## 2 Related Works
### Multi-Agent Simulation-Based Robustness Evaluation Indicator  
Based on the multi-agent model in Section 3.1 and the order-task sequence, the dynamic simulation of the CMP can be realized, and the results data (e.g., the order completion time, logistics transportation distance, and resource occupation) can be output to evaluate the performance of the CMP. Quality of service (QoS) is commonly used in academia to evaluate the CMP, with QoS values mostly being evaluated from multiple dimensions, such as the time, cost, and reliability [43; 44; 45]. Referring to the definition of QoS, this paper proposes robustness of service (RoS) as a robustness measurement indicator from the perspective of the simulation of four dimensions: service time, service cost, reliability, and order completion rate. The specific calculation formulae for these four dimensions are as follows:  
1. Service time The sum of all orders' completion times during the simulation cycle is represented by the following formula: \[T=\sum\limits_{j=1}^{m}t_{j}\] (11) where \(m\) denotes the overall number of orders, \(j=1,2,\dots,m\) denotes the \(j\)th order in the order sequence, and \(t_{j}\) denotes the finish time of the \(j\)th order, which can be derived from the results of the simulation. 2. Service cost The cloud resource service fee, logistics service fee, and cloud resource release fee, which together make up the overall cloud service cost, are determined as follows: \[ \begin{array}{ll}C=\sum\limits_{j=1}^{m}\sum\limits_{i=1}^{n_{j}}t_{i,j}^{ \text{serving}}&*\ p_{i,j}^{\text{resource}}\ +\ \sum\limits_{j=1}^{m}\sum\limits_{i=1}^{n_{j}}d_{i,j}*c^{\text{logistic}}\\ &+\ \sum\limits_{j=1}^{m}\sum\limits_{i=1}^{n_{j}}t_{i,j}^{\text{ releasing}}\ *\ p^{\text{release}\ n}\end{array} \] (12) where \(m\) represents the total amount of orders and \(n_{j}\) represents the number of assignments associated with each order; \(j=1,2,\dots,m\) is the \(j\)th order in the order sequence; \(i=1,2,\dots,n\) is the \(i\)th the task in the task sequence; \(t_{i,j}^{\text{serving}}\) represents the cloud service time of the \(i\)th task in the \(j\)th order; \(p_{i,j}^{\text{resource}}\) represents the service cost per unit time of the resource related to the task; \(d_{i,j}\) represents the logistics distance related to the task; \(c^{\text{logistic}}\) represents the logistics cost per unit distance; \(t_{i,j}^{\text{releasing}}\) represents the release time of the cloud resources for the task; and \(p^{\text{release}}\) represents the cost per unit time of releasing resources. 3. Service reliability The service reliability is measured by a multiplicative index [44], which has the following form: \[\mathit{rel}=\frac{\sum\limits_{j=1}^{m}\prod\
olimits_{i=1}^{n_{j}}\mathit{ rel}_{i,j}}{m}\] (13) where \(\mathit{rel}_{i,j}\) represents the service reliability of the \(i\)th task in the \(j\)th order, as specified in the order agent's \(\mathit{reliabilityAccum}\) property. The evaluation of the CMP's robustness in this paper also refers to the definition of robustness, which refers to the ability of the CMS to operate normally and maintain its original performance in the face of various unexpected disruptions and interruptions. For the CMS, the normal completion of cloud orders within a service cycle can reflect its normal operation capability more intuitively. Therefore, the order completion rate index is introduced: (4) Order completion rate The order completion rate is the proportion of total scheduled orders to orders actually completed throughout the simulation cycle. \[\mathit{off}=\frac{N_{1}}{N_{1}+N_{2}}\] (14)where \(N_{1}\) represents the number of orders fulfilled throughout the simulation cycle and \(N_{2}\) represents the number of incomplete orders. In summary, combining the definitions of robustness and QoS, this paper proposes a new robustness evaluation index, RoS, to comprehensively consider the normal operational capability of the CMS in the face of unexpected disturbances.