A splitting algorithm for network reliability estimation

Splitting is a variance reduction technique widely used to make efficient estimations of the probability of rare events in the simulation of Markovian models. In this article, splitting is applied to improve a well-known method called the Creation Process (CP), used in network reliability estimation. The resulting proposal, called here Splitting/CP, is particularly appropriate in the case of highly reliable networks; i.e., networks for which failure is a rare event. The article introduces the basis of Splitting/CP and presents a set of computational experiments based on network topologies taken from the literature. The results of these experiments show that Splitting/CP is accurate, efficient, and robust and is therefore a valid alternative to the best known methods used in network reliability estimation.

[1]  Paul Glasserman,et al.  Splitting for rare event simulation: analysis of simple cases , 1996, Winter Simulation Conference.

[2]  Luca Podofillini,et al.  Optimal design of reliable network systems in presence of uncertainty , 2005, IEEE Transactions on Reliability.

[3]  Jose Emmanuel Ramirez-Marquez,et al.  Two-terminal reliability analyses for a mobile ad hoc wireless network , 2007, Reliab. Eng. Syst. Saf..

[4]  Gerardo Rubino,et al.  A new simulation method based on the RVR principle for the rare event network reliability problem , 2012, Ann. Oper. Res..

[5]  M. Lomonosov.  On Monte Carlo Estimates in Network Reliability , 1994, Probability in the Engineering and Informational Sciences.

[6]  José Villén-Altamirano.  Importance Functions for RESTART Simulation of Highly-Dependable Systems , 2007, Simul..

[7]  Sheldon M. Ross,et al.  A NEW SIMULATION ESTIMATOR OF SYSTEM RELIABILITY , 1994 .

[8]  Hans R. Künsch,et al.  A variant of importance splitting for rare event estimation: Fixed number of successes , 2011, TOMC.

[9]  Héctor Cancela,et al.  A recursive variance-reduction algorithm for estimating communication-network reliability , 1995 .

[10]  Lin Lin,et al.  A Self-controlled Genetic Algorithm for Reliable Communication Network Design , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[11]  Gerardo Rubino,et al.  Splitting in the simulation of the network creation process , 2008 .

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

[13]  Richard M. Karp,et al.  A new Monte-Carlo Method for Estimating the Failure Probability of an N-Component System , 1983 .

[14]  Malcolm C. Easton,et al.  Sequential Destruction Method for Monte Carlo Evaluation of System Reliability , 1980, IEEE Transactions on Reliability.

[15]  David W. Coit,et al.  MOMS-GA: A Multi-Objective Multi-State Genetic Algorithm for System Reliability Optimization Design Problems , 2008, IEEE Transactions on Reliability.

[16]  S. Ross,et al.  System Reliability by Simulation: Random Hazards Versus Importance Sampling , 1992 .

[17]  Verónika Peralta,et al.  Reliability Models for Data Integration Systems , 2010 .

[18]  Angel A. Juan,et al.  Simulation Methods for Reliability and Availability of Complex Systems , 2010 .

[19]  Bruno Tuffin,et al.  Rare events, splitting, and quasi-Monte Carlo , 2007, TOMC.

[20]  Héctor Cancela,et al.  The recursive variance-reduction simulation algorithm for network reliability evaluation , 2003, IEEE Trans. Reliab..

[21]  E. Henley,et al.  Dagger-Sampling Monte Carlo For System Unavailability Evaluation , 1980, IEEE Transactions on Reliability.

[22]  George S. Fishman,et al.  A Monte Carlo Sampling Plan for Estimating Network Reliability , 1984, Oper. Res..

[23]  Dirk P. Kroese,et al.  A comparison of RESTART implementations , 1998, 1998 Winter Simulation Conference. Proceedings (Cat. No.98CH36274).

[24]  José Villén-Altamirano.  RESTART simulation of non-Markov consecutive-k-out-of-n: F repairable systems , 2010, Reliab. Eng. Syst. Saf..

[25]  Gerardo Rubino,et al.  Rare Event Analysis by Monte Carlo Techniques in Static Models , 2009, Rare Event Simulation using Monte Carlo Methods.

[26]  Dirk P. Kroese,et al.  Efficient Monte Carlo simulation via the generalized splitting method , 2012, Stat. Comput..

[27]  Gerardo Rubino,et al.  New measures of robustness in rare event simulation , 2005, Proceedings of the Winter Simulation Conference, 2005..

[28]  Hiromitsu Kumamoto,et al.  Efficient Evaluation of System Reliability by Monte Carlo Method , 1977, IEEE Transactions on Reliability.

[29]  Miro Kraetzl,et al.  THE TREE CUT AND MERGE ALGORITHM FOR ESTIMATION OF NETWORK RELIABILITY , 2003 .

[30]  Pierre L'Ecuyer,et al.  Splitting Techniques , 2009, Rare Event Simulation using Monte Carlo Methods.

[31]  José Villén-Altamirano,et al.  On the efficiency of RESTART for multidimensional state systems , 2006, TOMC.

[32]  Silvio Levy,et al.  The CWEB system of structured documentation - version 3.0 , 1994 .

[33]  L. Schruben.  A Coverage Function for Interval Estimators of Simulation Response , 1980 .

[34]  José Villén-Altamirano,et al.  Analysis of restart simulation: Theoretical basis and sensitivity study , 2002, Eur. Trans. Telecommun..

[35]  J. Scott Provan,et al.  The Complexity of Counting Cuts and of Computing the Probability that a Graph is Connected , 1983, SIAM J. Comput..

[36]  Tov Elperin,et al.  Estimation of network reliability using graph evolution models , 1991 .

[37]  Dirk P. Kroese,et al.  Handbook of Monte Carlo Methods , 2011 .

[38]  Marnix J. J. Garvels,et al.  The splitting method in rare event simulation , 2000 .

[39]  F. Sibel Salman,et al.  Assessing the reliability and the expected performance of a network under disaster risk , 2011, OR Spectr..

[40]  Miro Kraetzl,et al.  The Cross-Entropy Method for Network Reliability Estimation , 2005, Ann. Oper. Res..