DETERMINATION OF THE MOST RELIABLE PATH OF A PLANAR FLOW NETWORK

Abstract

For a planar stochastic flow network with binary states of elements, this paper presents an algorithm for determining the most reliable path (MRP) for transmitting a required amount of flow from a source to a terminal. We first establish a theorem stating that the MRP is one of the minimal upper paths (MUPs). This implies that the criteria, developed in a previous article (Lee and Yum, Reliab. Engng System Safety, 39 (1993) 1-10) to eliminate those subnetworks that cannot be a MUP, are still effective in determining the MRP. In the present article, we develop two additional elimination criteria based upon the inherent property of the MRP. An example is included to illustrate the proposed procedures, and computational results are reported.