Quickest Multistate Flow Networks With the Deterioration Effect

Min-Fan He,Yeou-Ren Shiue,Wei-Chang Yeh,Neal N Xiong,Chia-Chen Kuo,Zhifeng Hao

doi:10.1109/access.2020.3014439

Abstract

In a traditional multistate quickest path problem (MQPP), the system reliability is evaluated based on a strict assumption that the net flow into and out of a system is equal to zero. However, certain networks, which are known as deteriorated networks, suffer a loss due to the deterioration effect, resulting a delivery shortage. For example, the data or goods will deteriorate or decay because the transmission distance is too long, which affects whether the delivered data or goods arrive intact. To provide a practical solution to this problem, a novel MQPP model, known as the deteriorated MQPP (MQPP de ) model, is proposed in this work. The goal is to evaluate the system reliability, which is defined as the probability that the end user receives at least $d$ units of data or goods in transmission time $T$ in the case of a MQPP with the deterioration effect. A simple path-based algorithm based on an integer programming model of the flow conservation law is presented to generate all of the lower boundary points ( $d$ , $T$ )-MP de s. Next, the reliability of the MQPP de model can be calculated in terms of all of the ( $d$ , $T$ )-MP de s.

Highlights

The quickest path problem (QPP), which is a variation of the shortest path problem, has been proposed by Chen and Chin [1]
The multistate QPP (MQPP) is an extension of the QPP in a multistate flow network (MFN) in which the capacities of nodes and arcs may be uncertain due to failure, maintenance, etc
A modified model of the MQPPde reliability problem that is based on an integer programming model of the flow conservation law [27], called the F-IPde, is presented in the following equations, where X = xi and each ei ∈ Pj and W is the maximum capacity of the ith arc with the deterioration effect, i.e., W =

Summary

INTRODUCTION

The quickest path problem (QPP), which is a variation of the shortest path problem, has been proposed by Chen and Chin [1]. A modified model of the MQPPde reliability problem that is based on an integer programming model of the flow conservation law [27], called the F-IPde, is presented in the following equations, where X (ei) = xi and each ei ∈ Pj and W (ei) is the maximum capacity of the ith arc with the deterioration effect, i.e., W (ei) =. The system-state vector Xj, which has the minimum capacity that allows the end user to receive d units of data along Pj within time T when the deterioration effect is included, can be generated as follows:.

EXAMPLE ILLUSTRATION

DISCUSSION AND CONCLUSION