The most recent and important developments in the field of computer networks are cloud and fog computing. In this study, modern cloud computer networks comprising computers, internet of things (IoT), fog servers, and cloud servers for data transmission, is investigated. A cloud computer networks can be modeled as a network with nodes and arcs, in which each arc represents a transmission line, and each node represents an IoT device, a fog server, or a cloud server. Each transmission line has several possible capacities and is regarded as a multistate. The network is termed a multi-state cloud computer network (MCCN). this study firstly constructs the mathematic model to elucidate the flow relationship among the IoT devices, edge servers, and cloud servers and subsequently develop an algorithm to evaluate the performance of the MCCN by calculating network reliability which is defined as the probability of the data being successfully processed by the MCCN.