Fuzzy Timed Petri Nets Research Articles

MODELING THE DYNAMIC INTERACTION PROCESSES USING OF FUZZY TIMED PETRI NETS OF TYPE VF

The dynamic interacting processes modeling is examined in the article, which shows the complex objects operation in the condition of uncertainty. A formalism intended for the development and analysis models of complex parallel and distributed systems is proposed. It is based on the mathematical apparatus of the fuzzy timed Petri nets (FTPN) of type Vf, representing generalized FTPN of type Vf , combining deterministic and non-deterministic character. The algorithm for the functioning FTPN of type Vf is developed. The proposed algorithm provides a solution to the problem of the triggering solvability of transitions occurring in conflict states, the imposition of a fuzzy structure on the network marking with fuzzy composition laws that determine the values the degrees of belonging the input and output transition positions. The model of parallel functioning processing devices is presented in the FTPN form of type Vf. An approach is proposed for modeling dynamic interacting processes based on the matrix theory of Petri nets, that provides an effective form of structure representation, model state dynamics, the space of achievable states, and triggering transitions sequence in the form of vectors and matrices set. On the example of the production model of mechanical processing, it is shown that the accepted triggering transitions rules fully show the functioning FTPN process of type Vf. As a result of the simulation, the reachability tree is obtained as a sequence of matrices.

Analysis of real-time system conflict based on fuzzy time Petri nets

The time uncertainty and the resource conflict are two very important aspects in modeling and analyzing real-time system. The paper defines a kind of Fuzzy Time Petri Nets FTPN to simulate the behavior of real-time system limited by time. It studies the conflict with time attribute and space-time collision in real-time system and utilizes time constraints property and the collision possibility to resolve the conflict through knowledge reasoning of fuzzy time interval. Compared with existing methods of conflict analysis and resolution, it takes into account the uncertainty of the time with the system of conflict and contact behavior, which could be better to simulate and analyze real-time system in reality.

Fuzzy timed Petri nets — analysis and implementation

In [Z. Ding, H. Bunke, M. Schneider, A. Kandel, Fuzzy timed Petri net — definitions, properties and applications, Math. Comput. Modelling (2005) (in press)], we posed two fuzzy timed Petri Net models. Based on the mark changing rate, they can be classified either as a discrete Fuzzy Timed Petri Net model (discrete-FTPN), or as a continuous Fuzzy Timed Petri Net model (continuous-FTPN). In this paper, we present an algorithm developed to compute reachable states for discrete-FTPN models. We also present properties of the continuous-FTPN model, which are used to describe the system’s behavior. From the investigation presented in this paper, we conclude that it is easier to implement a discrete-FTPN model, but for a theoretical study the continuous-FTPN model is better.

Fuzzy timed Petri nets

The study is concerned with a new temporal version of fuzzy Petri nets—fuzzy timed Petri nets (ftPNs). These nets are augmented by temporal fuzzy sets that allow for the representation of timing effect (e.g., aging of information). We show how the time factor can be added as an integral part of the models of transitions and places. The formalism of the extended net is introduced and studied in depth. A series of illustrative examples are presented with intent of developing a better qualitative insight into the temporal behavior of the nets. A detailed learning scheme for the net is also given.

Modeling and performance analysis using extended fuzzy-timing Petri nets for networked virtual environments

Despite their attractive properties, networked virtual environments (net-VEs) are notoriously difficult to design, implement, and test due to the concurrency, real-time and networking features in these systems. Net-VEs demand high quality-of-service (QoS) requirements on the network to maintain natural and real-time interactions among users. The current practice for net-VE design is basically trial and error, empirical, and totally lacks formal methods. This paper proposes to apply a Petri net formal modeling technique to a net-VE-NICE (narrative immersive constructionist/collaborative environment), predict the net-VE performance based on simulation, and improve the net-VE performance. NICE is essentially a network of collaborative virtual reality systems called the CAVE-(CAVE automatic virtual environment). First, we introduce extended fuzzy-timing Petri net (EFTN) modeling and analysis techniques. Then, we present EFTN models of the CAVE, NICE, and transport layer protocol used in NICE: transmission control protocol (TCP). We show the possibility analysis based on the EFTN model for the CAVE. Then, by using these models and design/CPN as the simulation tool, we conducted various simulations to study real-time behavior, network effects and performance (latencies and jitters) of NICE. Our simulation results are consistent with experimental data.

Embedding fault-tolerant properties in the design of complex software systems

A systematic way to introduce time-dependent and non-time-dependent properties into a component of a complex software system incorporating real-time restrictions is presented. The approach is based on the decomposition of an extended Petri net model, called the G-Net system. The approach to introduce non-time-dependent fault-tolerant properties is based on the analysis of G-Net systems. The idea is to avoid interference in the behavior of a component caused by faulty behavior in a hardware or software component that interacts with it, and also introduce means by which a component can detect a fault in its behavior and prevent itself from generating more errors. Performance analysis based on the introduction of fuzzy time Petri nets is used to define timing constraints. When violated, these timing constraints may trigger the execution of recovery blocks.