New Method in Searching for All Minimal Paths for the Directed Acyclic Network Reliability Problem

The directed acyclic network (DAN) is a directed network without directed cycles and is always modeled various information, processes, and events or potential events of systems. Network reliability has been a popular tool to evaluate and validate the performance of DAN. In this study, a new simple algorithm is proposed to find all minimal paths to evaluate the DAN reliability. The proposed algorithm outperforms the existing known algorithms in calculating the DAN reliability from both theoretical and experimental aspects. The correctness and time complexity of the proposed algorithm are demonstrated and analyzed. The proposed algorithm is demonstrated on a benchmark DAN and tested its efficiency by applying it to another 20 randomly generated networks.

[1]  P. A. Jensen,et al.  An Implicit Enumeration Scheme for Proper Cut Generation , 1970 .

[2]  G. Jasmon,et al.  A Method for Evaluating All the Minimal Cuts of a Graph , 1987, IEEE Transactions on Reliability.

[3]  D. Shier.  Network Reliability and Algebraic Structures , 1991 .

[4]  Sayeed Ahmad.  Simple enumeration of minimal cutsets of acyclic directed graph , 1988 .

[5]  Wei-Chang Yeh,et al.  A novel node-based sequential implicit enumeration method for finding all d-MPs in a multistate flow network , 2015, Inf. Sci..

[6]  K.D. Heidtmann.  Inverting Paths & Cuts of 2-State Systems , 1983, IEEE Transactions on Reliability.

[7]  Sheng-De Wang,et al.  Reliability evaluation for distributed computing networks with imperfect nodes , 1997 .

[8]  S. Arunkumar,et al.  Enumeration of All Minimal Cut-Sets for a Node Pair in a Graph , 1979, IEEE Transactions on Reliability.

[9]  M. O. Locks.  Inverting and Minimalizing Path Sets and Cut Sets , 1978, IEEE Transactions on Reliability.

[10]  D. R. Shier,et al.  Algorithms for Generating Minimal Cutsets by Inversion , 1985, IEEE Transactions on Reliability.

[11]  M. Samad,et al.  An efficient algorithm for simultaneously deducing minimal paths as well as cuts of a communication network , 1987 .

[12]  Mikkel Thorup,et al.  Undirected single-source shortest paths with positive integer weights in linear time , 1999, JACM.

[13]  J. M. Nahman.  Minimal paths and cuts of networks exposed to common-cause failures , 1992 .

[14]  David W. Coit,et al.  Reliability Analysis for Multi-Component Systems Subject to Multiple Dependent Competing Failure Processes , 2014, IEEE Transactions on Reliability.

[15]  David W. Coit,et al.  A generalized multistate-based path vector approach to multistate two-terminal reliability , 2006 .

[16]  Suresh Rai,et al.  Comments On "Inverting and Minimalizing Path sets and Cut sets , 1979 .

[17]  Wei-Chang Yeh.  A MCS-RSM approach for network reliability to minimise the total cost , 2003 .

[18]  Yi-Kuei Lin,et al.  Search for All Minimal Paths in a General Large Flow Network , 2012, IEEE Transactions on Reliability.

[19]  Charles J. Colbourn,et al.  The Combinatorics of Network Reliability , 1987 .

[20]  Terje Aven,et al.  Some considerations on reliability theory and its applications , 1988 .

[21]  Yuanlong Shen,et al.  A new simple algorithm for enumerating all minimal paths and cuts of a graph , 1995 .

[22]  Fang-Ming Shao,et al.  A practical bounding algorithm for computing two-terminal reliability based on decomposition technique , 2011, Comput. Math. Appl..

[23]  Wei-Chang Yeh.  Evaluation of all one-to-many reliabilities for acyclic multistate-node distributed computing system under cost and capacity constraints , 2007, Comput. Commun..

[24]  N. A. Mokhles,et al.  A new technique in a cutset evaluation , 1993 .

[25]  Kishor S. Trivedi,et al.  A BDD-Based Algorithm for Analysis of Multistate Systems with Multistate Components , 2003, IEEE Trans. Computers.

[26]  Wei-Chang Yen.  A Simple Heuristic Algorithm for Generating All Minimal Paths , 2007, IEEE Transactions on Reliability.

[27]  Terje Aven,et al.  Availability evaluation of oil/gas production and transportation systems , 1987 .

[28]  Wei-Chang Yeh,et al.  A revised layered-network algorithm to search for all d-minpaths of a limited-flow acyclic network , 1998 .

[29]  Clyde L. Monma,et al.  Reliability of Computer and Communication Networks , 1991 .

[30]  Wei-Chang Yeh,et al.  Economic-based resource allocation for reliable Grid-computing service based on Grid Bank , 2012, Future Gener. Comput. Syst..

[31]  K. D. Heidtmann.  Inverting Paths & Cutsof2-State Systems , 1983 .

[32]  Gregory Levitin,et al.  The Universal Generating Function in Reliability Analysis and Optimization , 2005 .

[33]  Wei-Chang Yeh.  Multistate-node acyclic networks reliability evaluation based on MC , 2003, Reliab. Eng. Syst. Saf..

[34]  Chin-Chia Jane,et al.  On reliability evaluation of a capacitated-flow network in terms of minimal pathsets , 1995, Networks.

[35]  Ming Jian Zuo,et al.  Reliability and Availability Analysis of a Repairable k-out-of-n: G System With R Repairmen Subject to Shut-Off Rules , 2011, IEEE Trans. Reliab..

[36]  R. V. Slyke,et al.  Reliability of computer-communication networks , 1971, WSC '71.

[37]  Alberto Martelli.  A Gaussian Elimination Algorithm for the Enumeration of Cut Sets in a Graph , 1976, JACM.

[38]  Suresh Rai,et al.  On Complementation of Pathsets and Cutsets , 1980, IEEE Transactions on Reliability.

[39]  Wei-Chang Yeh.  Evaluating the reliability of a novel deterioration-effect multi-state flow network , 2013, Inf. Sci..

[40]  R.N. Allan,et al.  An Efficient Computational Technique for Evaluating the Cut/Tie Sets and Common-Cause Failures of Complex Systems , 1981, IEEE Transactions on Reliability.

[41]  Robert Sedgewick,et al.  Algorithms, 4th Edition , 2011 .

[42]  Jacek Malinowski,et al.  Reliability evaluation for tree-structured systems with multistate components , 1996 .

[43]  Wei-Chang Yeh.  Multistate-node acyclic network reliability evaluation , 2002, Reliab. Eng. Syst. Saf..

[44]  Wei-Chang Yeh,et al.  A Simple Universal Generating Function Method to Search for All Minimal Paths in Networks , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.