Stochastic-flow Network Research Articles

Network reliability of a stochastic flow network by wrapping linear programming models into a Monte-Carlo simulation

A stochastic flow network (SFN) serves as a fundamental framework for real-life network-structured systems and various applications. Network reliability NRd is defined as the probability that an SFN can successfully send at least d units of demand from a source to a terminal. Current analytical algorithms for the network reliability evaluation are classified into an NP-hard problem. This limitation hinders the ability of decision-makers to monitor and manage decisions for an SFN flexibly and immediately. Therefore, this paper develops an algorithm to estimate network reliability by wrapping developed linear programming (LP) models based on minimal paths (MPs) into a Monte-Carlo simulation. The developed LP models present satisfaction of the demand d in the SFN in terms of minimal paths. The effectiveness and efficiency of the proposed algorithm are verified using a series of numerical investigations. Contributions are manifold: (1) an integrated model with the simulation and LP models is provided to estimate network reliability in terms of the MPs, thereby filling a crucial gap in existing research; (2) the scalability and efficiency of the proposed method are shown for the complex SFNs; (3) decision-making capabilities can be provided under real-time reliability predictions.

Reliability Assessment for a Stochastic Air Transport Network with Multiple Demands

Air transport networks play a significant role in the modern tourism industry, and their operational performance and stability can be measured by reliability analysis. This study, from the perspective of a travel agency, attempts to assess the reliability of a stochastic air transport network (SATN) by considering multiple passenger demands generated by both the starting airport and several connection airports. The SATN is modeled as a stochastic flow network comprised of several nodes and arcs where nodes represent airports, and arcs represent flights connecting two airports. Each flight is associated with a predetermined stochastic capacity following a specific probability distribution, departure time, arrival time, and discount fare. Accordingly, network reliability refers to the probability that the network can successfully transport passengers from their respective source airports to the destination airport within the given travel time and travel cost limit. An algorithm in terms of the concept of lower boundary point is developed to compute network reliability. Furthermore, a simple example and a case study are presented to demonstrate the proposed reliability method and the managerial implications of reliability for travel agencies.

Research on Reliability Prediction Methods for Dynamic Networks Based On Deep Neural Networks

In reality many networks, such as information storage networks, can be modelled as a multi-state stochastic flow network. The reliability of an information storage network is the probability that the network is able to deliver the required amount of information data to the specified server, and its an important metric to assess the performance of an information storage network. Most existing multi-state network reliability assessment algorithms are calculated using very small capacity vectors. However, calculating the reliability of such a network requires reuse of algorithms and is inefficient when the network size, demand, etc., changes rapidly, resulting in managers not making timely decisions accordingly. In order to obtain reliability metrics quickly, this paper proposes a dynamic network reliability prediction model based on deep neural networks (DNNs), which allows the corresponding reliability to be obtained quickly even when the network is changing rapidly. Finally, a local information storage network is used as an example for validation to illustrate the feasibility of the prediction model.

An algorithm to generate all d-lower boundary points for a stochastic flow network using dynamic flow constraints

Several practical systems, including manufacturing and computer networks, can be modeled as stochastic flow networks (SFNs). In order to learn the performance of the SFNs, network reliability is defined as the probability that a demand d can successfully be transmitted through an SFN. Nevertheless, calculating network reliability belongs to an NP-hard problem. For further probability evaluation (network reliability), existing algorithms based on minimal paths (MPs) are developed to systematically obtain all lower boundary points for d termed d-LBPs. When facing more complex SFNs, our perpetual motivation lies in enhancing the efficiency of generating all d-LBPs. Based on the dominant property of capacity constraints over flow constraints, this study develops a series of techniques to dynamically adjust the flow constraints to generate available (remaining) capacity state vectors. All the generated solutions would directly satisfy the capacity constraints, ignoring the flow constraints. Besides, the exact d-LBPs are calculated using element-wise addition and cycle check constraints. An algorithm is collected with an illustrative example. Furthermore, numerical experiments, including a practical network, are conducted to show at least two times faster for the d-LBP generation using the proposed algorithm compared with the newest algorithm.

A network reliability algorithm for a stochastic flow network with non-conservation flow

A network reliability algorithm for a stochastic flow network with non-conservation flow

Robust Design Problem for Multi-Source Multi-Sink Flow Networks Based on Genetic Algorithm Approach

Robust design problems in flow networks involve determining the optimal capacity assignments that enable the network to operate effectively even in the case of events’ occurrence such as arcs or nodes’ failures. Multi-source multi-sink flow networks (MMSFNs) are frequent in many real-life systems such as computer and telecommunication, logistics and supply-chain, and urban traffic. Although numerous studies on the design of MMSFNs have been conducted, the robust design problem for multi-source multi-sink stochastic-flow networks (MMSFNs) remains unexplored. To contribute to this field, this study addresses the robust design problem for MMSFNs using an approach of two steps. First, the problem is mathematically formulated as an optimization problem and second, a sub-optimal solution is proposed based on a genetic algorithm (GA) involving two components. The first component, an outer genetic algorithm, is employed to search the optimal capacity assigned to the network components with minimum sum. The second component, an inner genetic algorithm, is used to find the optimal flow vectors that maximize the system’s reliability. Through extensive experimentation on three different networks with different topologies, the proposed solution has been found to be efficient.

Framework for evaluating reliability of stochastic flow networks under different constraints

Framework for evaluating reliability of stochastic flow networks under different constraints

Usage of task and data parallelism for finding the lower boundary vectors in a stochastic-flow network

In a stochastic-flow network, a minimal system state vector under which the maximum flow of the network from a source node to a destination node is equal to d is called a lower boundary vector (LBV). As the number of LBVs increases exponentially with the size of the network, the available algorithms in the literature could be improved to be more practical for real-world large-sized systems. We employ task and data parallelism to propose an efficient algorithm for determining all the LBVs to tackle this problem. We present an efficient approach for removing duplicate solutions to improve an available algorithm to find all the LBVs. We show the correctness and compute the complexity results of the proposed approach and demonstrate its efficiency. Then, we propose vectorized, parallelized, and vectorized–parallelized versions of the main algorithm. We illustrate the standard version through a benchmark example and discuss the other proposed versions’ correctness. We conduct several experimental results on two known benchmark networks and more than one thousand random problems to demonstrate the practical efficiency of the vectorized–parallelized version. Moreover, Dolan and Moré’s performance profile is used to provide a more intuitive comparison between all four versions.

An efficient sum of disjoint product method for reliability evaluation of stochastic flow networks using d-MPs

An efficient sum of disjoint product method for reliability evaluation of stochastic flow networks using d-MPs

Reliability Estimation for Stochastic Flow Networks With Dependent Arcs

The creation and the destruction processes (CPs and DPs) are the basis of many efficient Monte Carlo methods for estimating the unreliability of highly reliable networks on both, the static and the stochastic flow network models, for the case of independent components. Some of these methods are based on the splitting variance reduction techniques. Due to the splitting basic mechanism, they operate over CP. Here, we propose a splitting-based Monte Carlo method, using the Marshall–Olkin copula for the case of nonindependent components. This proposal operates on the DP, because the Marshall–Olkin copula model over networks is quite related—and somehow similar—to DP, which is unusual but here necessary. Before addressing the proposal, the article presents a review of the methods based on CP and DP. At the end, a comparative experimental analysis shows the efficiency of the proposed approach.

Hybrid flow-shop manufacturing network reliability optimization using genetic algorithm and absorbing Markov chain

In this study, we adopt a strategy of machine configuration to construct a reliable hybrid flow-shop manufacturing system (HFSMS) with reworking and scrapping actions, in which the reworking and scrapping actions are due to the yield rates of the configured machines. The machine configuration determines the machine suppliers and the number of machines for each production stage in the HFSMS, which may affect the stability of the HFSMS. The machines configured to a production stage in parallel are provided by the same supplier. Accordingly, each production stage has multiple states, following a probability distribution. The HFSMS is a typical stochastic-flow network under machine configuration, and network reliability indicates the probability that order demand d can be fulfilled by the HFSMS and used as a decision reference. Our study integrates genetic algorithm (GA) and absorbing Markov chain (AMC) to solve the reliability-oriented machine configuration problem of HFSMS subject to a configuration budget, where the GA is utilized to find the optimal machine configuration with maximum network reliability and the AMC model constructed based on the yield rates is used for network reliability evaluation. For validating the applicability and computational efficiency of the proposed AMC and GA-based approach, a simple manufacturing system and two practical manufacturing systems are used to compare the proposed approach with four popular meta-heuristic algorithms. The experimental results show that the proposed approach can find the exact optimal solution and has better computational efficiency than the other four meta-heuristic algorithms.

An Improved Vectorization Algorithm to Solve the d-MP Problem

The d-minimal path (d-MP) problem is to find all the system state vectors (SSV) under which d units of data can be transmitted from a source node to a destination node in a stochastic-flow network (SFN). This problem has been very attractive in the last decades as one can compute the exact amount of the network’s reliability through the d-MPs. Although several algorithms have been proposed in the literature to address the problem, the research continues because it is NP-hard. Since the number of d-MPs grows exponentially with the size of the network, the available algorithms in the literature are not so practical. Hence, we employ the vectorization techniques for proposing an improved algorithm to address the problem. We conduct many experimental results on the known benchmarks and two hundred randomly generated SFNs in the sense of performance profile introduced by Dolan and Moré. The experimental results show the vectorization algorithm to be considerably more efficient than the non-vectorization ones.

Functional healthy state evaluation approach for manufacturing systems considering imperfect inspection based on extended stochastic flow network

The core function of a manufacturing system is to consistently and efficiently output a specified number of qualified products that can meet production demands. However, the imperfect inspection can sometimes bring disturbances to the work-in-process (WIP) quality and the processing machine degradation in the function realization process, and this aspect has not been paid due attention in existing research on manufacturing system health evaluation researches. Therefore, a functional healthy state evaluation approach for manufacturing systems considering imperfect inspection based on extended stochastic flow network (ESFN) is proposed in this paper. First, a function realization-oriented operational mechanism is expounded from the systematic perspective. On this basis, the connotation of the functional healthy state of the manufacturing system considering imperfect inspection is further defined. Second, an ESFN model is established to describe the relationship among processing machines, WIPs, and inspection machines in a running manufacturing system. Third, a functional healthy state evaluation approach for a manufacturing systems considering imperfect inspection is proposed. Finally, the effectiveness of the approach is verified by an illustrative example.

Mission reliability–centered maintenance approach based on quality stochastic flow network for multistate manufacturing systems

Previous studies of reliability centered maintenance (RCM) rarely consider the maintenance quality for the operation condition monitoring of manufacturing system. Therefore, a quality-oriented maintenance approach for the multistate manufacturing system with the aid of mission reliability is proposed. First, connotations of the mission reliability and maintenance quality of the multistate manufacturing system are expounded on the basis of the operational mechanism. Second, a quality stochastic flow network (QSFN) model of the multistate manufacturing system is established, and a novel mission reliability model is presented. Third, a quality-oriented mission reliability–centered maintenance framework for multistate manufacturing systems is proposed, and the optimal integrated maintenance strategy is obtained by minimizing the total cost. Finally, an industrial example of subway flow receiver is presented to verify the proposed method. Results show that the proposed method can simultaneously balance the maintenance cost and maintenance quality of the multistate manufacturing system.

Graph-Informed Neural Networks for Regressions on Graph-Structured Data

In this work, we extend the formulation of the spatial-based graph convolutional networks with a new architecture, called the graph-informed neural network (GINN). This new architecture is specifically designed for regression tasks on graph-structured data that are not suitable for the well-known graph neural networks, such as the regression of functions with the domain and codomain defined on two sets of values for the vertices of a graph. In particular, we formulate a new graph-informed (GI) layer that exploits the adjacent matrix of a given graph to define the unit connections in the neural network architecture, describing a new convolution operation for inputs associated with the vertices of the graph. We study the new GINN models with respect to two maximum-flow test problems of stochastic flow networks. GINNs show very good regression abilities and interesting potentialities. Moreover, we conclude by describing a real-world application of the GINNs to a flux regression problem in underground networks of fractures.

Maintainable stochastic communication network reliability within tolerable packet error rate

The communication networks are complex and considered a stochastic flow network. This throws enormous challenges for the service provider to provide a desired Quality of Service (QoS) to the customer. Due to the stochastic behavior of the network, ensuring QoS requires serious efforts to make the entire system work within the given time constraint, cost, and failure rate. When the communication problem is time-bound, providing a quick and reasonable solution with a permissible error rate is of great importance. Therefore, in this paper, fast solutions to data communication problems are proposed to send the required d units of user’s data from the desired source node to the destination node within some constraints such as permissible error rate ε, time constraint T and maintenance budget constraints B. System reliability and the performance of the proposed approaches are evaluated using minimal paths. All the minimal flow vectors evaluated from minimal paths that satisfy all the above-mentioned constraints are considered for network reliability evaluation. Further, the proposed approaches are observed as faster concerning computation time than the existing approaches.

Reliability Modeling and Maintenance Optimization of Manufacturing System Based on Stochastic Flow Network and Markov Process

Reliability Modeling and Maintenance Optimization of Manufacturing System Based on Stochastic Flow Network and Markov Process

System reliability evaluation using budget constrained real [formula omitted]-MC search

In the network flow problems, it is the most challenging task to maintain the system reliability and high quality of service (QoS). Most of these networks are stochastic and ensuring optimal data flow under some constraints especially, budget and time, is a very challenging task. If the user’s data can be transferred within the budget then the network is called budget constrained stochastic flow network (SFN). The system reliability can be checked through minimal paths and minimal cuts in the network. In this paper, it is aimed to evaluate the system reliability of the budget constrained SFN with the help of minimal cuts in the network. The problem is to find out all the minimal cuts, such that d units of data can be communicated within a specified budget B. All the minimal cuts that satisfy budget constraint are employed for system reliability evaluation. From the results, it can be said that the proposed approach is much faster than the earlier approaches without any compromise in the network reliability.

System Reliability Optimization of Multi-Source Multi-Sink Stochastic Flow Networks With Budget Constraint

In this paper, we investigate system reliability optimization of multi-source multi-sink flow networks subject to transmission budget constraints. More specifically, we present a mathematical model of the optimization problem and a genetic algorithm (GA) to solve it. The GA is based on determining the optimal set of lower boundary points that maximize system reliability such that transmission cost does not exceed a specified upper bound. Finally, to ensure the efficiency of our approach, we apply our proposed algorithm to various network examples.

Reliability of spare routing via intersectional minimal paths within budget and time constraints by simulation

A stochastic flow network composed of multistate arcs can be utilized to describe several practical systems such as computer networks, where transmission time taken for sending data to a sink is an important index. Determining a path with minimum transmission time is known as the quickest path problem (QPP). All algorithms addressing the QPP assume that the determined minimal paths (MPs) are disjoint. Further, for the general case of intersectional MPs, if a congestion phenomenon occurs during the transmission process, these algorithms will lead to an incorrect outcome. Moreover, in practical scenarios, as a budget limit is considered, spare routing is applied to consolidate the system. The objective is to develop an algorithm based on Monte Carlo simulations (MCSs) for evaluating the system reliability while considering the congestion phenomenon. The system reliability is the probability that a specific amount of data can be transmitted successfully through multiple MPs under both time and budget constraints. Furthermore, spare routing to increase the system reliability is established in advance to specify the main and spare MPs. Experiments validate the evaluation of system reliability based on MCSs. The credibility and efficiency of the proposed algorithm are also discussed.