Reduced Reachability Graph Research Articles

Robustness Analysis of Automated Manufacturing Systems With Uncontrollable Events Using Petri Nets

In this paper, we address the robustness analysis problem of automated manufacturing systems with uncontrollable events in the paradigm of Petri nets (PNs). First, we formalize unreliable resource failures as the removal of all ingoing transitions of unreliable resource places (denoted by unreliable transitions hereafter). Second, we obtain a necessary and sufficient condition to check the robustness of markings, so called robustness controllability theorem (abbreviated as RCT hereafter) in the paradigm of reduced reachability graph (abbreviated as R2G hereafter). All markings involved in the R2G of a PN are equivalent to that of its reachability graph, except that all arcs associated to unreliable transitions are removed from R2G. Based on RCT, the robustness of all markings in an R2G can be determined. An example is proposed to illustrate the approach. Note to Practitioners—In reality, it is an urgent issue to analyze the behaviors of automated manufacturing systems (AMSs) so as to guarantee their stable operation against resource failures, e.g., the missing of a signal or the failure of a sensor. In this connection, different methods are proposed to deal with the robustness analysis and control problem of AMSs with unreliable resources. The objective is to avoid any deadlock in the AMSs or to ensure the liveness of the subsystems that require only reliable resources when there exist resource failures. Due to limited actuating and sensing abilities, AMSs may be partially controlled, i.e., there exist events whose firing may not be inhibited by an external action. However, fewer research works consider this practical situation when handling robustness analysis and control issue, which renders the existing approaches impracticable. In this paper, we solve the robustness analysis problem of AMSs with uncontrollable events by using Petri nets. A necessary and sufficient condition is proposed to check the robustness of markings, called robustness controllability theorem (abbreviated as RCT hereafter) in the paradigm of reduced reachability graph. With the aid of RCT, the robustness of all markings can be determined so as to guarantee the flexibility of AMSs.

Robustness Analysis of Automated Manufacturing Systems With Unreliable Resources Using Petri Nets

This paper studies the maximally permissive robustness analysis of automated manufacturing systems (AMSs) with unreliable resources in the paradigm of Petri nets (PNs). Two types of robust markings, i.e., strongly robust markings and weakly robust markings, are defined in this paper. We propose robustness equivalence and non-robustness equivalence to characterize the markings that exhibit the same robustness and non-robustness, respectively. Reachability graph (or RG hereafter) is directly used to determine the robustness of markings; however, it is difficult to use in large-scale systems due to formidable computational difficulty. As an alternative, we present a reduced reachability graph (or R2G hereafter) based necessary and sufficient condition to check the robustness of markings, in terms of the liveness analysis of markings in R2G. We show that all safe markings of an R2G correspond to strongly robust markings of the corresponding RG, and deadlock markings as well as their bad markings and livelock markings as well as their bad markings of an R2G correspond to non-robust markings and weakly robust markings of the corresponding RG, respectively. Hence, the robustness of markings in an RG can be determined effectively and efficiently through the liveness analysis of markings in the corresponding R2G. Note to Practitioners—In practical manufacturing scenarios, it is urgent to analyze and control the automated manufacturing systems (AMSs) so as to ensure their continual production against any resource failure. If the failures of an AMS are not handled gracefully, the whole system may fall into a blocking. As a consequence, system production does not meet rapid manufacturing goals and objectives. In this paper, we focus on the maximally permissive robustness analysis of AMSs with unreliable resources in the paradigm of Petri nets. We define two types of robustness in terms of markings, i.e., strong robustness and weak robustness. From the viewpoint of reachability graph, we propose robustness equivalence and non-robustness equivalence among markings and present the procedures to check the robustness of markings. Furthermore, a set of necessary and sufficient conditions are established to provably ensure that the robustness of markings can be determined through liveness analysis in a reduced reachability graph. Therefore, the robustness of markings can be determined in a computationally efficient way.

Development of Collaborative Business Processes: A Correctness Enforcement Approach

Collaborative business processes gather a set of business processes with complementary competencies and knowledge to cooperate to achieve more business successes. To ensure their successful implementation, correctness is a key issue that needs to be addressed during their development. To this end, a novel correctness enforcement approach is proposed to support the development of collaborative business processes. In this approach, we first give an algorithm to check the correctness of an original process specified by Petri nets. Then, we prune its reachability graph to obtain its core in case of partially correct, which is a reduced reachability graph that doesn't cover invalid states. Finally, we generate a set of controllers from the core using coordination mapping (i.e., inserting some coordination activities into controllers), and then an enforced process is built by the composition of the original process and the controllers. Our approach is implemented as an analysis module called cetool in the PIPE (Platform Independent Petri Net Editor) and it is validated on a set of real-world cases. The results show the effectiveness and efficiency of the proposed approach.

Detecting data-flow errors based on Petri nets with data operations

In order to guarantee the correctness of business processes, not only control-flow errors but also data-flow errors should be considered. The control-flow errors mainly focus on deadlock, livelock, soundness, and so on. However, there are not too many methods for detecting data-flow errors. This paper defines Petri nets with data operations (PN-DO) that can model the operations on data such as read, write and delete. Based on PN-DO, we define some data-flow errors in this paper. We construct a reachability graph with data operations for each PN-DO, and then propose a method to reduce the reachability graph. Based on the reduced reachability graph, data-flow errors can be detected rapidly. A case study is given to illustrate the effectiveness of our methods.

MRSPN analysis of Semi-Markovian finite source retrial queues

In this paper, the analysis of Semi-Markovian single server retrial queues by means of Markov Regenerative Stochastic Petri Nets (MRSPN) is considered. We propose MRSPN models for the two retrial queues M/G/1/N/N and M/G/1/N/N with orbital search. By inspecting the reduced reachability graph of both MRSPN models, the qualitative analysis is obtained. The quantitative analysis is carried out after constructing their one step transition probability matrix and computing the steady state probability distribution of each tangible marking. As an example, the queue $$M/Hypo_{2}/1/2/2$$ is treated in order to illustrate the functionality of the MRSPN approach. The exact performance measures (mean number of customers in the system, mean response time, mean waiting time,...) are computed for different parameters of the two systems by an algorithm elaborated in Matlab environment.

Analysis of the Petri net model of parallel manufacturing processes with shared resources

A method of analysis for a class of Petri nets (PNs) called parallel process net with resources ( PPNRs) is presented in this paper. The proposed analysis method is based on reduced reachability graph (RRG) of PPNRs to verify the correspondence between required specification of manufacturing system and its PN representation. In order to reduce the reachability graph (RG), a new technique is proposed which incorporates the transition vectors (TVs) to determine all the enabled transitions at a given state of system and to recognize them as dependent or independent. An algorithm, based on the idea of simultaneous execution of concurrently enabled independent transitions, is developed to reduce the RG and its analysis is also performed. Moreover, relationship between the reduction of RG and parallel structure in the PN model is discovered. The proposed technique replaces the RG by a structure which directly depicts concurrent execution and does not show the irrelevant states by presenting the concurrent behavior of system in the reduced state space. The analysis of PPNRs based on RRG generated by proposed method is also presented and demonstrated by a practical example.

A symbolic reachability graph for coloured petri nets

Coloured Petri nets are well suited to the modelling of symmetric systems. Model symmetries can be usefully exploited for the sake of analysis efficiency as well as for modelling convenience. We present a reduced reachability graph called symbolic reachability graph that enjoys the following properties: (1) it can be constructed directly by an efficient algorithm without considering the actual state space of the model; (2) it can be substantially smaller than the ordinary reachability graph; (3) its analysis provides equivalent results as the analysis of the ordinary reachability graph. The construction procedure for the symbolic reachability graph is completely effective in the case of a syntactically restricted class of coloured nets called “well-formed nets”, while for the unrestricted case of coloured nets some procedures may not be easily implementable in algorithmic form.