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An efficient sum of disjoint product method for reliability evaluation of stochastic flow networks using d-MPs

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Abstract

Stochastic flow network evaluation methods often compute a set of success events as d-MPs and obtain reliability from d-MPs. Both finding d-MPs and obtaining reliability from d-MPs are NP-Hard problems. This work addresses the problem of finding the reliability from d-MPs. In particular, we propose three rules to identify redundant and disjoint d-MPs as well as to disjoint the non-disjointed d-MPs. The non-disjointed d-MPs have shared capacity states which needs to be eliminated while evaluating reliability from the d-MPs. We implemented the proposed method in MATLAB and compared its performance with the existing methods using benchmark networks available in the literature. The experimental results show that the proposed SDP method performs better than the existing methods. This improvement is attributed to avoiding certain redundant computations which are part of the existing methods. We also present some practical applications of the stochastic network reliability analysis.

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Abbreviations

d:

Demand required pass from s to t.

s, t:

Source node, terminal node.

MS2TR\(_d\) :

Multi-state two-terminal reliability for d.

G(V, E):

Stochastic-flow network.

V:

Nodes of a network.

E:

Links of a network.

c\(_i\) :

A network component.

M\(_{c_i}\) :

Maximum capacity of a component c\(_i\).

n:

Total number of components in G(V,E).

p\(_i\) :

Minimal path.

LBFV:

Lower Boundary Flow Vectors.

\(d-\)MP:

\(d-\)Minimal Path, alternative name for LBFV.

K:

Valid feasible flow vector.

X\(_j\) :

Jth flow vector.

\(a_{i,j}\) :

Current capacity of c\(_i\) in X\(_j\).

\(a_{i,j}^{lp}\) :

Lowest capacity of c\(_i\) in X\(_j\).

\(a_{i,j}^{up}\) :

Uppermost capacity of c\(_i\) in X\(_j\).

i:

Index of components 1 to n in X\(_j\).

m:

Total number of flow vectors.

j:

Index of flow vectors 1 to m.

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  1. Subir Chowdhury School of Quality and Reliability, Indian Institute of Technology, Kharagpur, India

    Esha Datta & Neeraj Goyal

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  1. Esha Datta
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Datta, E., Goyal, N. An efficient sum of disjoint product method for reliability evaluation of stochastic flow networks using d-MPs. Int J Syst Assur Eng Manag 14, 1228–1246 (2023). https://doi.org/10.1007/s13198-023-01927-y

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