scholarly journals Reliability Evaluation for a Stochastic Flow Network Based on Upper and Lower Boundary Vectors

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1115
Author(s):  
Huang ◽  
Huang ◽  
Lin
Keyword(s):  
Lower Boundary ◽  
Reliability Evaluation ◽  
Exclusion Principle ◽  
Stochastic Flow ◽  
Decomposition Approach ◽  
Flow Network ◽  
Boundary Points ◽  
Classic Problem ◽  
Upper Boundary

For stochastic flow network (SFN), given all the lower (or upper) boundary points, the classic problem is to calculate the probability that the capacity vectors are greater than or equal to the lower boundary points (less than or equal to the upper boundary points). However, in some practical cases, SFN reliability would be evaluated between the lower and upper boundary points at the same time. The evaluation of SFN reliability with upper and lower boundary points at the same time is the focus of this paper. Because of intricate relationships among upper and lower boundary points, a decomposition approach is developed to obtain several simplified subsets. SFN reliability is calculated according to these subsets by means of the inclusion-exclusion principle. Two heuristic options are then established in order to calculate SFN reliability in an efficient direction based on the lower and upper boundary points.

A Comparative Study of Different Approaches for Finding the Upper Boundary Points in Stochastic-Flow Networks

2014 ◽  
Vol 10 (3) ◽  
pp. 13-23 ◽  
Author(s):  
Seyed Mehdi Mansourzadeh ◽  
Seyed Hadi Nasseri ◽  
Majid Forghani-elahabad ◽  
Ali Ebrahimnejad
Keyword(s):  
Information System ◽  
Comparative Study ◽  
Test Problems ◽  
Stochastic Flow ◽  
Flow Networks ◽  
Flow Network ◽  
Random Test ◽  
Boundary Points ◽  
Exclusion Method ◽  
Upper Boundary

An information system network (ISN) can be modeled as a stochastic-flow network (SFN). There are several algorithms to evaluate reliability of an SFN in terms of Minimal Cuts (MCs). The existing algorithms commonly first find all the upper boundary points (called d-MCs) in an SFN, and then determine the reliability of the network using some approaches such as inclusion-exclusion method, sum of disjoint products, etc. However, most of the algorithms have been compared via complexity results or through one or two benchmark networks. Thus, comparing those algorithms through random test problems can be desired. Here, the authors first state a simple improved algorithm. Then, by generating a number of random test problems and implementing the algorithms in MATLAB, the proposed algorithm is demonstrated to be more efficient than some existing ones in medium-sized networks. The performance profile introduced by Dolan and More is used for analyzing the output of programs.

scholarly journals Genetic Algorithm for solving flow problems in a Stochastic-flow Network under Budget Constraints

2014 ◽  
Vol 12 (8) ◽  
pp. 3749-3757
Author(s):  
M. R. Hassan
Keyword(s):  
Genetic Algorithm ◽  
Lower Boundary ◽  
Flow Network ◽  
Total Transmission ◽  
Flow Problems ◽  
Boundary Points ◽  
Transmission Cost ◽  
Flow Vector ◽  
Feasible Solutions ◽  
The Given

The system reliability (Rd,c) calculation is based on the generation of all the lower boundary points for the given demand, d, such that the total transmission cost is less than or equal to c (budget). This generation of the lower boundary points is based on finding all feasible solutions to the flow vector, F. The number of feasible solutions cannot be anticipated. Thus, a genetic algorithm is useful for solving this problem. Therefore, this paper presents a genetic algorithm to generate all feasible solutions to the flow vector, F, and then calculate Rd,c. The algorithm is applied to two problem models. In the first, each arc of a flow network has several capacities and may fail. In the second, both the arc and node have several capacities and may fail. The results show that the algorithm is efficient at solving a flow problem and is useful for calculating Rd,c.

Mission Reliability Evaluation for Fuzzy Multistate Manufacturing System Based on an Extended Stochastic Flow Network

2020 ◽  
Vol 69 (4) ◽  
pp. 1239-1253 ◽  
Author(s):  
Yihai He ◽  
Zhaoxiang Chen ◽  
Yixiao Zhao ◽  
Xiao Han ◽  
Di Zhou
Keyword(s):  
Manufacturing System ◽  
Reliability Evaluation ◽  
Stochastic Flow ◽  
Flow Network
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