Title: On multi-state two separate minimal paths reliability problem with time and budget constraints

Authors: Majid Forghani-Elahabad; Nezam Mahdavi-Amiri; Nelson Kagan

Addresses: Department of Electrical Engineering, University of São Paulo, São Paulo, Brazil ' Faculty of Mathematical Sciences, Sharif University of Technology, Tehran, Iran ' Department of Electrical Engineering, University of São Paulo, São Paulo, Brazil

Abstract: In a stochastic-flow network, a (d, T, b, P1, P2)-MP is a system state vector for which d units of flow can be transmitted through two separate minimal paths (SMPs) P1 and P2 simultaneously from a source node to a sink node satisfying time and budget limitations T and b, respectively. Problem of determining all the (d, T, b, P1, P2)-MPs, termed as the (d, T, b, P1, P2)-MP problem, has been attractive in reliability theory. Here, some new results are established for the problem. Using these results, a new algorithm is developed to find all the (d, T, b, P1, P2)-MPs, and its correctness is established. The algorithm is compared with a recently proposed one to show the practical efficiency of the algorithm.

Keywords: stochastic quickest path reliability problem; transmission time; budget constraint; minimal paths; MPs; (d, T, b, P1, P2)-MP.

DOI: 10.1504/IJOR.2020.105764

International Journal of Operational Research, 2020 Vol.37 No.4, pp.479 - 490

Received: 04 Nov 2016
Accepted: 05 May 2017

Published online: 03 Mar 2020 *

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