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.

For stochastic flow network (SFN), given all the lower (or upper) boundary points, the classic problem is to calculate the probability that the capacity vectors are greater than or equal to the lower boundary points (less than or equal to the upper boundary points). However, in some practical cases, SFN reliability would be evaluated between the lower and upper boundary points at the same time. The evaluation of SFN reliability with upper and lower boundary points at the same time is the focus of this paper. Because of intricate relationships among upper and lower boundary points, a decomposition approach is developed to obtain several simplified subsets. SFN reliability is calculated according to these subsets by means of the inclusion-exclusion principle. Two heuristic options are then established in order to calculate SFN reliability in an efficient direction based on the lower and upper boundary points.

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.