol. R-32, pp. 461-462, December 1983.
57. M. Hayashi, "System failure-frequency analysis using a differential operator, " IEEE Trans. Reliability, vol. 40, pp. 601-609, 614, December 1991.
58. A. Druault-Vicard and C. Tanguy, "Exact Failure Frequency Calculations for Extended Systems, " unpublished (arXiv:cs.PF/0612141).
59. N. L. Biggs, R. M. Damerell, and D. A. Sands, "Recursive families of graphs, " J. Combin. Theory B, vol. 12, pp. 123-131, 1972.
60. N. L. Biggs, "Matrix method for chromatic polynomials, " J. Combin. Theory B, vol. 82, pp. 19-29, 2001.
61. J. Salas and A. D. Sokal, "Transfer matrices and partition-function zeros for antiferromagnetic Potts models. I. General theory and square-lattice chromatic polynomial, " J. Statist. Phys., vol. 104, pp. 609-699, 2001; cond-mat/0004330.
62. G. F. Royle and A. D. Sokal, "The Brown-Colbourn conjecture on zeros of reliability polynomials is false, " J. Combin. Theory B, vol. 91 (2), pp. 345-360, 2004; arXiv:math.CO/0301199.
63. S.-C. Chang and R. Shrock, "Reliability polynomials and their asymptotic limits for families of graphs, " J. Statist. Phys., vol. 112, pp. 1019-1077, 2003; arXiv:cond-mat/0208538.
64. S. Beraha, J. Kahane, and N. J. Weiss, "Limits of zeros of recursively defined families of polynomials, " Studies in Foundations and Combinatorics, Advances in Mathematics Supplementary Studies, vol. 1, G.-C. Rota (Editor), Academic Press, New York, 1978, pp. 213-232.
65. A. D. Sokal, "The multivariate Tutte polynomial (alias Potts model) for graphs and matroids, " Surveys in Combinatorics 2005, London Mathematical Society Lecture Note Series 327, Bridget S. Webb (Editor), Cambridge University Press, Cambridge, 2005, pp. 173-226; arXiv:math.CO/0503607.
66. D. W. Coit, T. Jin, and N. Wattanapongsakorn, "System optimization with component reliability estimation uncertainty: a multi-criteria approach, " IEEE Trans. Reliability, vol. 53 (3), pp. 369-380, 2004.