Abstract
In current decades, we used the network reliability widely into several realistic situations. In practical application, the transmitting utility may be restricted by specific swerve angle i.e., automated guided vehicle, the oil transmission system and military robot. Hence, a novel binary-state network (BN)/multi-state flow network (MFN) model called the 2D binary-state angle network (2DBAN)/2D multi-state flow angle network (2DMFAN), in which each arc has a probability of different capacity as well as each node has a specific swerve angle restriction, is offered to deal with those realistic problems. An efficient algorithm constructed with the cosine law and Euclidean distance formula is introduced in searching for all minimal path set at capacity level d (d-MPs) which is a simple path satisfied all angle restrictions and capacity level d to the sink node from the source node in 2DBAN/2DMFAN. We can calculate the reliability of a 2DBAN/2DMFAN by all MPs (d-MPs) satisfy the swerve angle restriction. Finally, we use some examples to illustrate how the reliability of a 2DBAN and 2DMFAN are evaluated using the proposed algorithm.