Sharif Digital Repository

In recent decades, multistate two-terminal reliability problem has attracted several researchers, and accordingly many exact and approximation approaches have been proposed in the literature in terms of minimal cuts (MCs) or minimal paths (MPs) to address this problem. Here, an MP-based approximation approach is developed based on exact algorithms. With all the MPs at hand, the approach rearranges the MPs ascendingly with respect to their lengths and then sets the flow on some MPs to be zero which turns to reduce the computing cost in solving the problem. We provide the complexity results, and by employing some benchmarks and one thousand randomly generated networks illustrate that not only... 

There are several exact or approximating approaches that apply {m d}-MinCuts (d-MCs) to compute multistate two-Terminal reliability. Searching for and determining d-MCs in a stochastic-flow network are important for computing system reliability. Here, by investigating the existing methods and using our new results, an efficient algorithm is proposed to find all the d-MCs. The complexity of the new algorithm illustrates its efficiency in comparison with other existing algorithms. Two examples are worked out to show how the algorithm determines all the d -MCs in a network flow with unreliable nodes, and in a network flow of moderate size. Moreover, using the d-MCs found by the algorithm, the... 

An information system network (ISN) can be modeled as a stochastic-flow network (SFN). There are several algorithms to evaluate reliability of an SFN in terms of Minimal Cuts (MCs). The existing algorithms commonly first find all the upper boundary points (called d-MCs) in an SFN, and then determine the reliability of the network using some approaches such as inclusion-exclusion method, sum of disjoint products, etc. However, most of the algorithms have been compared via complexity results or through one or two benchmark networks. Thus, comparing those algorithms through random test problems can be desired. Here, the authors first state a simple improved algorithm. Then, by generating a... 

The d-MinCut (d-MC) problem has been extensively studied in the past decades and various algorithms have been proposed. The existing algorithms often consist of two general stages, finding all the d-MC candidates and testing each candidate for being a d-MC. To find all the d-MC candidates, a system of equations and inequalities should be solved. Here, we propose a novel efficient algorithm to solve the system. Then, using our new results, an improved algorithm is proposed for the d-MC problem. Computing its complexity, we show the proposed algorithm to be more efficient than the other existing algorithms with respect to the number of minimal cuts. A medium-size network example is worked... 

The quickest path reliability problem evaluates the probability of transmitting some given units of flow from a source node to a sink node through a single minimal path in a stochastic-flow network within some specified units of time. This problem has been recently extended to the case of transmitting flow through q separate minimal paths (SMPs) simultaneously within a budget constraint. Here, we propose a new algorithm to solve such problems. The algorithm finds all the minimal vectors for which a given demand level d units of flow can be transmitted through q SMPs from a source node to a sink node satisfying some given time and budget limits. In our proposed algorithm, a special...