Performance regulation of event-driven dynamical systems using infinitesimal perturbation analysis

In this paper we focused our attention on a particular hybrid PN model called FOHPN, that is based on the fluidification of discrete PNs, and whose main feature is that the instantaneous firing speed of continuous transitions keeps constant during each macroperiod. In the first part of the paper we discuss in detail the advantages of fluidification, and provide a brief survey of the most important formalisms within the hybrid PN framework. Finally, we showed how FOHPNs can be efficiently used to model SC, and how interesting optimization problems can be solved via numerical simulation, by simply solving on-line a certain number of LPPs.

The emergence of Supply Chains (SCs) is an outcome of the recent advances in logistics and information technology. SCs are complex networks interconnecting different independent manufacturing and logistics companies integrated with material, information and financial flows (Viswanadham & Raghavan, 2000). Typically, SC management decisions are classified into three hierarchical levels according to the time horizon of decisions: strategic (longterm), tactical (medium-term), and operational (short-term, real-time) (Chopra & Meindl, 2001; Shapiro, 2001). Accordingly, different models have to be defined at each level of the decision hierarchy to describe the multiple aspects of the SC. While the development of formal models for SC design at strategic and tactical levels was addressed in the related literature (Dotoli et al., 2005; Dotoli et al., 2006; Gaonkar & Viswanadham, 2001; Luo et al., 2001; Vidal & Goetschalckx, 1997; Viswanadham & Gaonkar, 2003), research efforts are lagging behind in the subject of modeling and analyzing the SC operational performance. At the operational level, SCs can be viewed as Discrete Event Dynamical Systems (DEDSs), whose dynamics depends on the interaction of discrete events, such as customer demands, departure of parts or products from entities, arrival of transporters at facilities, start of assembly operations at manufacturers, arrival of finished goods at customers etc (Viswanadham & Raghavan, 2000). Among the available DEDS analytical formalisms, Petri Nets (PNs) may be singled out as a graphical and mathematical technique to model systems concurrency and synchronization. Moreover, PNs are able to capture precedence relations and structural interactions and may be executed in standard engineering software packages simply implementing their dynamics via the corresponding matrix equations. However, most SC models based on PNs proposed in the related literature share the limitation that products are modelled by means of discrete quantities, called tokens (Desrochers et al., 2005; Dotoli & Fanti, 2005; Elmahi et al., 2003; Viswanadham & Raghavan, 2000; Von Mevius & Pibernik, 2004; Wu & O’Grady, 2005). This assumption is not realistic in large systems with a huge amount of material flow: the state space of the SC model generally turns out to be excessively large, so that inconveniences in the simulation and performance optimization often arise, leading to large computational efforts. Since SCs are DEDSs whose number of reachable states is very large, PN formalisms using fluid approximations provide an

Simulation of IPA gradients in hybrid network systems

In this paper we investigate the problem of delivering quality of service (QoS) guarantees in the context of communication networks, studied through stochastic fluid models. The paper follows the approach developed in (C. G. Cassandras, et al., 2002), (C. Panayiottou, et al., 2004). Its main contribution is that it develops infinitesimal perturbation analysis (IPA) estimators of a cost function that also includes delay violation constraints, rather than the average delay that is typically investigated in [1], [2] and other similar work.

Modeling Hybrid Systems in SIMTHESys

This paper presents a new framework for traffic flow control based on an integrated model description by means of a Hybrid Dynamical System (HDS). The geometrical information on the traffic network is characterized by a Hybrid Petri Net (HPN). Then, the algebraic behavior of traffic flow is transformed into a Mixed Logical Dynamical System (MLDS) in order to introduce an optimization technique. These expressions involve both continuous evolution of traffic flow and event driven behavior of traffic light. HPN allows us to formulate the problem easily for complicated and large-scale traffic network due to its graphical understanding. MLDS enables us to optimize the control policy for traffic light by means of its algebraic manipulability and use of model predictive control framework. Since the behavior represented by HPN can be directly transformed into corresponding MLDS, the seamless incorporation of two different modeling schemes provide a systematic design for traffic flow control.

This paper presents a new framework for traffic flow control based on an integrated model description by means of a Hybrid Dynamical System (HDS). The geometrical information on the traffic network is characterized by a Hybrid Petri Net (HPN). Then, the algebraic behavior of traffic flow is transformed into a Mixed Logical Dynamical System (MLDS) form in order to introduce an optimization technique. These expressions involve both continuous evolution of traffic flow and event driven behavior of traffic light. HPN allows us to formulate the problem easily for complicated and large-scale traffic network due to its graphical understanding. MLDS enables us to optimize the control policy for traffic light by means of its algebraic manipulability and use of model predictive control framework. Since the behavior represented by HPN can be directly transformed into corresponding MLDS form, the seamless incorporation of two different modeling schemes provide a systematic design scenario for traffic flow control.

We propose a generalized concept of hybrid Petri nets as a modeling and design tool for the distributed dynamical systems involving asynchronous event-based communication. The proposed Petri net machine represents an extension of the standard discrete-event Petri nets, but differs conceptually from the conventional hybrid Petri nets in that dynamical processes are stored in the continuous places, similarly as in hybrid automata. In particular, the firing semantics of the corresponding continuous arcs is defined to capture the information exchange between the network nodes. While being primarily a graphical modeling tool, the proposed formalism of hybrid Petri nets infers a hybrid dynamical setting of event-triggered control problems, an approach that has been missing in the literature. The usability of our approach is illustrated in the context of the distributed event-triggered LQR and consensus problems, in conjunction with a systematic methodology for designing optimal adaptive scheduling schemes, governing the communication resources.

On fluidification of Petri Nets: from discrete to hybrid and continuous models

This paper presents a decentralized Petri net (PN) based wireless sensor node architecture (PN-WSNA) to construct a flexible and reconfigurable WSN for intelligent monitoring systems. PN is a graphic based discrete event dynamic system (DEDS) modeling approach, and it is advantageous for modeling the system with concurrent and asynchronous systems. Therefore, the PN is usually used to construct agent based intelligent monitoring systems. The PN-WSNA system consists of a PN-WSNA kernel program and a PN-WSNA management program. The PN-WSNA kernel program is developed as an agent that is installed in the sensor node, and it is responsible of receiving and decoding PN models, collecting sensor data from analog and digital channels, intercommunication between sensor nodes, PN model inference and decision. On the other hand, the PN-WSNA management program is executed on a remote host computer, and it is responsible of distance sensor node managements via routing tables. More specially, a user interface is provided for system managers to edit PN models in a graphic manner, and the PN models can be delivered to the corresponding sensor node online without physical visits. Therefore, the proposed PN-WSNA system not only performs a reconfigurable WSN architecture, but also provides an easy graphical PN edit environment for constructing intelligent agents. Such a system can be applied to the factory automation, intelligent diagnosis, climate monitoring, etc. Finally, a simple prototype system is constructed using the Zigbee BAT mote modules to verify the proposed PN-WSNA system.

Half a century after Carl Adam Petri’s Ph.D. thesis: A perspective on the field

In this chapter, modeling of GRNs using Petri net theory is considered. It aims at providing a conceptual understanding of Petri nets to enable the reader to explore GRNs applying Petri net modeling and analysis techniques. Starting with an overview on modeling biochemical networks using Petri nets, the state-of-the-art with focus on GRNs is described. Other modeling techniques, for example, hybrid Petri nets are discussed. Basic concepts of Petri net theory are introduced involving special analysis techniques for modeling biochemical systems, for example, MCT-sets, T-clusters, and Mauritius maps. To illustrate these Petri net concepts, a more complex case study–the gene regulation in Duchenne Muscular Dystrophy–is explained in detail, considering the biological background and the interpretation of analysis results. Considering both, advantages and disadvantages, the chapter demonstrates the usefulness of Petri net modeling, in particular for GRNs.

Investigated the environmental assessment from the point of system simulation, the environment assessment system belongs to the discrete event dynamic system. According to the comparison between the environment assessment system and the military command automation system, there are many common grounds in essence. Therefore, in order to solve the problems exist in environmental assessment field nowadays, the relative theories of the military command automation system (C4ISR) were transplanted to environmental assessment field. Finally, based on the information technology and the simulation technology one solution was constructed named Environmental Assessment Automation System-C4ISRE (Command, Control, Communications, Computer, Intelligence, Surveillance, Reconnaissance, Environmental Assessment). The relative theories of C4ISRE including Discrete Event Dynamic Systems (DEDS), the technology of using Petri Net (PN) to analyze and model the DEDS, Distributed Virtual Reality (DVR), Computer Generated Forces (CGF), Synthetic Natural Environment (SNE), Dynamic Environment Simulation (DSE), Environmental Assessment(EA). The integration of upper contents constructs the theory frame of Informatization Environmental Assessment (IEA?and also makes a stable theoretical base for IEA’s further research.

THE SUPERVISORY CONTROL PROBLEM SOLVED VIA PETRI NETS

A new Petri net modeling technique for the performance analysis of discrete event dynamic systems