Capacity Reliability Calculation and Sensitivity Analysis for a Stochastic Transport Network

Abstract

A major performance index for analyzing a stochastic transport network is the two-terminal capacity reliability R d , defined as the probability that d units of goods can be successfully transported via stochastic arc capacities from the source to the destination. This paper presents an efficient d-minimal path method to calculate R d based on some newly obtained results. The proposed method uses a simple method to check d-minimal path candidates and a more efficient approach to remove duplicate d-minimal paths that are the biggest obstacle in solving d-minimal paths, along with an indication of the advantage over the existing methods. Besides, sensitivity analysis is adopted to explore the most important arc whose reliability change affects the network reliability most significantly, which helps supervisor identify and enhance the critical arcs for improving the network reliability more effectively. Computational and application examples demonstrate the efficiency and utility of the method, respectively.

Notice of Retraction: Reliability Sensitivity Analysis for Dynamic Stiffness of Motor Spindles in a Machining Center

“…These parameters are basically random variables, which also cause randomness in the structural performance. Sensitivity analysis is mainly used to identify the key parameters with the greatest effect in a reliability model [25,26], so that a sensitivity analysis of random structure reliability is adopted to study the influencing criteria of random variables or their parameters in a reliability model. The model can be used to provide the horizontal contrast of the importance degree among random variables or parameters, to supply important information for reliability design and to have guiding functions in the areas of reliability design and modification, reliability optimization design, reliability maintenance, etc.…”

An Improved Vectorization Algorithm to Solve the d-MP Problem

“…There are three types of data transmission in an SFN: (1) two-terminal, in which the data is transmitted from a source node to a sink node, (2) k-terminal, in which the data is transmitted among k components, and (3) all-terminal, in which the data is transmitted among all the components in the network. The focus of this work is on the first case, where the network reliability at demand level d, denoted by R d , is the probability of transmitting at least d units of data from a source node to a destination node in the network [15,19,31].…”

“…One can model many real-world systems such as transportation networks, computer and communication networks, distribution systems, and power transmission systems as SFNs [4,13,22,38]. Therefore, the reliability evaluation of SFNs has been a very attractive problem in the last decades, and several direct and indirect algorithms have been proposed in the literature to address it [1,4,5,7,8,9,10,11,12,13,14,16,17,18,22,23,25,26,27,28,29,30,31,34,35,36,37,39].…”

A simple vectorization algorithm to address the d-MP problem without generating duplicate candidates

“…This is why the problem of reliability evaluation of MFNs has turned to be of great importance [2]. The reliability of two-terminal MFN can be evaluated indirectly in terms of minimal paths (MPs) [2,4,6,7,13,14,16,18] or minimal cuts (MCs) [3,5,[8][9][10][11]15] through a three-stage process; (1) determining all the MPs or MCs, (2) finding all the d-MP s or d-MC s, which are called the d-MP or d-MC problem, and (3) calculating a union probability as the network reliability. The focus of this work is on the second stage and the d-MP problem, and hence we assume that all the MPs are available in advance.…”