Majid Forghani-elahabad

A New Efficient Approach to Search for All Multi-State Minimal Cuts

There are several exact or approximating approaches that apply 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 system reliability of a sample network is computed by the inclusion-exclusion method. Finally, to illustrate the efficacy of using the new presented techniques, computational results on random test problems are provided in the sense of the performance profile introduced by Dolan and Moré.

An improved algorithm for RWA problem on sparse multifiber wavelength routed optical networks

Abstract Hitherto, several algorithms have been proposed for routing and wavelength assignment (RWA) problem on single or multifiber wavelength routed optical network (WRON) with or without wavelength converters. However, due to budget limit, we may equip only a few links in the network with multi fibers, and hence we have a sparse multifiber WRON (SM-WRON). Here, we consider the RWA problem on an SM-WRON without wavelength conversion. Different number of links are considered to equip with multi fibers to make an SM-WRON. Two basic techniques to select the required links to make them multifiber are random-choice and first-choice. The earlier one selects some links randomly and the later one selects the first numbered links. Here, in order to propose an improved algorithm, we define a cost for every link in the network, and then equip the most expensive links with multi fibers. The numerical results made on the well known benchmark networks, i.e., ARPANET and NSF topologies, show the proposed technique to be more efficient than the basic ones taking the blocking probability into account.

A New Algorithm for Generating All Minimal Vectors for the

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 Diophantine system is needed to be solved, for which we provide a particularly efficient procedure with linear time complexity in terms of the number of its solutions. The complexity results are derived to demonstrate the efficiency of our proposed algorithm in comparison with others. To illustrate the practical efficiency of the algorithm, a network example is considered to compare our algorithm with a recently proposed one. Moreover, a comparative computational experiment is conducted on an extensive collection of random test problems using the performance profile of Dolan and Moré.

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System reliability of a stochastic-flow network (SFN) can be computed in terms of either upper boundary points for demand level d called d-minimal cuts (d-MCs) or lower boundary points for demand level d called d-minimal paths (d-MP s). A number of different algorithms have been proposed in the literature to search for and determine all the d-MCs or d-MP s in an SFN. Majority of those algorithms need to solve a special Diophantine system. Here, we consider the Diophantine system appeared in d-MC and d-MP problems and propose a novel efficient algorithm to solve it. The proposed algorithm finds all the system solutions in a increasing lexicographic order. We illustrate the algorithm through an example and show its time complexity to be linear according to the number of its solutions.

SMPs Reliability Problem With Time and Budget Constraints

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 number of random test problems and implementing the algorithms in MATLAB, the proposed algorithm is demonstrated to be more efficient than some existing ones in medium-sized networks. The performance profile introduced by Dolan and More is used for analyzing the output of programs.