Derivation of Minimal Cutsets from Minimal Pathsets for a Multi-State System and Utilization of Both Sets in Checking Reliability Expressions

This paper addresses two important useful extensions of binary reliability techniques to multi-state reliability techniques, namely: (a) the problem of complementation or inversion of the function of system success to that of system failure (or equivalently, of deriving the logical minimal cutsets in terms of the logical minimal paths), and (b) the associated problem of hand-checking of a symbolic reliability expression. The paper deals specifically with the reliability of a multi-state delivery network. It presents two complementation procedures, one via the application of multi-state De Morgan’s rules, and the other via the multi-state Boole-Shannon expansion. The paper also illustrates one case in which this complementation is needed, as it outlines a method for checking the reliability of the multi-state system in terms of its logical minimal paths and logical minimal cutsets.

Assess the Impacts of Discount Policies on the Reliability of a Stochastic Air Transport Network

In this study, an algorithm for reliability evaluation is proposed in order to assess the discount policy based on its effect on an air transport network. An air transport network is a typical stochastic air transport network (SATN) because its capacity (available seats) is regarded as stochastic. Under different discount policies, the term “reliability” refers to the ability to meet a certain travel demand within a limited budget. To better describe the flow of SATN, the methods of the sum of disjoint products and minimal paths are combined in the proposed algorithm. A reliability analysis is conducted at ranges of budgets and travel demands for a more accurate assessment. The outcomes of this study help the travel agents assess and select an appropriate discount policy, which is one of the important contributions. This study also contributes to enhancing the reliability fluctuation under the impact of multiple discount policies.

A Minimal Path-Based Method for Computing Multistate Network Reliability

Most of modern technological networks that can perform their tasks with various distinctive levels of efficiency are multistate networks, and reliability is a fundamental attribute for their safe operation and optimal improvement. For a multistate network, the two-terminal reliability at demand level d, defined as the probability that the network capacity is greater than or equal to a demand of d units, can be calculated in terms of multistate minimal paths, called d-minimal paths (d-MPs) for short. This paper presents an efficient algorithm to find all d-MPs for the multistate two-terminal reliability problem. To advance the solution efficiency of d-MPs, an improved model is developed by redefining capacity constraints of network components and minimal paths (MPs). Furthermore, an effective technique is proposed to remove duplicate d-MPs that are generated multiple times during solution. A simple example is provided to demonstrate the proposed algorithm step by step. In addition, through computational experiments conducted on benchmark networks, it is found that the proposed algorithm is more efficient.

Parcours d’étude et de recherche : une étude sur les chemins minimauxStudy and research course: a study on minimal paths

RésuméCette étude vise à exposer le progrès d'un projet de recherche doctorale dont l'objectif est d'analyser les limites et les possibilités d'un parcours d'étude et de recherche (PER) en tant que stratégie didactique pour faire face au paradigme monumentaliste des mathématiques scolaires. Nous ne présentons dans ce rapport que les résultats préliminaires.Mots-clés : Optmisation; Parcours d´étude et de recherche, Distance, Trajectoires.AbstractThe aim of this study is to expose the progress of a doctoral research project whose objective is the analysis of the limits and possibilities of a study and research course (SRC) as a didactical strategy to face the monumental paradigm of school mathematics. Only preliminaryr esults are presented in this report.Keywords: Optimization; Course of study and research, Distance, Trajectories.

Enumeration of the minimal node cutsets based on necessary minimal paths

<p>Reliability evaluation is an important research field for a complex network. The most popular methods for such evaluation often use Minimal Cuts (MC) or Minimal paths (MP). Nonetheless, few algorithms address the issue of the enumeration of all minimal cut sets from the source node s to the terminal node t when only the nodes of the network are subject to random failures. This paper presents an effective algorithm which enumerates all minimal node cuts sets of a network. The proposed algorithm runs in two steps: The first one is used to generate a subset of paths, called necessary minimal paths, instead of all minimal paths. Whereas, the second step stands to build all minimal cutsets from the necessary minimal paths.</p>