Cost-benefit Analysis for Traffic Network Reliability Improvement

A highly reliable traffic network is very important for both abnormal and normal periods. Network reliability can be improved effectively by improving the most important key link in the network. When such an important link has been identified, network reliability can be efficiently improved and maintained. An index of reliability importance (RI) has been proposed; however, it does not reflect that it is more difficult to improve a highly reliable link than it is to improve a less reliable link. Thus, an index of criticality importance (CI) has been proposed. However, in a parallel network, use of the CI will result in only the more reliable links being improved, and the less reliable links will not be improved. Thus, Wakabayashi proposed an advanced index of the criticality importance (CIW). However, the degree of importance is the same for the links in a parallel network. Thus, none of these indices can find the most important key link in the network. Therefore, these indices cannot obtain a good solution for improving network reliability. A cost-benefit analysis is also important.This paper contains the following sections: First, previously proposed indices, such as RI, CI, and CIW, are summarized. Second, since the calculation work for network reliability increases exponentially with the number of links of the network (an NP-hard problem), an enormous amount of CPU time and memory size is needed. Therefore, we propose an efficient calculation algorithm with a partial differential, the calculation algorithm for Boolean absorption (CABA). It enables us to automatically calculate the reliability and importance of links, even for a very large-scale network. Using the CABA, the processes of network improvement with the RI, CI, and CIW are compared for a small network. Then the features and defects of these indices are compared. Third, a method of cost-benefit analysis is proposed in order to improve the previously proposed indices, especially complementing the CIW. Series, parallel, and simple bridge networks are discussed. Depending on the reliability-cost function, the behavior of the network improvement process will differ. Last, we conclude with a summary of our method for effective and efficient network improvement.