An algorithm to evaluate the system reliability for multicommodity case under cost constraint

System reliability evaluation for flow networks is an important issue in our modern society. This paper studies the system reliability that a given amount of multicommodity can be transmitted through a stochastic-flow network, in which each are has several capacities, under the cost constraint. A simple algorithm is proposed to generate all (d^1, d^2,..., d^p; C)-MPs where d^i is the demand of commodity i. The system reliability can then be calculated in terms of (d^1, d^2,..., d^p; C)-MPs.

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

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

[3]  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..

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

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

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

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

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

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

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

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

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

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

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

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

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