An efficient alternative to the exact evaluation of the quickest path flow network reliability problem

In this paper we consider the evaluation of the probability that a stochastic flow network allows the transmission of a given amount of flow through one path, connecting the source and the sink node, within a fixed amount of time. This problem, called the quickest path flow network reliability problem, belongs to the NP-hard family. This implies that no polynomial algorithm is known for solving it exactly in a CPU runtime bounded by a polynomial function of the network size. As an alternative, we propose to perform estimations by a Monte-Carlo simulation method. We illustrate that the proposed tool evaluates, with high precision and within small CPU runtime, configurations which cannot be handled, in reasonable CPU runtime, by means of a well-known exact method. HighlightsEfficient alternative to the NP-hard exact evaluation of the quickest path reliability problem.Fast and accurate Monte-Carlo estimator when the reliability is not very close to 1.For a fixed sample size, CPU runtime is a linear function of the network parameters.

[1]  Gen-Huey Chen,et al.  Algorithms for the constrained quickest path problem and the enumeration of quickest paths , 1994, Comput. Oper. Res..

[2]  Guoliang Xue,et al.  End-to-end data paths: quickest or most reliable? , 1998, IEEE Commun. Lett..

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

[4]  Stefan Ruzika,et al.  Reliable and Restricted Quickest Path Problems , 2011, INOC.

[5]  George S. Fishman,et al.  Discrete-event simulation , 2001 .

[6]  Yi-Kuei Lin,et al.  Extend the quickest path problem to the system reliability evaluation for a stochastic-flow network , 2003, Comput. Oper. Res..

[7]  D. T. Lee,et al.  The All-Pairs Quickest Path Problem , 1993, Inf. Process. Lett..

[8]  Herminia I. Calvete.  The quickest path problem with interval lead times , 2004, Comput. Oper. Res..

[9]  Nageswara S. V. Rao,et al.  Algorithms for All-Pairs Reliable Quickest Paths , 2003, International Conference on Computational Science.

[10]  Héctor Cancela,et al.  Topological optimization of reliable networks under dependent failures , 2015, Oper. Res. Lett..

[11]  João C. N. Clímaco,et al.  A comprehensive survey on the quickest path problem , 2006, Ann. Oper. Res..

[12]  Yi-Kuei Lin.  Calculation of minimal capacity vectors through k minimal paths under budget and time constraints , 2010, Eur. J. Oper. Res..

[13]  Michael H. Moore.  On the Fastest Route for Convoy-Type Traffic in Flowrate-Constrained Networks , 1976 .

[14]  Kishor S. Trivedi.  Probability and Statistics with Reliability, Queuing, and Computer Science Applications , 1984 .

[15]  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.

[16]  João C. N. Clímaco,et al.  An algorithm for ranking quickest simple paths , 2005, Comput. Oper. Res..

[17]  Y. L. Chen,et al.  Finding the k Quickset Simple Paths in a Network , 1994, Inf. Process. Lett..

[18]  George S. Fishman,et al.  Monte Carlo estimation of the maximal flow distribution with discrete stochastic arc capacity levels , 1989 .

[19]  George S. Fishman,et al.  Discrete-Event Simulation : Modeling, Programming, and Analysis , 2001 .

[20]  Y. H. Chin,et al.  The quickest path problem , 1990, Comput. Oper. Res..

[21]  Wei-Chang Yeh,et al.  A simple method for the multi-state quickest path flow network reliability problem , 2009, 2009 8th International Conference on Reliability, Maintainability and Safety.

[22]  David W. Coit,et al.  A Monte-Carlo simulation approach for approximating multi-state two-terminal reliability , 2005, Reliab. Eng. Syst. Saf..

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

[24]  Ronald L. Wasserstein,et al.  Monte Carlo: Concepts, Algorithms, and Applications , 1997 .

[25]  Yi-Kuei Lin,et al.  Stochastic computer network under accuracy rate constraint from QoS viewpoint , 2013, Inf. Sci..

[26]  Yi-Kuei Lin,et al.  System reliability of a stochastic-flow network through two minimal paths under time threshold , 2010 .

[27]  Stéphane Bulteau,et al.  A new importance sampling Monte Carlo method for a flow network reliability problem , 2002 .

[28]  Ernesto de Queirós Vieira Martins,et al.  An algorithm for the quickest path problem , 1997, Oper. Res. Lett..

[29]  Yi-Kuei Lin,et al.  Reliability of $k$ Separate Minimal Paths Under Both Time and Budget Constraints , 2010, IEEE Transactions on Reliability.

[30]  Herminia I. Calvete,et al.  Algorithms for the quickest path problem and the reliable quickest path problem , 2012, Comput. Manag. Sci..

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

[32]  S. Johari,et al.  Quickest path problems in stochastic-flow networks with time constraint: A fast and reliable solution , 2013, 2013 3rd IEEE International Advance Computing Conference (IACC).

[33]  Wei-Chang Yeh,et al.  A New Universal Generating Function Method for Solving the Single $(d, \tau)$-Quick-Path Problem in Multistate Flow Networks , 2012, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[34]  J. Ben Rosen,et al.  Algorithms for the quickest path problem and the enumeration of quickest paths , 1991, Comput. Oper. Res..

[35]  Reuven Y. Rubinstein,et al.  Simulation and the Monte Carlo method , 1981, Wiley series in probability and mathematical statistics.