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Evaluating Reliability of a Stochastic-flow Network in Terms of All Upper and Lower Boundary Points

Forghani Elahabad, Majid | 2014

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 45759 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Mahdavi Amiri, Nezam
  7. Abstract:
  8. In recent years, stochastic-flow networks (SFNs) have been extensively applied to many problems such as distribution, power transmission, and telecommunication. In quality management and decision making, an important task is to design some performance indices in order to measure the performance of an SFN. The system reliability and unreliability are such two common performance indices.Hitherto, several research works have been conducted for evaluating these two performance indices.One approach for evaluating the reliability of SFNs is determining all the upper or lower boundary points (respectively, UBPs or LBPs).Here, we study four problems to determine: (1) all the UBPs in a two-terminal mono-commodity SFN, (2) UBPs in an SFN with budget constraint, (3) UBPs in a multi-commodity SFN, and (4) LBPs in a two-terminal mono-commodity SFN. However, our main problem is problem (1), since problems (2) and (3) are some extensions of problem (1) to SFNs with budget constraint and multi-commodity SFNs respectively. Also, problem (4) has been investigated less than problem (1). We present some new algorithms for all the problems. The given algorithms for problems (1), (2), and (3) are in terms of minimal cuts, and the given algorithms for problem (4) are in terms of minimal paths. We first show some existing results and an existing algorithm for problem (1) to be incorrect. We give some correct versions of the incorrect results and improve some results. Modifying and improving an incorrect algorithm, an improved algorithm is proposed. Then, obtaining some new results and proposing a new data structure, a new algorithm is developed. Computing the time complexities of the algorithms, we demonstrate the efficiency of our algorithm as compared to the others. Next, we study problem (2) and present some new results related to the budget constraint. We then employ some useful results obtained for problem (1), to propose an improved algorithm for problem (2). The complexity results also show the efficiency of our proposed algorithm as compared to the other existing algorithms. Extending the results to a multi-commodity SFN, an extended algorithm is proposed to solve problem (3).Finally, we propose an algorithm for problem (4). For practical comparison of the algorithms, we generate a number of random test problems using Matlab software environment. For this aim, stating and using a simple algorithm, we generate the networks whose arcs and their capacities are randomly determined. Since the proposed algorithms for problems (2) and (3) are the extensions of the proposed ones for problem (1), we only implement the algorithms for problem (1). Then, we compare the performance results with respect to the running times on solving the random generated problems.For a more comprehensive comparison, we use the performance profile scheme introduced by Dolan and More′. The Dolan-More′ diagrams clearly show the efficiency of our algorithms in comparison with other existing algorithms
  9. Keywords:
  10. Reliability ; Minimum Cut ; Upper Bound Method ; Lower Bound ; Minimal Paths

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