## 1 Introduction
[13] evaluated the system-level seismic risk assessment of a bridge transportation network in South Korea based on the maximum flow capacity, which was defined as the maximum number of vehicles per unit time. [PERSON] et al. [14] estimated the post-hazard flow capacity of a bridge transportation network in the USA considering the deterioration of the bridge. However, for bridge transportation networks, novel measures such as total system travel time (TSTT) are required because not only node-to-node capacity but also all nodes in the network can be candidates for source or destination nodes. TSTT can be introduced as a more realistic performance measure of bridge transportation networks because it is based on the travel times of all vehicles and considers the traffic and topology of the bridge transportation network. For these reasons, [PERSON] and [PERSON] [15] introduced TSTT to a multi-objective network design problem, and [PERSON] et al. [16] adopted TSTT as a system measure to assess the physical damage and functional loss of transportation infrastructure systems. [PERSON] et al. [17] also used TSTT to conduct a study on earthquake loss assessment and mitigation measures in the transportation network of Charleston County, South Carolina, USA. However, their research has not been applied to high-order complex network problems, but also has the disadvantage of having to calculate the TSTT directly for each scenario. Therefore, since a large computational time cost is required to calculate the performance index of each scenario, the entire analysis time exponentially increases as the network dimension increases. Methods for evaluating the performance of a network can be divided into sampling-based methods and non-sampling-based methods. Sampling-based methods are straightforward and easy to use; hence, various previous studies have carried out seismic risk assessments by adopting sampling-based methods such as Monte Carlo simulation (MCS) [13]. However, when an analysis necessitating MCS with a large number of samples (e.g., probabilistic seismic hazard analysis (PSHA) and network design optimization) is of interest, a sampling-based method may require a significant amount of computational time [18]. To overcome this limitation, [PERSON] et al. [19] evaluated the seismic performance of the California water network through logistic regression and the kernel support vector classifier, and [PERSON] and [PERSON] [20] proposed a radial topology to measure the system reliability effectively. In addition, a non-sampling-based method, termed the matrix-based system reliability (MSR) method, has been developed in several previous studies to predict various system reliabilities [21; 22]. Moreover, a recursive decomposition algorithm (RDA) was developed as another new non-sampling-based approach, and various network reliabilities have been evaluated using the RDA methodology [23; 24; 25; 26]. However, this previous research has the disadvantage of simply performing connectivity analysis according to the bi-state of network components without taking into account the network flow analysis. Therefore, the previously proposed methods can only depict the tendency of the overall performance degradation of the network. In addition, the existing sampling- and non-sampling-based methods have some limitations in seismic risk assessment with a robust performance measure for complex networks. Many of the existing methods have been applied only to critical urban infrastructure systems by adopting relatively simple measures of network performance such as connectivity and maximum flow capacity. Furthermore, although some researchers developed methods such as multi-scale approaches [27; 28] and the branch-and-bound method [21] to deal with complex network problems, the preliminary studies have not been applied to extremely-complex network systems and have not aimed to reduce the time cost of iterative calculations for various epicenters and earthquake magnitudes.