Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-06T02:35:36.634Z Has data issue: false hasContentIssue false

5 - Network Reliability

from Part II - Non-State-Space (Combinatorial) Models

Published online by Cambridge University Press:  30 August 2017

Kishor S. Trivedi
Affiliation:
Duke University, North Carolina
Andrea Bobbio
Affiliation:
Università degli Studi del Piemonte Orientale, Italy
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Reliability and Availability Engineering
Modeling, Analysis, and Applications
, pp. 150 - 200
Publisher: Cambridge University Press
Print publication year: 2017

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] A., Rosenthal, “Computing the reliability of complex networks,SIAM Journal on Applied Mathematics, vol. 32, pp. 384–393, 1977.Google Scholar
[2] M., Ball, “Computing network reliability,Operations Research, vol. 27, pp. 823–838, 1979.Google Scholar
[3] A., Agrawal and R. E., Barlow, “A survey of network reliability and domination theory,Operations Research, vol. 32, pp. 478–492, 1984.Google Scholar
[4] C. J., Colbourn, The Combinatorics of Network Reliability. Oxford University Press, 1987.
[5] A., Bobbio and A., Premoli, “Fast algorithm for unavailability and sensitivity analysis of series-parallel systems,IEEE Transactions on Reliability, vol. R-31, pp. 359–361, 1982.Google Scholar
[6] L., Page and J., Perry, “A practical implementation of the factoring theorem for network reliability,IEEE Transactions on Reliability, vol. 37, pp. 259–267, 1988.Google Scholar
[7] G., Hardy, C., Lucet, and N., Limnios, “Computing all-terminal reliability of stochastic networks by BDDs,” in Proc. Applied Stochastic Modeling and Data Analysis, ASMDA2005, 2005.
[8] A., Balan and L., Traldi, “Preprocessing minpaths for sum of disjoint products,IEEE Transaction on Reliability, vol. 52, no. 3, pp. 289–295, Sep. 2003.Google Scholar
[9] J., Abraham, “An improved algorithm for network reliability,IEEE Transactions on Reliability, vol. 28, pp. 58–61, 1979.Google Scholar
[10] M., Veeraraghavan and K., Trivedi, “An improved algorithm for the symbolic reliability analysis of networks,IEEE Transactions on Reliability, vol. 40, pp. 347–358, 1991.Google Scholar
[11] R., Bryant, “Graph-based algorithms for Boolean function manipulation,IEEE Transactions on Computers, vol. C-35, pp. 677–691, 1986.Google Scholar
[12] R., Bryant, “Symbolic Boolean manipulation with ordered binary decision diagrams,ACM Computing Surveys, vol. 24, pp. 293–318, 1992.Google Scholar
[13] L., Xing and S., Amari, Binary Decision Diagrams and Extensions for System Reliability Analysis. Wiley-Scrivener, 2015.
[14] A., Satyanarayana and R. K., Wood, “A linear-time algorithm for computing k-terminal reliability in series-parallel networks,” SIAM Journal on Computing, vol. 14, no. 4, pp. 818–832, 1985.
[15] K., Brace, R., Rudell, and R., Bryant, “Efficient implementation of a BDD package,” in Proc. 27th ACM/IEEE Design Automation Conf., 1990, pp. 40–45.Google Scholar
[16] List of BDD software libraries. [Online]. Available: https://github.com/johnyf/tool_lists/ blob/master/bdd.md (last accessed April 12, 2017).
[17] W., Schneeweiss, Boolean Functions with Engineering Applications and Computer Programs. Springer Verlag, 1989.
[18] K., Dohmen, “Inclusion–exclusion and network reliability,” The Electronic Journal of Combinatorics, vol. 5, no. R36, pp. 1–8, 1998.Google Scholar
[19] K., Trivedi, Probability and Statistics with Reliability, Queueing and Computer Science Applications, 2nd ed. John Wiley & Sons, 2001.
[20] T., Luo and K., Trivedi, “An improved algorithm for coherent-system reliability,IEEE Transaction on Reliability, vol. 47, pp. 73–78, 1998.Google Scholar
[21] K., Heidtmann, “Statistical comparison of two sum-of-disjoint product algorithms for reliability and safety evaluation,” in Proc. 21st Int. Conf. SAFECOMP 2002. LNCS-2434, 2002, pp. 70–81.Google Scholar
[22] J., Xing, C., Feng, X., Qian, and P., Dai, “A simple algorithm for sum of disjoint products,” in Proc. Ann. IEEE Reliability and Maintainability Symp., 2012.
[23] G., Hardy, C., Lucet, and N., Limnios, “k-terminal network reliability measures with binary decision diagrams,” IEEE Transactions on Reliability, vol. 56, pp. 506–515, 2007.
[24] T., Cormen, C. E., Leiserson, and R. L., Rivest, Introduction to Algorithms. MIT Press and McGraw-Hill, 1990.
[25] S., Rai, M., Veeraraghavan, and K. S., Trivedi, “A survey of efficient reliability computation using disjoint products approach,Networks, vol. 25, no. 3, pp. 147–163, 1995.Google Scholar
[26] 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, no. 1, pp. 33–42, 2003.Google Scholar
[27] A., Kaufmann, D., Grouchko, and R., Cruon, Mathematical Models for the Study of the Reliability of Systems. Academic Press, 1977.
[28] L., Yan, H. A., Taha, and T. L., Landers, “A recursive approach for enumerating minimal cutset in a network,IEEE Transaction on Reliability, vol. 43, no. 3, pp. 383–387, Sep. 1994.Google Scholar
[29] P., Jensen and M., Bellmore, “An algorithm to determine the reliability of a complex system,IEEE Transactions on Reliability, vol. R-18, no. 4, pp. 169–174, Nov. 1969.Google Scholar
[30] Y., Tung, L., Mays, and M., Cullinane, “Reliability analysis of systems,” in Reliability Analysis of Water Distribution Systems, ed. L. W., Mays. American Society of Civil Engineers, 1989, ch. 9, pp. 259–298.
[31] R., Gupta and P., Bhave, “Reliability analysis of water-distribution systems,Journal of Environmental Engineering, vol. 120, no. 2, pp. 447–461, 1994.Google Scholar
[32] L., Page and J., Perry, “Reliability of directed networks using the factoring theorem,IEEE Transactions on Reliability, vol. 38, pp. 556–562, 1989.Google Scholar
[33] R. K., Wood, “Factoring algorithms for computing k-terminal network reliability,” IEEE Transactions on Reliability, vol. R-35, pp. 269–278, 1986.
[34] K., Sekine and H., Imai, “A unified approach via BDD to the network reliability and path number,” Dept. Information Science, University of Tokyo, Tech. Rep. TR-95-09, 1995.
[35] X., Zang, H., Sun, and K., Trivedi, “A BDD-based algorithm for reliability graph analysis,” Dept. of Electrical Engineering, Duke University, Tech. Rep., 2000.
[36] A., Rauzy, “New algorithms for fault tree analysis,Reliability Engineering & System Safety, vol. 40, pp. 203–211, 1993.Google Scholar
[37] GARR, Italian Research, and Education Network. [Online]. Available: www.garr.it
[38] A., Bobbio and R., Terruggia, “Reliability and QoS analysis of the Italian GARR network,” Tech. Rep. TR-INF-2008-06-04-UNIPMN, Dip. Informatica, Università Piemonte Orientale. [Online]. Available: www.di.unipmn.it/TechnicalReports/TR-INF-2008-06-04- UNIPMN.pdf
[39] A., Bobbio, G., Bonanni, E., Ciancamerla, R., Clemente, A., Iacomini, M., Minichino, A., Scarlatti, R., Terruggia, and E., Zendri, “Unavailability of critical SCADA communication links interconnecting a power grid and a telco network,Reliability Engineering and System Safety, vol. 95, pp. 1345–1357, 2010.Google Scholar
[40] Integrated Risk Reduction of Information-based Infrastructure Systems. [Online]. Available: www.irriis.org/
[41] M., Newman, “Analysis of weighted networks,” Phys. Rev. E, vol. 70, p. 056131, Nov. 2004.Google Scholar
[42] C.-C., Jane and J., Yuan, “A sum of disjoint products algorithm for reliability evaluation flow of flow networks,European Journal of Operational Research, vol. 127, no. 3, pp. 664–675, Jun. 2001.Google Scholar
[43] S., Soh and S., Rai, “An efficient cutset approach for evaluating communication-network reliability with heterogeneous link-capacities,IEEE Transactions on Reliability, vol. 54, no. 1, pp. 133–144, 2005.Google Scholar
[44] E. M., Clarke, M., Fujita, P. C., McGeer, K., McMillan, and J., Yang, “Multi-terminal binary decision diagrams: An efficient data structure for matrix representation,” in IWLS'93: Int. Workshop on Logic Synthesis, Carnegie Mellon University, Report 5-1993, 1993, pp. 6a:1–15.
[45] E., Clarke, M., Fujita, and X., Zhao, “Applications of multi-terminal binary decision diagrams,” Technical Report CMU-CS-95-160, 1995. [Online]. Available: www.dtic.mil/ dtic/tr/fulltext/u2/a296385.pdf
[46] M., Fujita, P., McGeer, and J. Y., Yang, “Multi-terminal binary decision diagrams: An efficient data structure for matrix representation,Formal Methods in System Design, vol. 10, no. 2–3, pp. 149–169, 1997.Google Scholar
[47] G. D., Hachtel and F., Somenzi, “A symbolic algorithms for maximum flow in 0-1 networks,Form. Methods Syst. Des., vol. 10, no. 2–3, pp. 207–219, 1997.Google Scholar
[48] T., Gu and Z., Xu, “The symbolic algorithms for maximum flow in networks,Computers and Operations Research, vol. 34, pp. 799–816, 2007.Google Scholar
[49] A., Bobbio and R., Terruggia, “Reliability and quality of service in weighted probabilistic networks using algebraic decision diagrams,” in Proc. IEEE Ann. Reliability and Maintainability Symp., Fort Worth, TX, 2009, pp. 19–24.
[50] K., Kolowrocki, “On limit reliability functions of large multi-state systems with ageing components,Appl. Math. Comput., vol. 121, no. 2–3, pp. 313–361, 2001.Google Scholar
[51] A., Lisnianski and G., Levitin, Multi-State System Reliability: Assessment, Optimization and Applications, Series on Quality, Reliability and Engineering Statistics: Volume 6. World Scientific, 2003.
[52] E., Zaitseva and V., Levashenko, “Investigation multi-state system reliability by structure function,” in DEPCOS-RELCOMEX '07: Proc. 2nd Int. Conf. on Dependability of Computer Systems. IEEE Computer Society, 2007, pp. 81–90.
[53] J., Meyer, “On evaluating the performability of degradable systems,IEEE Transactions on Computers, vol. C-29, pp. 720–731, 1980.Google Scholar
[54] X., Zang, D., Wang, H., Sun, and K., Trivedi, “A BDD-based algorithm for analysis of multistate systems with multistate components,IEEE Transactions on Computers, vol. 52, no. 12, pp. 1608–1618, 2003.Google Scholar
[55] L., Xing and Y., Dai, “A new decision diagram based method for efficient analysis on multi-state systems,IEEE Transactions on Dependable and Secure Computing, vol. 6, no. 3, pp. 161–174, 2009.Google Scholar
[56] S., Amari, L., Xing, A., Shrestha, J., Akers, and K., Trivedi, “Performability analysis of multistate computing systems using multivalued decision diagrams,IEEE Transactions on Computers, vol. 59, no. 10, pp. 1419–1433, 2010.Google Scholar
[57] E., Zaitseva and V., Levashenko, “Multi-state system analysis based on multiple-valued decision diagram,Journal of Reliability and Statistical Studies, vol. 5, pp. 107–118, 2012.Google Scholar
[58] K., Gopal, K., Aggarwal, and J., Gupta, “Reliability analysis of multistate device networks,IEEE Transactions on Reliability, vol. 27, no. 3, pp. 233–236, Aug. 1978.Google Scholar
[59] S., Ross, “Multivalued state component systems,The Annals of Probability, vol. 7, no. 2, pp. 379–383, 1979.Google Scholar
[60] J., Hudson and K., Kapur, “Reliability analysis of multistate systems with multistate components,IIE Transactions, vol. 15, pp. 127–135, 1983.Google Scholar
[61] A., Shrestha, L., Xing, and Y., Dai, “Decision diagram based methods and complexity analysis for multi-state systems,IEEE Transactions on Reliability, vol. 59, no. 1, pp. 145–161, 2010.Google Scholar
[62] G., Levitin, “Reliability of multi-state systems with two failure-modes,IEEE Transactions on Reliability, vol. R-52, no. 3, pp. 340–348, 2003.Google Scholar
[63] G., Levitin and A., Lisnianski, “A new approach to solving problems of multi-state system reliability optimization,Quality and Reliability Engineering International, vol. 17, pp. 93–104, 2001.Google Scholar
[64] R., Terruggia and A., Bobbio, “QoS analysis of weighted multi-state probabilistic networks via decision diagrams,” in Computer Safety, Reliability, and Security, ed. E., Schoitsch. Springer Verlag, LNCS, Vol 6351, 2010, pp. 41–54.
[65] T., Kam, T., Villa, R., Brayton, and A., Sangiovanni-Vincentelli, “Multi-valued decision diagrams: Theory and applications,Multiple-Valued Logic, vol. 4, no. 1, pp. 9–62, 1998.Google Scholar
[66] G., Ciardo, G., Lüttgen, and A., Miner, “Exploiting interleaving semantics in symbolic state-space generation,Formal Methods in System Design, vol. 31, no. 1, pp. 63–100, 2007.Google Scholar
[67] D., Miller and R., Drechsler, “On the construction of multiple-valued decision diagrams,” in Proc. IEEE 32nd Int. Symp. on Multiple-Valued Logic, 2002, pp. 264–269.Google Scholar
[68] I. S. U. Research Foundation, Meddly decision diagram library. [Online]. Available: http:// meddly.sourceforge.net/
[69] J., Babar and P., Miner, “Meddly: Multi-terminal and Edge-valued Decision Diagram Library,” in Proc. 7th Int. Conf. on Quantitative Evaluation of Systems (QEST'10), 2010, pp. 195–196.Google Scholar
[70] F., Yeh, S., Lu, and S., Kuo, “OBDD-based evaluation of k-terminal network reliability,” IEEE Transactions on Reliability, vol. 51, no. 4, pp. 443–451, 2002.
[71] A., Bobbio, R., Terruggia, E., Ciancamerla, and M., Minichino, “Evaluating network reliability versus topology by means of BDD algorithms,” in Int. Probabilistic Safety Assessment and Management Conf. (PSAM-9), 2008.
[72] J., Herrmann, “Improving reliability calculation with augmented binary decision diagrams,” in 24th IEEE Int. Conf. on Advanced Information Networking and Applications, 2010, pp. 328–333.Google Scholar
[73] M., Beccuti, A., Bobbio, G., Franceschinis, and R., Terruggia, “A new symbolic approach for network reliability analysis,” in IEEE Int. Conf. on Dependable Systems and Networks, DSN2012, 2012, pp. 1–12.Google Scholar
[74] M. O., Ball and J. S., Provan, “Calculating bounds on reachability and connectedness in stochastic networks,Networks, vol. 13, no. 2, pp. 253–278, 1983.Google Scholar
[75] F., Beichelt and L., Spross, “Bounds on the reliability of binary coherent systems,IEEE Transactions on Reliability, vol. 38, pp. 425–427, 1989.Google Scholar
[76] C.-C., Jane, W.-H., Shen, and Y. W., Laih, “Practical sequential bounds for approximating two-terminal reliability,European Journal of Operational Research, vol. 195, no. 2, pp. 427–441, Jun. 2009.Google Scholar
[77] S., Sebastio, K., Trivedi, D., Wang, and X., Yin, “Fast computation of bounds for two-terminal network reliability,European Journal of Operational Research, vol. 238, no. 3, pp. 810–823, 2014.Google Scholar
[78] K., Trivedi, D., Wang, T., Sharma, A. V., Ramesh, D., Twigg, L., Nguyen, and Y., Liu, “Reliability estimation for large networked systems,” U.S. Patent 20 090 323 539, 11, 2011.
[79] R., Sahner, K., Trivedi, and A., Puliafito, Performance and Reliability Analysis of Computer Systems: An Example-based Approach Using the SHARPE Software Package. Kluwer Academic Publishers, 1996.
[80] I., Gertsbakh and Y., Shpungin, Network Reliability Calculations Based on Structural Invariants. John Wiley & Sons, Ltd, 2013, pp. 135–146.
[81] M. O., Ball, C. J., Colbourn, and J. S., Provan, “Network reliability,Handbooks in Operations Research and Management Science, vol. 7, pp. 673–762, 1995.Google Scholar
[82] G., Rubino, “Network reliability evaluation,” in State-of-the-Art in Performance Modeling and Simulation, eds. K., Bagchi and J., Walrand. Gordon and Breach, 1998, ch. 11, pp. 275–302.
[83] G. S., Fishman, “A Monte Carlo sampling plan for estimating network reliability,Operations Research, vol. 34, no. 4, pp. 581–594, 1986.Google Scholar
[84] R., Albert and A., Barabasi, “Statistical mechanics of complex networks,Review Modern Physics, vol. 74, pp. 47–97, 2002.Google Scholar
[85] S., Dorogovtsev and J., Mendes, “Evolution of networks,Advances in Physics, vol. 51, pp. 1079–1187, 2002.Google Scholar
[86] M., Newman, “The structure and function of complex networks,SIAM Review, vol. 45, pp. 167–256, 2003.Google Scholar
[87] S., Boccaletti, V., Latora, Y., Moreno, M., Chavez, and D. U., Hwang, “Complex networks: Structure and dynamics,Physics Reports, vol. 424, no. 4–5, pp. 175–308, 2006.Google Scholar
[88] G., Caldarelli and M., Catanzaro, Networks: A Very Short Introduction. Oxford University Press, 2012.

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×