Network reliability: Heading out on the highway

Jason I. Brown; Charles J. Colbourn; Danielle Cox; Christina Graves; Lucas Mol

doi:10.1002/net.21977

Network reliability: Heading out on the highway

Jason I. Brown, Charles J. Colbourn, Danielle Cox, Christina Graves, Lucas Mol

Computing, Informatics and Decision Systems Engineering, School of (CIDSE)

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

A variety of probabilistic notions of network reliability of graphs and digraphs have been proposed and studied since the early 1950s. Although grounded in the engineering and logistics of network design and analysis, the research also spans pure and applied mathematics, with connections to areas as diverse as combinatorics and graph theory, combinatorial enumeration, optimization, probability theory, real and complex analysis, algebraic topology, commutative algebra, the design and analysis of algorithms, and computational complexity. In this paper we describe the landscape of various notions of network reliability, the roads well traveled, and some that appear likely to lead to meaningful and important journeys.

Original language	English (US)
Pages (from-to)	146-160
Number of pages	15
Journal	Networks
Volume	77
Issue number	1
DOIs	https://doi.org/10.1002/net.21977
State	Published - Jan 2021

Keywords

coherent system
digraph
fixed point
graph
inflection point
matroid
network
optimal graph
reliability
reliability polynomial
root

ASJC Scopus subject areas

Software
Information Systems
Hardware and Architecture
Computer Networks and Communications

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10.1002/net.21977

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title = "Network reliability: Heading out on the highway",

abstract = "A variety of probabilistic notions of network reliability of graphs and digraphs have been proposed and studied since the early 1950s. Although grounded in the engineering and logistics of network design and analysis, the research also spans pure and applied mathematics, with connections to areas as diverse as combinatorics and graph theory, combinatorial enumeration, optimization, probability theory, real and complex analysis, algebraic topology, commutative algebra, the design and analysis of algorithms, and computational complexity. In this paper we describe the landscape of various notions of network reliability, the roads well traveled, and some that appear likely to lead to meaningful and important journeys.",

keywords = "coherent system, digraph, fixed point, graph, inflection point, matroid, network, optimal graph, reliability, reliability polynomial, root",

author = "Brown, {Jason I.} and Colbourn, {Charles J.} and Danielle Cox and Christina Graves and Lucas Mol",

note = "Funding Information: J. Brown and D. Cox acknowledge research support from Natural Sciences and Engineering Research Council of Canada (NSERC), grants RGPIN 2018‐05227 and RGPIN 2017‐04401, respectively. The authors thank for 50 years of excellence, and wish the journal a very happy birthday and a long life. Networks Publisher Copyright: {\textcopyright} 2020 Wiley Periodicals LLC.",

year = "2021",

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doi = "10.1002/net.21977",

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pages = "146--160",

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AU - Mol, Lucas

N1 - Funding Information: J. Brown and D. Cox acknowledge research support from Natural Sciences and Engineering Research Council of Canada (NSERC), grants RGPIN 2018‐05227 and RGPIN 2017‐04401, respectively. The authors thank for 50 years of excellence, and wish the journal a very happy birthday and a long life. Networks Publisher Copyright: © 2020 Wiley Periodicals LLC.

PY - 2021/1

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N2 - A variety of probabilistic notions of network reliability of graphs and digraphs have been proposed and studied since the early 1950s. Although grounded in the engineering and logistics of network design and analysis, the research also spans pure and applied mathematics, with connections to areas as diverse as combinatorics and graph theory, combinatorial enumeration, optimization, probability theory, real and complex analysis, algebraic topology, commutative algebra, the design and analysis of algorithms, and computational complexity. In this paper we describe the landscape of various notions of network reliability, the roads well traveled, and some that appear likely to lead to meaningful and important journeys.

AB - A variety of probabilistic notions of network reliability of graphs and digraphs have been proposed and studied since the early 1950s. Although grounded in the engineering and logistics of network design and analysis, the research also spans pure and applied mathematics, with connections to areas as diverse as combinatorics and graph theory, combinatorial enumeration, optimization, probability theory, real and complex analysis, algebraic topology, commutative algebra, the design and analysis of algorithms, and computational complexity. In this paper we describe the landscape of various notions of network reliability, the roads well traveled, and some that appear likely to lead to meaningful and important journeys.

KW - coherent system

KW - digraph

KW - fixed point

KW - graph

KW - inflection point

KW - matroid

KW - network

KW - optimal graph

KW - reliability

KW - reliability polynomial

KW - root

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Network reliability: Heading out on the highway

Abstract

Keywords

ASJC Scopus subject areas

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