## 2 Related Works
### Multi-Agent Simulation Study of Cloud Manufacturing System  
The existing research on the robustness of advanced manufacturing systems mostly uses the complex network analysis method, which is well suited to reflect the structural characteristics of the system. As a type of networked manufacturing mode, the structural characteristics of cloud manufacturing is a key topic in robustness research; however, the dynamic operation process, logical judgment, and dynamic temporal relationship among entities are also aspects of cloud manufacturing that should be focused on.  
The CMS contains a variety of entities, and various forms of behavior interaction and information transfer exist between the same entities and different entities, showing the characteristics of the complex system. Analyzing the complexity through simple, intelligent, and autonomous entities, such as agents in multi-agent systems, is considered an appropriate approach to address this challenge in industrial scenarios [32]. Further, the multi-agent simulation modeling of the CMS is presently a popular research topic. For example, [PERSON] et al. designed and implemented an agent-based cloud manufacturing simulation platform, where the simple reflective agent was used to encapsulate the resources and the complex agent was used to encapsulate the services. This gave the cloud platform a five-layer architecture (i.e., the data layer, low tool layer, management layer, upper tool layer, and application layer). [PERSON] et al. [33] proposed a cloud simulation platform to provide computing resources and services for the hybrid simulation of virtual manufacturing systems, and [PERSON] and [PERSON] [34] developed a cloud-based factory simulation experiment system. [PERSON] et al. [35] analyzed typical smart manufacturing simulation techniques from three aspects: manufacturing unit simulation, manufacturing integration simulation, and manufacturing intelligence simulation. In addition, some scholars have conducted multi-agent simulation modeling research on cloud manufacturing from multiple perspectives, such as cloud service entity encapsulation [36; 37], selection and scheduling [38; 39; 40], and trust and security issues [5; 8], among others. Multi-agent simulation has become an important tool for cloud manufacturing research, yet current multi-agent simulation research on the robustness of cloud manufacturing appears relatively rare.  
This paper proposes a robustness analysis method that combines the complex network and multi-agent simulation to investigate the optimization and enhancement of CMS robustness under multiple resource substitution strategies. The complex network perspective can reflect the structural robustness of CMSs, while multi-agent simulation can consider the process robustness of CMSs from multiple dimensions, such as time, cost, quality, and reliability. The combination of these two perspectives extends the robustness analysis object of the CMS from the CMN to the CMP, thereby realizing the dual-dimensional analysis of the static structure and dynamic process of CMS robustness.  
The rest of this paper is arranged as follows. Section 3 constructs a multi-agent simulation model of the CMP and proposes process robustness indexes from the simulation perspective. Section 4 establishes a complex network model of cloud manufacturing resources and selects structural robustness metrics from the network perspective. Section 5 defines four types of resource node failure modes and three types of resource replacement strategies to deal with resource failure. Section 6 conducts a case study, combining multi-agent simulation software Anylogic and Python 3.0 tools to study the changes in the robustness of cloud manufacturing under different failure modes. Section 7 provides the research conclusions and future prospects.  
Model of the Cloud Manufacturing Process and Robustness Evaluation Indicator Based on Multi-Agent Simulation