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Simulation approach with MC-reduction for multi-state flow network reliability estimation

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Abstract

A multistate flow network (MSFN) is an applicable model for constructing and evaluating practical systems, including an information system in resilient supply chain network. When assessing the performance of an MSFN, system reliability is a critical indicator in determining the probability that a given demand will be transmitted by the MSFN. This study develops a minimal cut (MC)-based simulation approach for estimating the system reliability of an MSFN. This simulation approach does not require the upper boundary points for the demand, which are essential in many existing simulation approaches. Additionally, the concept of a cut size limit is integrated into the simulation to reduce the number of MCs, with the computational time exhibiting a linear dependence on the number of MCs. The novel MC-reduction simulation approach proposed in this study estimates system reliability more efficiently than traditional approaches. The effectiveness of the MC-reduction simulation approach is validated on a series of examples, including a time-series analysis of a real-life computer system. Therefore, the proposed approach is advantaged to evaluate the performance of information system in a large supply chain network.

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Abbreviations

MSFN:

Multistate flow network

MP:

Minimal path

MC:

Minimal cut

TANET:

Taiwan academic network

n :

Number of arcs

A :

{a1, a2, …, an}: set of n arcs

a i :

ith arc for i = 1, 2, …, n

N :

Set of perfectly reliable nodes

c i :

Capacity of each component in ai

C :

(c1, c2, …, cn): (vector of) component capacity

r i :

Reliability of each component in ai

R :

(r1, r2, …, rn): (vector of) component reliability

m i :

Number of components in ai

M :

(m1, m2, …, mn): (vector of) number of components

G :

(A, N, C, R, M): An MSFN

y i :

Available number of components in ai

x i :

Capacity state of ai; xi = yici

X :

(x1, x2, …, xn): System state

V(X):

Maximal capacity under X

d :

Demand

q :

Number of MC

K j :

jth MC for j = 1, 2, …, q

||K j||:

Size of Kj; number of arcs in Kj

z :

Cut size limit

V(X | K j):

Capacity of Kj under state X

R sys :

System reliability

γ all :

Average system reliability estimated by using all MCs

γ z :

Average system reliability estimated with size limit z

Γ :

Effectiveness index

δ all :

Average computation time using all q MCs

δ z :

Average computation time with size limit z

Δ:

Efficiency index

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Funding

This work was supported by the National Science and Technology Council, Taiwan, Republic of China [grant number NSTC 112-2223-E-027-001-MY3 and 110-2221-E-027-130-MY3].

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  1. Department of Industrial Engineering and Management, National Taipei University of Technology, Taipei, 10608, Taiwan, ROC

    Ping-Chen Chang

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Chang, PC. Simulation approach with MC-reduction for multi-state flow network reliability estimation. Ann Oper Res (2024). https://doi.org/10.1007/s10479-024-05840-w

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