## 2 Literature Review  
CPS consist of two parts: the cyber space and the physical space. Control of entities in physical space of CPS is based on the cyber space model. To analyze CPS, proper modeling tools to construct the cyber space model of the CPS are relied upon. A modeling tool must be able to capture concurrent, synchronous and asynchronous operations/events in CPS and must support construction, edition and representation of the model in industrial standard format. A variety of modeling approaches/tools can be used to capture the operations of CPS by constructing the cyber space model of CPS, e.g., Discrete Event System [16], Extended Hybrid Automata [17] and Petri nets (PN) [18]. Among these tools, Petri nets [19] provide an easy-to-use graphical user interface that can capture concurrent, synchronous and asynchronous operations/events in CPS. Petri nets can be represented by the Petri Net Markup Language (PNML) [20], an XML-based interchange format widely supported by many software tools [21]. Therefore, we adopt Petri nets in this paper to model CPS. Despite the variety of Petri net tools such as the ones in [22; 23] available for modeling CPS, these tools do not provide a method for analyzing the influence of resource failures on performance. As the objective of this paper is to analyze the influence of resource failures on temporal property of CPS, Petri nets supporting modeling of time are adopted. In the literature, some Petri net models assign time delay to transitions while others assign time delay to places in the nets [24]. A timed Petri net is called deterministic timed Petri net if the time delay is deterministic [25; 26; 27; 28; 29]. A timed Petri net is called stochastic timed Petri net if the time delay is probabilistically specified [30; 31; 32; 33]. As this paper focuses on influence of resource failures on temporal property of CPS, a class of deterministic discrete timed Petri nets are adopted. Different models have been proposed to capture resource failures. Some of the works (e.g., [34; 35]) model resource failures as loss of tokens in untimed Petri nets models and develop methods to assess the impact of resource failures on the system after the occurrence of failures. The works [36; 37] classify the resources into reliable resources and unreliable resources based on a class of untimed Petri nets (S4 PR) and develop methods to allocate resources. The works [12; 13] consider uncertainties due to the interruptions of operations and unreliable resources and take performance and risk into account in the objective function to deal with uncertainties in manufacturing systems based on timed Petri nets. As the goal of this paper is to develop a method to assess the impact of resource failures on the system after the occurrence of failures, we model resource failures as loss of tokens in discrete timed Petri nets. Although the proposed discrete timed Petri nets can capture the characteristics of CPS, there still lacks a theory to analyze the robustness property. For this reason, this paper is devoted to development of theory to facilitate the analysis of robustness property of CPS based on the proposed discrete timed Petri nets. To study robustness property of CPS, a nominal solution must be generated first. Robustness analysis for CPS is done based on the nominal solution. To generate a nominal solution, models that can capture the spatial and temporal properties of workflows are constructed. In this paper, we consider order requirements with multiple product demands and a deadline. A spatial-temporal network (STN) model is constructed for each type of production process required by the orders. The STN models are constructed based on transformation of the DTPN models of CPS. The STNs constructed for CPS are capable of capturing the dynamics of workflows in space and time. The STNs can only capture the nominal operations of CPS.