Forghani-elahabad, M.; Alsalami, O.M. Using a Node–Child Matrix to Address the Quickest Path Problem in Multistate Flow Networks under Transmission Cost Constraints. Mathematics2023, 11, 4889.
Forghani-elahabad, M.; Alsalami, O.M. Using a Node–Child Matrix to Address the Quickest Path Problem in Multistate Flow Networks under Transmission Cost Constraints. Mathematics 2023, 11, 4889.
Forghani-elahabad, M.; Alsalami, O.M. Using a Node–Child Matrix to Address the Quickest Path Problem in Multistate Flow Networks under Transmission Cost Constraints. Mathematics2023, 11, 4889.
Forghani-elahabad, M.; Alsalami, O.M. Using a Node–Child Matrix to Address the Quickest Path Problem in Multistate Flow Networks under Transmission Cost Constraints. Mathematics 2023, 11, 4889.
Abstract
The quickest path problem in the multistate flow networks, also known as the quickest path reliability problem (QPRP), aims at calculating the probability of transmitting a minimum of d units of flow/dat/commodity from a source node to a destination node through one single path within T units of time. Several exact and approximation algorithms have been proposed in the literature to address this problem. Most of the exact algorithms in the literature need prior knowledge of all the network’s minimal paths (MPs), which is considered a weak point. In addition to the time, the budget is always limited in real-world systems, making it an essential consideration in the analysis of systems’ performance. Hence, this study considers the QPRP under the cost constraints and provides an efficient approach based on the node-child matrix to address the problem without knowing the MPs. We show the correctness of the algorithm, compute its complexity results, illustrate it through a benchmark example, and conduct extensive experimental results on the known benchmarks and one thousand randomly generated test problems to demonstrate its practical superiority compared to the existing algorithms in the literature.
Computer Science and Mathematics, Discrete Mathematics and Combinatorics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
