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A cloud–fog computing system is modeled as a network topology where each edge represents a transmission line, and each node represents a hub, an Internet of Things (IoT) device, a fog server, or a cloud server. Such a system with several capacities at each edge is called a stochastic-flow cloud–fog computing network (SCCN). There are three phases of transmitting data: the first is to transmit data from the IoT devices to the fog servers. The second and third phases are transmitting a part of the data from the fog servers to the cloud servers for the further operations and back to the IoT devices for the immediate operations, respectively. Based on the transmission mechanisms, two demands, including initial demands and processed demands, should be satisfied simultaneously, where an initial demand (a processed demand) is outing from an IoT device (a fog server). An algorithm is developed to evaluate reliability, the probability of successfully transmitting the data through the SCCN, by elucidating the flow relationship among the IoT devices, edge servers, and cloud servers. Furthermore, another approach to adjust the flow assignment is also proposed for the case that demand may not be an integer. A large real case is provided to validate the applicability and scalability of the proposed methodology. [ABSTRACT FROM AUTHOR]

Many real-world problems, such as power line transmission planning, computer network management, water pipe planning, and traffic flow planning, can be modeled using multistate network systems. One of the most interesting aspects of these problems is that one typically wishes to know the reliability of such a plan, namely the network reliability. To evaluate the reliability of a specific network system, the three-stage method (TSM) is typically applied. TSM consists of 1) finding all minimal paths, 2) finding all $d$ -system vectors, and 3) calculating the union probability for reliability, where 1) is one of the most challenging problems discussed in the literature. This article proposes an improved merge search method that combines the advantages of both enumeration and searching technologies. A step-by-step exploration of the proposed method is presented and several benchmark comparisons are performed using well-known algorithms to demonstrate the efficiency of the proposed method. The results show that the computation time of the proposed algorithm can save as much as 10 times against the well-known methods in the literature. [ABSTRACT FROM AUTHOR]

As transport is a vital component in the modern tourism industry, determining reliable-performance tourism transport networks is critical for tour operators and travel agencies. The performance of a tourism transport network in this study is investigated by evaluating system reliability, which is the probability of successfully transporting requested passengers between multiple origins and multiple destinations within a time constraint when tardiness may occur. A stochastic multiple-origin-destination tourism transport network with tardiness (SMTNT) is formulated for system reliability evaluation. Identify all minimal travel paths (MTP) and corresponding maximum tardiness vectors that successfully connect each origin–destination pair under a time constraint. System reliability is derived from all flow vectors enabling delivery via MTPs a requested number of passengers at different tardiness levels. The proposed algorithm is successful in handling a combination of time constraints in the case of tardiness with multiple origin–destination pairs. Furthermore, it helps travel agencies obtain an insight into the performance of their SMTNT. An example describing the working of the proposed algorithm with an analysis of system reliability is provided. The results of the study can be used for improving the algorithm in the future. [ABSTRACT FROM AUTHOR]

A reliability evaluation method is proposed for production systems by applying the capacitated-flow production network (CFPN) model. In particular, this article considers in-line stockers to monitor and to avoid blockage and starvation in the CFPN. First, the minimal capacity that all cells (group of machines) should provide to meet demand is generated. Second, status of stocker is monitored via the proposed “stocker volume check table” to calculate the volume usage of a stocker, and the stocker nonutilization is then obtained. Finally, the system reliability is derived in terms of the minimal capacity vector and stocker nonutilization. An important contribution of this article is to avoid complicated dependency calculation when multiple stockers are considered. A practical case of printed circuit board production is further studied to illustrate the applicability of the proposed method. [ABSTRACT FROM AUTHOR]

Network reliability evaluation for a stochastic flow network (SFN) can be computed in terms of all lower boundary points (LBPs). Although several algorithms have been presented in the literature as solutions for the LBP problem, the efficiency is always occurring at the present for the large SFN. In this paper, a binding technique generating binding-flow vectors is therefore developed to narrow down the searching range of flows for demand. This technique is able to reduce the loading of the candidate comparison procedure greatly. An algorithm based on this binding technique is proposed to solve the LBP problem. We compare the performance of the proposed algorithm to well-known algorithms in terms of CPU time, through three benchmark networks and a practical case. The experimental results show the functional efficiency of our proposed binding LBP algorithm. [ABSTRACT FROM AUTHOR]

A fast retransmit, which reduces the sender’s waiting time before retransmitting a lost segment, is applied to guarantee data integrity with no data loss in transmission. Based on fast retransmit, many application protocols have been enhanced and evolved to ensure quality of service and reduce data transmission time. One of application protocols is the multipath transmission control protocol which is catholically applied in modern computer networks. Communication lines used in this kind of network have different states, namely, failure, partial failure, and maintenance. Therefore, a computer network with a fast retransmit can be classified as stochastic and is called a stochastic-flow computer network with a fast retransmit (SCNFR). This paper assesses the system reliability of SCNFR for the successful transmission of demand d through ${k}$ (${k} \,\, >1$) separate minimal paths (${k}$ SMiP) under the latency. An algorithm is proposed to find all minimal capacity vectors (MCVs) that satisfy the demand and latency. Then, the system reliability is computed based on all MCVs. We adopt two practical cases of the pan-European research and education network and the Taiwan academic network to explore the effectiveness of the algorithm. The results show that the system reliability can be classified as decision reference while the manager decides the better ${k}$ SMiP with higher system reliability. [ABSTRACT FROM AUTHOR]

Completion time and cost in a project are affected by uncertainties, such as weather, human resources availability, equipment efficiency, etc. The activity durations of the project, thus, should be regarded as stochastic. Such a project is usually modeled as a stochastic project network (SPN). The SPN can be represented in the form of an activity-on-arc diagram, in which each activity has several possible durations and different costs. Every activity duration possesses a corresponding cost and probability. Based on the concept of minimal paths, two algorithms are utilized to find the upper and lower duration vectors under both time and budget constraints. For an SPN, the project reliability is defined as the probability that the project can be completed under both time and budget thresholds. Theoretically, it is difficult to compute project reliability using the upper and lower duration vectors directly because of the domination property among the duration vectors. Therefore, this paper proposes the derivation of project reliability interval depending on the relationships among the upper and lower duration vectors. The exact project reliability is proved to be contained within the interval. Two examples, including a practical case of disaster recovery system construction, are presented to demonstrate the scalability and practicability of the proposed solution procedure. [ABSTRACT FROM PUBLISHER]

For a hybrid flow shop (HFS), due to the maintenance, partial failure, and possibility of failure, the number of machines at a workstation presents multiple levels, meaning that capacity of each workstation is stochastic. This study considers the stochastic capacity of each workstation and proposes a performance index based on system reliability to measure the probability that the HFS can complete demand d within time constraint T. The HFS is modeled as a stochastic-flow network, in which each arc is regarded as a workstation with stochastic capacity and each node as a buffer. An algorithm is then developed to find the lower capacity vectors that satisfy (d, T) and system reliability is evaluated. In addition, a practical example of an IC card manufacturing system is utilized to illustrate the proposed algorithm and show that such an index can provide enough information for managers to make decisions. [ABSTRACT FROM AUTHOR]

Production network performance and reliability are essential to satisfy customer orders in a timely manner. This paper proposes a statistical method for a production system to satisfy customer demand with a desired level of confidence, referred to as yield confidence, while simultaneously considering system reliability, defined as the probability that the amount of input can be processed based on the capacities of the individual workstations. The approach models a production system as a stochastic-flow production network, characterized by a discrete time Markov chain (DTMC), where one or more rework actions are possible. This model quantifies the probability that raw input is transformed into a finished product, which is subsequently used to calculate the amount of raw input needed to satisfy demand with a user-specified level of yield confidence. A pair of case studies, taken from the tile and circuit board industries, illustrates the assessment techniques as well as methods to identify workstation level enhancements that can improve network performance and reliability most significantly. Our results indicate that improving the reliability of workstations can enhance yield confidence because a lower volume of raw input can produce the desired volume of output, thereby minimizing the load placed on the production network. [ABSTRACT FROM PUBLISHER]

This paper presents a novel technique to measure the performance of a stochastic-flow manufacturing network (SMN) which violates the so-called flow conservation law due to the failure rates of stations. We address the mission reliability, the probability of demand satisfaction, as a performance indicator for the SMN while considering both the stochastic capacities and the multiple production lines. First, we construct a manufacturing system as an SMN through a graphical transformation, and decompose the transformed SMN into several paths for further analysis. Subsequently, two algorithms for different scenarios are designed to generate all minimal capacity vectors that stations should provide to satisfy the given demand. The first scenario is for the SMN with identical production lines in parallel. The second scenario is for distinct production lines with common stations in the SMN. We derive the mission reliability in terms of minimal capacity vectors by applying the recursive sum of disjoint products (RSDP) algorithm. A decision making issue is also discussed to decide a reliable production strategy. [ABSTRACT FROM PUBLISHER]

An active research field is the evaluation of the reliability of a complex network. The most popular methods for such evaluation often use Minimal Paths (MP) or Minimal Cuts (MC) of the network. Although there are many algorithms developed to search for MP or MC, most of them are inefficient for searching a large network due to the combinatorial explosion problem. Another disadvantage is that the existing algorithms are applicable to specific counts of source and sink nodes (e.g., one-to-one, one-to-many, and so on). This article proposes a novel approach to search for all MP in a general flow network. The term “general” means that the approach can be used to search for all MP with multi-sources, multi-sinks in the network. The edges can be directed, undirected, or hybrid (mixed with directed and undirected arcs). Some benchmarks from the well-known algorithms in the literature are examined and compared. Moreover, the comprehensive tests are also performed with the grid networks, as well as the well-known networks in the literature to show the efficiency of the approach. A sample code is provided in the article for quick validation. [ABSTRACT FROM AUTHOR]

This paper develops two techniques to analyse the performance of a stochastic-flow network (SFN) model, considering correlated failures. The first approach utilizes a correlated binomial distribution to characterize the failure behavior of the physical lines and routers internal to the individual edges and nodes in the network. The second employs a simulation technique, which can characterize correlated failures between every pair of physical lines and routers in the different edges and nodes comprising the network. Both approaches quantify the probability that a given amount of data can be sent from a source to a sink through this network. This probability that the network satisfies a specified level of demand is referred to as the SFN reliability. The techniques are demonstrated in the context of two case studies, including the Taiwan Academic Network, the backbone of the national computer network connecting all educational institutions in Taiwan. Experimental results demonstrate that correlation can produce a significantly negative impact on reliability, especially when there is a high level of network demand. The proposed approaches, thus, capture the influence of correlation on SFN reliability, offering methods to quantify the utility of reducing correlation. [ABSTRACT FROM PUBLISHER]

This paper proposes a performance indicator to evaluate the capability of a maintainable stochastic-flow network (MSFN). This MSFN is required to preserve a minimal service level so that it can send d units of data or commodity from the source to the sink through multiple paths within time T. The proposed system reliability performance indicator quantifies the probability that a MSFN delivers a capacity level above the minimal service level with a budget no greater than B. Two procedures are integrated in the proposed algorithm: a procedure to estimate system reliability, and an adjusting procedure that utilizes the branch-and-bound approach for exact system reliability. The estimated system reliability with lower and upper bounds, and the exact system reliability, are then computed by applying the recursive sum of disjoint products (RSDP) algorithm. [ABSTRACT FROM AUTHOR]

This paper constructs a time-based multistate network composed of multistate edges to study network reliability. Each edge involves three attributes: variable capacity, lead time, and cost. The transmission time from the source to the sink is thus not fixed. Two problems are discussed in this paper. First, we evaluate the probability that the given amount of data can be sent through p\ (p\geq 2) minimal paths simultaneously under both time threshold, and budget constraint. Such a probability we term network reliability. It can be treated as a performance index to measure the transmission ability of a complex multistate system. Then, the calculation procedures are proposed to make solution. To enhance network reliability, the network administrator decides the spare routing in advance to indicate the first and the second priority p minimal paths. The second path will be responsible for the transmission duty if the first fails. The second problem is addressed to evaluate network reliability according to the spare routing. [ABSTRACT FROM AUTHOR]