Reliability of a Multi‐State Computer Network Through k Minimal Paths Within Tolerable Error Rate and Time Threshold

A computer system is usually modeled as a network topology where each branch denotes a transmission medium and each vertex represents a station of servers. Each branch has multiple capacities/states due to failure, partial failure, and maintenance. Such a network is named a multi-state computer network (MSCN). From the viewpoint of quality management, transmission error rate and transmission time are both critical performance indicators to assess Internet quality for system managers and customers. Within both tolerable error rate and time threshold, the addressed problem is concentrated on an MSCN for computing the probability that d units of data can be sent through multiple minimal paths simultaneously. Such a probability is named system reliability. A solution procedure including an efficient algorithm based on MPs is proposed to derive the lower boundary vectors (LBVs) meeting the requirements. Then system reliability, which is represented as the probability of union of subsets, can be subsequently evaluated by the LBVs. Copyright © 2015 John Wiley & Sons, Ltd.

[1]  Wei-Chang Yeh.  Multistate network reliability evaluation under the maintenance cost constraint , 2004 .

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

[3]  Yi-Kuei Lin,et al.  On a multicommodity stochastic-flow network with unreliable nodes subject to budget constraint , 2007, Eur. J. Oper. Res..

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

[5]  John Yuan,et al.  Reliability evaluation of a limited-flow network in terms of minimal cutsets , 1993 .

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

[7]  Yi-Kuei Lin,et al.  System performance of a two-commodity stochastic-flow network with cost attributes in terms of minimal cuts , 2007, Appl. Math. Comput..

[8]  Hong-Zhong Huang,et al.  An efficient method for reliability evaluation of multistate networks given all minimal path vectors , 2007 .

[9]  Gregory Levitin,et al.  A new approach to solving problems of multi‐state system reliability optimization , 2001 .

[10]  K. Kobayashi,et al.  A new algorithm in enumerating all minimal paths in a sparse network , 1999 .

[11]  Charles J. Colbourn,et al.  Lower bounds on two-terminal network reliability , 1988, Discret. Appl. Math..

[12]  Yi-Kuei Lin.  Time version of the shortest path problem in a stochastic-flow network , 2009 .

[13]  Wei-Chang Yeh.  Search for minimal paths in modified networks , 2002, Reliab. Eng. Syst. Saf..

[14]  Paul D. Amer,et al.  A Measurement Center for the NBS Local Area Computer Network , 1982, IEEE Transactions on Computers.

[15]  Terje Aven,et al.  Reliability Evaluation of Multistate Systems with Multistate Components , 1985, IEEE Transactions on Reliability.

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

[17]  Yi-Kuei Lin,et al.  Multistate components assignment problem with optimal network reliability subject to assignment budget , 2011, Appl. Math. Comput..

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

[19]  Susan L. Albin,et al.  Monitoring a fraction with easy and reliable settings of the false alarm rate , 2009, Qual. Reliab. Eng. Int..

[20]  Anja Feldmann,et al.  Deriving traffic demands for operational IP networks: methodology and experience , 2001, TNET.

[21]  Gen-Huey Chen,et al.  On the Quickest Path Problem , 1990, Inf. Process. Lett..

[22]  Gen-Huey Chen,et al.  Distributed algorithms for the quickest path problem , 1992, Parallel Comput..

[23]  Amjed M. Al-Ghanim,et al.  A heuristic technique for generating minimal path and cutsets of a general network , 1999 .

[24]  Yen-Liang Chen,et al.  An algorithm for finding the k quickest paths in a network , 1993, Comput. Oper. Res..

[25]  Sheng-Tzong Cheng.  Topological optimization of a reliable communication network , 1998 .

[26]  Wei-Chang Yeh.  A new approach to evaluate reliability of multistate networks under the cost constraint , 2005 .

[27]  Imrich Chlamtac.  Issues in Design and Measurement of Local Area Networks , 1980, Int. CMG Conference.

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

[29]  Raj Jain,et al.  Packet Trains-Measurements and a New Model for Computer Network Traffic , 1986, IEEE J. Sel. Areas Commun..

[30]  João C. N. Clímaco,et al.  Internet packet routing: Application of a K , 2007, Eur. J. Oper. Res..

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

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

[33]  Yen-Liang Chen,et al.  Minimum time paths in a network with mixed time constraints , 1998, Comput. Oper. Res..

[34]  Soondal Park,et al.  A label-setting algorithm for finding a quickest path , 2004, Comput. Oper. Res..

[35]  Wei-Chang Yeh,et al.  A simple minimal path method for estimating the weighted multi-commodity multistate unreliable networks reliability , 2008, Reliab. Eng. Syst. Saf..

[36]  Shigeki Goto,et al.  Identifying Heavy-Hitter Flows from Sampled Flow Statistics , 2007, IEICE Trans. Commun..

[37]  Juan José Tarí,et al.  The individual effects of total quality management on customers, people and society results and quality performance in SMEs , 2008, Qual. Reliab. Eng. Int..

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

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