Reliability of a computer network in case capacity weight varying with arcs, nodes and types of commodity

The computer network can be modeled as a capacitated-flow network. This paper concentrates on a two-commodity capacitated-flow network with three characters: (1) nodes as well as arcs have multiple possible capacities and may fail, (2) each component (arc/node) has both capacity and cost attributes; and (3) the capacity weight varies with arcs, nodes and types of commodity (or named file). We study the possibility that a given quantity of two types of files can be transmitted through this network simultaneously under the budget constraint. Such a possibility is named the system reliability which is a performance index to measure the quality level of supply demand systems such as computer, telecommunication, electric-power transmission and transportation systems. The approach of minimal paths is applied to describe the relationship among flow assignments and capacity vectors. A simple algorithm in terms of minimal paths is proposed to evaluate the system reliability.

[1]  John E. Cremeans,et al.  THE MULTICOMMODITY NETWORK FLOW MODEL REVISED TO INCLUDE VEHICLE PER TIME PERIOD AND NODE CONSTRAINTS , 1972 .

[2]  Yi-Kuei Lin,et al.  A simple algorithm for reliability evaluation of a stochastic-flow network with node failure , 2001, Comput. Oper. Res..

[3]  Kailash C. Kapur,et al.  Reliability Bounds for Multistate Systems with Multistate Components , 1985, Oper. Res..

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

[5]  John E. Cremeans,et al.  Optimal multicommodity network flows with resource allocation , 1970 .

[6]  D. R. Fulkerson,et al.  Flows in Networks. , 1964 .

[7]  Wei-Chang Yeh.  A simple algorithm to search for all d-MPs with unreliable nodes , 2001, Reliab. Eng. Syst. Saf..

[8]  T. C. Hu.  Multi-Commodity Network Flows , 1963 .

[9]  A. M. Geoffrion,et al.  Multicommodity Distribution System Design by Benders Decomposition , 1974 .

[10]  Philip Wolfe,et al.  Validation of subgradient optimization , 1974, Math. Program..

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

[12]  Arjang A. Assad,et al.  Multicommodity network flows - A survey , 1978, Networks.

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

[14]  Yi-Kuei Lin,et al.  ON RELIABILITY EVALUATION OF A STOCHASTIC-FLOW NETWORK IN TERMS OF MINIMAL CUTS , 2001 .

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

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

[17]  B. Rothschild,et al.  On Two Commodity Network Flows , 1966, Oper. Res..

[18]  James R. Evans.  A combinatorial equivalence between A class of multicommodity flow problems and the capacitated transportation problem , 1976, Math. Program..

[19]  John J. Jarvis.  On the equivalence between the Node‐ARC and ARC‐Chain formulations for the multi‐commodity maximal flow problem , 1969 .

[20]  John Erik Hershey,et al.  Fast algorithm for computing the reliability of a communication network , 1991 .

[21]  J. A. Tomlin,et al.  Minimum-Cost Multicommodity Network Flows , 1966, Oper. Res..

[22]  Yi-Kuei Lin,et al.  Using minimal cuts to evaluate the system reliability of a stochastic-flow network with failures at nodes and arcs , 2002, Reliab. Eng. Syst. Saf..

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

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

[25]  W. Griffith.  MULTISTATE RELIABILITY MODELS , 1980 .

[26]  Suresh Rai,et al.  CAREL: Computer Aided Reliability Evaluator for Distributed Computing Networks , 1991, IEEE Trans. Parallel Distributed Syst..

[27]  K.K. Aggarwal,et al.  Capacity Consideration in Reliability Analysis of Communication Systems , 1982, IEEE Transactions on Reliability.

[28]  Xue Janan,et al.  On Multistate System Analysis , 1985, IEEE Transactions on Reliability.

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

[30]  J. Kennington.  Solving multicommodity transportation problems using a primal partitioning simplex technique , 1977 .

[31]  Yi-Kuei Lin.  An algorithm to generate all spanning trees with flow , 2002 .

[32]  Jsen-Shung Lin,et al.  Reliability evaluation of capacitated-flow networks with budget constraints , 1998 .

[33]  Lester Randolph Ford,et al.  A Suggested Computation for Maximal Multi-Commodity Network Flows , 2004, Manag. Sci..