Capacity Reliability Calculation and Sensitivity Analysis for a Stochastic Transport Network

A major performance index for analyzing a stochastic transport network is the two-terminal capacity reliability
$R_{d}$
, defined as the probability that
$d$
units of goods can be successfully transported via stochastic arc capacities from the source to the destination. This paper presents an efficient
$d$
-minimal path method to calculate
$R_{d}$
based on some newly obtained results. The proposed method uses a simple method to check
$d$
-minimal path candidates and a more efficient approach to remove duplicate
$d$
-minimal paths that are the biggest obstacle in solving
$d$
-minimal paths, along with an indication of the advantage over the existing methods. Besides, sensitivity analysis is adopted to explore the most important arc whose reliability change affects the network reliability most significantly, which helps supervisor identify and enhance the critical arcs for improving the network reliability more effectively. Computational and application examples demonstrate the efficiency and utility of the method, respectively.