Capacity Reliability Calculation and Sensitivity Analysis for a Stochastic Transport Network
Yi-Feng Niu, Xiu-Zhen Xu, Can He, Dong Ding, Zhizhong Liu
Abstract
A major performance index for analyzing a stochastic transport network is the two-terminal capacity reliability <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R_{d}$ </tex-math></inline-formula> , defined as the probability that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> units of goods can be successfully transported via stochastic arc capacities from the source to the destination. This paper presents an efficient <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> -minimal path method to calculate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R_{d}$ </tex-math></inline-formula> based on some newly obtained results. The proposed method uses a simple method to check <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> -minimal path candidates and a more efficient approach to remove duplicate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> -minimal paths that are the biggest obstacle in solving <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> -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.