Efficient Estimation of Stochastic Flow Network Reliability

Abstract

The Creation Process is an algorithm that transforms a static network model into a dynamic one. It is the basis of different variance reduction methods designed to make efficient reliability estimations on highly reliable networks in which links can only assume two possible values, operational or failed. In this article the Creation Process is extended to let it operate on network models in which links can assume more than two values. The proposed algorithm, called here Multi-Level Creation Process, is the basis of a method, also introduced here, to make efficient reliability estimations of highly reliable stochastic flow networks. The method proposed, which consists in an application of Splitting over the Multi-Level Creation Process, is empirically shown to be accurate, efficient, and robust.

Checking Correctness of a Symbolic Reliability Expression for a Capacitated Network

“…A mapping {0, 1} → where is the field of real numbers, i.e. ( ) is an assignment of a real number for each of the possible 2 values of [4,21,12,20,[22][23][24][25][26][27][28].…”

“…This example illustrates an alternative way of applying Test 3 to (11) & (12). Initially branch 2 alone is taken as a keystone element.…”

“…The aim of this paper is to show that correctness of reliability expressions for flow networks can be proved in a systematic way, though indeed for long expressions it is a formidable task. Lee [1] extended the concept of terminal-pair reliability to cover the case of a flow network, namely, a network that is good if and only if a specified amount of flow can be transmitted from the input node to the output node [2][3][4][5][6][7][8][9][10][11][12][13]. Terminal-pair reliability expressions for flow or capacitated networks can be checked by any of the three exhaustive tests given in Section 4.…”

“…It is easy to see that the above properties are enjoyed by (9), (12), (14), (16). If the components reliabilities are allowed to be equal, the reliability function becomes a polynomial of degree .…”

A Tutorial Exposition of Various Methods for Analyzing Capacitated Networks

“…Aggarwal [19], Trstensky and Bowron [20], Ramírez and Gebre [21], Yeh [22], Patra and Misra [23], Fusheng [24], El Khadiri and Yeh [25], Kabadurmus and Smith [26] and Cancela, et al [27] suggested methods for defining a composite performance index related to any network, that integrates the two aforementioned connectivity and capacity aspects. Moreover, Lin et al [28,29] presented an algorithm for evaluation of capacitated flow network in terms of minimal path sets or minimal cut-sets.…”