Reliability of acyclic multi-state networks with constant transmission characteristics of lines

Multi-state acyclic networks (MANs) consist of a number of independent multi-state nodes (MNs). Each network has a root MN (source), a number of intermediate MNs and a sink node. All the nodes are ordered and each node (except the sink) is connected by edges with a set of nodes with greater numbers. Each MN can have different states determined by a subset of available edges. Probability of each MN state is assumed to be known for every MN. The aim of the MAN is transmission of information or material flow from source to sink. The transmission process intensity depends on transmission characteristics (TCs) of network elements. In this paper we suggest a method for determining TC of the entire MAN based on TCs and availability of its elements. The MAN reliability is defined as probability that its TC meets some specified demand. A universal generating function approach is suggested for estimating reliability of MANs of different physical nature. In order to demonstrate the flexibility of the approach two different types of MANs are considered: minimal transmission time networks and maximal flow path networks. Illustrative examples are presented.