Data for the article "A New Ecient Algorithm Addressing the Problem of Reliability Evaluation of Multistate Flow Networks with Budget Constraint in Terms of Minimal Cuts"

Citation Author(s):
Paul
Kozyra
Submitted by:
Paul Kozyra
Last updated:
Tue, 11/09/2021 - 16:42
DOI:
10.21227/8fmh-3d09
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0
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Abstract 

Many real-world systems can be modeled by multistate flow networks (MFNs) and their reliability evaluation features in designing and control of these systems. Considering the cost constraint makes the problem of reliability evaluation of an MFN more realistic. For a given demand value d and a given cost limit c, the reliability of an MFN at level (d, c) is the probability of transmitting at least d units from the source node to the sink node through the network within the cost of c. This article addresses the so-called (d, c)-MC problem, i.e., the problem of reliability evaluation of an MFN with cost constraint in terms of minimal cuts. It presents new results on which a new algorithm is based. This algorithm finds all (d, c)-MC candidates without duplicates and verifies them more efficiently than existing ones. The complexity results for this algorithm and an example of its use are provided. Finally, numerical experiments with R language implementations of the presented algorithm and other competitive algorithms are considered. Both, the time complexity analysis and numerical experiments demonstrate the presented algorithm to be more efficient than other existing ones in the majority of cases.

Instructions: 

The data set contains three folders: 'MCs lists', 'd_c_MCs lists', 'd_c_MCs lists2', and an additional file arr_tib.csv.

The folder 'MCs lists' contains 7 files in the csv format. Each of these files contains the list of all minimal cuts for an appropriate multistate flow network (MFN) from figures 2-4. The arcs in networks 1,2,3,5,6,7 are ordered firstly according to the order of their beginning nodes and secondly on the order of their ending nodes. Only in the network Id 4 from Fig. 3 the order of the arcs is another, and this order is visible in Fig. 3.

The folder 'd_c_MCs lists' contains 126 files and the folder 'd_c_MCs lists2' contains 315 files in the csv format. Each of these files has the name of the form i_j_(d,c)-MCs, where i denotes the MFN ID, j - the number of the variant of the greatest state vector, d - demand level, and c- cost constraint. Each of these files contains all (d,c)-MCs determined for given MFN ID - i, and the greatest state vector of the number of the variant - j.

The file 'arr_tib.csv' contains experimental results of numerical experiments conducted on a computer with Intel(R) Core(TM) i7-8750H CPU and 16 GB of RAM. This file is a result of the file 'Params_all.csv' containing the raw data from the numerical experiments, where computational times are expressed in nanoseconds.

Column 1 contains the consecutive numbers of cases;Column 2 'i' - MFN ID; Column 3 'j' - the number of the variant of the greatest state vector;Column 4 'm' - the number of edges in a given MFN;Column 5 'p' - the number of all MCS of this MFN;Column 6 'W' - coordinates of the greatest SSV W;Column 7 'd' - given level d of multistate minimal cuts; Column 8 'c' - the total budget c;Column 9 'q1/p' - the ratio of the number of elements of set Q_1 defined by (19) in Lemma 8 in the related article to p;Column 10 'q2/p' - the ratio of the number of elements of set Q_2 defined by (20) in Lemma 8 in the related article to p; Column 11 '#(d,c)-MCs' - the number of all (d,c)-MCs; Column 12 'T_F_K' - expressed in seconds the mean computational time T_{FK} of the algorithm described in the article M. Forghani-elahabad, N. Kagan, Assessing Reliability of Multistate Flow Networks Under Cost Constraint in Terms of Minimal Cuts Int. J. Reliab. Qual. Saf. Eng.2019,26, 1950025; Column 13 'T_K' - expressed in seconds the mean computational time of the main algorithm from the presented algorithm;Column 14 'R" - the ratio T_F_K/T_K;Column 15 'T_aux' - expressed in seconds the mean computational time of the introductory algorithm from the presented algorithm;Column 16 'T_K_t' - expressed in seconds the total mean computational time of the presented algorithm;Column 17 'R_p' - the ratio T_F_K/T_K_t

Computational times in columns 12, 13, 15, and 16 in file 'arr_tib.csv' are expressed in seconds and are results of the use of the microbenchmark procedure from the microbenchmark library implemented in R.

 

There are 4 scripts in R. Script 'Init_params.r.r' enables us to load the list of MCs from the folder 'MCs lists' and initialize other parameters used in numerical experiments. Sometimes to establish some parameters it is necessary to compile some procedures from the script 'kozyra_d_c_MCs.r' which contains R implementations of presented algorithms. The script 'Forghani.r' contains R implementation of the algorithm described in Forghani-elahabad, M. and N. Kagan (2019a). Assessing reliability of multistate flow networks under cost constraint in terms of minimal cuts. Int. J. Reliab. Qual. Saf. Eng. 26 (5), 1-18. The script 'tests.r' contains code that enables us to execute numerical experiments described in the last section of the article to compare the time complexity of the presented algorithm and the algorithm described in Forghani-elahabad, M. and N. Kagan (2019a). Assessing reliability of multistate flow networks under cost constraint in terms of minimal cuts. Int. J. Reliab. Qual. Saf. Eng. 26 (5), 1-18.