Discrete event dynamic systems

Glasserman, R, and Yao, D. D. (1996), Structured Buffer Allocation Problems, Discrete Event Dynamic Systems Theory and Applications, Vol. 6, pp. 9-42. 

Deconstructing value/supply chains, 43 DE (design eflSciency), 369 Dedicated material-handling systems, 1660 Dedicated storage, 2092 DEDS, see Discrete event dynamic system Deep-lane warehousing systems, 2089 Defect concentration diagram (SPC), 1860, 1861... 

Geist, S., Gromov, D., Raisch, J. Timed Discrete Event Control of Parallel Production Lines with Continuous Outputs. Discrete Event Dynamic Systems 18(2), 241-262 (2008)... 

Many of the operations in the process industries are examples of discrete-event dynamic systems. Discrete process states and the transitions between states characterize these systems. 

Batch processes are examples of discrete-event dynamic systems they include start-up and shutdown processes, valving operations, recipe execution. Different methodologies have been proposed to model, analyse and control this type of systems. 

Petri Net is a mathematical formalism it can be considered as a graph theoretical tool to model and analyze discrete event dynamic systems which exhibit parallel evolution and whose behavior is characterized by synchronization and sharing phenomena [19],... 

Simulation is the dynamic observation of an abstract model of a system through time with particular attention to the system s key attributes. The term is used extensively in manufacturing to refer to different types of such observations ranging from visual simulation of factories or individual machine tools to stochastic simulation of entire supply chains. Today, most simulation activities are carried out by computer software systems. Simulation systems are often categories into discrete-event simulation system and continuous time simulation systems based on the approach they take with regards to advancing the time of the simulation forward. 

Dynamic simulation with discrete-time events and constraints. In an effort to go beyond the integer (logical) states of process variables and include quantitative descriptions of temporal profiles of process variables one must develop robust numerical algorithms for the simulation of dynamic systems in the presence of discrete-time events. Research in this area is presently in full bloom and the results would significantly expand the capabilities of the approaches, discussed in this chapter. 

Process Control. The traditional process control will be expanded toward new applications such as nonlinear process control of biosystems. However, in the commodity chemicals industry there will be increased need for synthesizing plantwide control systems, as well as integrating dynamics, discrete events, and safety functions, which will be achieved through new mathematical and computer science developments in hybrid systems. 

TA are used to model and analyze dynamic systems with discrete and timed behavior. One of their strengths is the easy modeling in a decomposed fashion as a set of often small and individually acting automata. Time in TA is modeled in a very natural way by a set of clocks that simply measure the time between events. This is a major difference to MIP techniques, where time and dynamic components are described in a rather artificial way by providing variables and inequalities for every point of time within a discretized time horizon. In addition to the advantages in modeling, TA serve as a computational model which can be analyzed by techniques for reachability analysis. These techniques are widely used in the context of verification, in which the objective is to detect possible undesired (bad or forbidden) behaviors [9-11]. The success of these techniques was pushed by the availability and increasing performance of tools for TA, e.g., Uppaal [9, 10, 12, 13]. 

Not all systems can be modeled with discrete event simulation. Some events are continuous, such as the rate of evaporation. These occurrences can be modeled, but they require a different approach. For more information see Theory of Modeling and Sinnulation Integrating Discrete Event and Continuous Complex Dynamic Systems, second edition, by B. Zeigler, H. Praehofer, and T. C. Kim, New York Academic Press, 2000. 

Venkateswaran, J., Son, Y., and Jones, A. Hierarchical production planning using a hybrid system dynamic-discrete event simulation architecture. In Proceedings of the 2004 Winter Simulation Conference, volume 2, pages 1094-1102, 2004. 

The Petri Nets are a powerfirl method to approach various kinds of discrete event systems. They allow expressing efficiently a variety of phenomena such as sequences, parallelism, synchronized start and stop, etc. They get the advantage to be able to be used both for the modelling of a static structure and the dynamic behaviour. They allow in this way to examine not only the system architecture but also its temporal evolution andreactions to stimuli. This makes them very suitable for the dependability, safety and performance evaluation. CPN can be employed throughout the complete process development cycle one can thus preserve the same formalism to imderstand the architecture and the behaviour of the process (as well as the lunctional analysis). The driver model and various test scenarios can be also implemented in this formalism. 

Hybrid models may be described by a single set of DAEs including discrete state variables, e.g. switch state variables that change their discrete values at discrete events. That is, for each set of values of the discrete state variables representing a physically feasible system mode a set of DAEs is obtained that describes the dynamic behaviour in that system mode. Such a set of wyDAE systems... 

If the abstraction of instantaneous state transitions is adopted then a switching device such as a mechanical clutch causes a change in the model stmcture. As a result, storage elements may become dependent. That is, the number of state variables become mode-dependent. One approach to this problem is to detect discrete system mode changes while simulating the dynamic system behaviour, to use a different mathematical model for the dynamics in each mode and to re-initialise numerical integration at the event of a discrete mode change when necessary. In order to keep... 

Hybrid system model A hybrid system model makes use of the abstraction of instantaneous state changes and captures the dynamic behaviour in various system modes as well as discrete events. The latter ones are either controlled by local automata or take place autonomously and cause the system to instantaneously change from one mode into another. 

For dynamic systems with very fast state transitions in some components, e.g. caused by an abrupt fault, it is appropriate to model these state transitions as discrete events. That is, besides time continuous changes also discrete changes happen. In other words, there are a number of system modes and discrete changes... 

Zeigler, B. P. H. Praehofer T. G. Kim (2000). Theory of modeling and simulation integrating discrete event and continuous complex dynamic systems. San Diego, Academic Press. 

ABSTRACT In dependability studies of dynamic systems it is important to assess the probability of occurrence for the events sequences which describe the system evolution or which are critical for the mission of the system or for the humans and environment safety. In this paper we use the probabilistic languages framework in order to realize the quantitative assessment and we start by modeling the system as a finite state automaton. This is ulterior transformed in a probabilistic automaton using the embedded discrete Time Markov Chain. The determination of the languages afferents at each state of the automaton enable to calculate the probabihty of occurrence for every events sequence that can be subtract from these languages. 

To represent the dynamic behavior of the analyzed system, we need to rely on a simulation model. Several simulation model formalisms exist. Among them we can find PN. PN are a very powerM graphical and mathematical formalism used to representand analyze complex Discrete Event Systems (DES). They were first introduced in 1962 (Petri 1962). They represent a suitable formalism for performance analysis (Ajmone Marsan, Bobbio, Donatelli 1998). The power of PN relies on their flexibihty and their Evolution. In fact many classes of PN were introduced to cope with the increasing complexity of analyzed systems (Reisig, Wolfgang 2013). 

---