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 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.

Modeling and Applications on Timed Stochastic-Flow Networks

2015 ◽  
Vol 22 (05) ◽  
pp. 1550023
Author(s):  
Shin-Guang Chen
Keyword(s):  
Network Reliability ◽  
Daily Life ◽  
Transportation Network ◽  
Stochastic Flow ◽  
Production Network ◽  
Flow Networks ◽  
Stochastic Behavior ◽  
Flow Network ◽  
Numerical Examples ◽  
Time Consumption

A stochastic-flow network (SFN) is a network whose flow has stochastic behavior or probabilistic multi-states. A timed stochastic-flow network (TSFN) is a SFN whose flow spends time to go through the network. Traditionally, the evaluation of network reliability does not consider time consumption for the flow to get through the network. However, there are lots of daily-life networks which can be regarded as TSFNs, such as the transportation network, the production network, etc. Their flow spends time to get through the network, and they are not yet explored in the literature. This paper proposes approaches to evaluate the reliability of such networks. Some numerical examples are discussed to illustrate the proposed method.

PERMUTATIONAL METHODS FOR PERFORMANCE ANALYSIS OF STOCHASTIC FLOW NETWORKS

2013 ◽  
Vol 28 (1) ◽  
pp. 21-38 ◽  
Author(s):  
Ilya Gertsbakh ◽  
Reuven Rubinstein ◽  
Yoseph Shpungin ◽  
Radislav Vaisman
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Performance Analysis ◽  
Failure Probability ◽  
Stochastic Flow ◽  
Maximal Flow ◽  
Convergence Properties ◽  
Flow Networks ◽  
Flow Network ◽  
Random Failures

In this paper we show how the permutation Monte Carlo method, originally developed for reliability networks, can be successfully adapted for stochastic flow networks, and in particular for estimation of the probability that the maximal flow in such a network is above some fixed level, called the threshold. A stochastic flow network is defined as one, where the edges are subject to random failures. A failed edge is assumed to be erased (broken) and, thus, not able to deliver any flow. We consider two models; one where the edges fail with the same failure probability and another where they fail with different failure probabilities. For each model we construct a different algorithm for estimation of the desired probability; in the former case it is based on the well known notion of the D-spectrum and in the later one—on the permutational Monte Carlo. We discuss the convergence properties of our estimators and present supportive numerical results.

scholarly journals Maximum Entropy Analysis of Flow Networks: Theoretical Foundation and Applications

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 776 ◽  
Author(s):  
Robert K. Niven ◽  
Markus Abel ◽  
Michael Schlegel ◽  
Steven H. Waldrip
Keyword(s):  
Maximum Entropy ◽  
Joint Probability ◽  
Financial Economic ◽  
Flow Networks ◽  
Flow Network ◽  
Physical Constraints ◽  
Generalized Maximum Entropy ◽  
Deterministic Solution ◽  
Network Properties ◽  
The Cost

The concept of a “flow network”—a set of nodes and links which carries one or more flows—unites many different disciplines, including pipe flow, fluid flow, electrical, chemical reaction, ecological, epidemiological, neurological, communications, transportation, financial, economic and human social networks. This Feature Paper presents a generalized maximum entropy framework to infer the state of a flow network, including its flow rates and other properties, in probabilistic form. In this method, the network uncertainty is represented by a joint probability function over its unknowns, subject to all that is known. This gives a relative entropy function which is maximized, subject to the constraints, to determine the most probable or most representative state of the network. The constraints can include “observable” constraints on various parameters, “physical” constraints such as conservation laws and frictional properties, and “graphical” constraints arising from uncertainty in the network structure itself. Since the method is probabilistic, it enables the prediction of network properties when there is insufficient information to obtain a deterministic solution. The derived framework can incorporate nonlinear constraints or nonlinear interdependencies between variables, at the cost of requiring numerical solution. The theoretical foundations of the method are first presented, followed by its application to a variety of flow networks.

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