The term ‘discrete event system’ is supposed to be commonly used in a narrow meaning in order to refer to a 'process' simulation, where the dynamics of the system is represented as a sequence of operations (arrival, delay, capturing the resource division, etc.) by some of the entities. They can represent clients, documents, calls, data packets, vehicles, etc. These entities are generally acknowledged to be passive for they do not control their dynamics. However, they are likely to have certain attributes that affect the process of treatment, for instance, a type of a call, the complexity of work, etc. or to accumulate statistics (total waiting time, cost).
It is known that the essential purpose of the fuzzy discrete events systems mainly consists in the fact of reproduction of interactions involving the components. Besides, it deals with the studying of behavior samples and functionality of the system under the study. To achieve this, it is important to emphasize on the state of the system under analysis and describe the necessary amount of steps that have a tendency to carry it from one state to another. Thus, the aim of the literature review is to study and analyze the essential findings in the field of the fuzzy discrete event system. It is assumed that the detectability of the discrete event system is of great importance due to the fact that it contributes to the analysis of the most important stages of the process as well as its subsequent and current states.
Findings in the Generalized Detectability for Discrete Event Systems
The fuzzy discrete events system is known to be in a certain state when all of its key components are generally agreed to be compatible with the range of values that describe the characteristics of this state. Thus, the fuzzy discrete events system can be characterized with one of the most significant terms such as imitation, which, in practice, presupposes a dynamic 'portrait' of states of the system in time, i.e. the playback behavior sample of the system which is being observed over time.
The investigation conducted by Shu and Lin (2011) demonstrated that the discrete systems of a non-deterministic character are of greater importance that deterministic discrete systems. This fact has been proved by the detectability checking polynomial algorithms. The mechanism of the research showed that the implementation of the new tool is the best concept which has been referred to as a detector. This fact permitted the scholars extend on the D-detectability for a larger amount of applications (Shu and Lin, 2011).
Shu and Lin (2011) are convicted that the fact of applying the approach of generalized detectability for the discrete events system describes the actions which have a tendency to involve necessary elements of the system. In addition to this, it sets conditions that help determine the beginning and end of the action. According to the authors, the events that contribute to the start or completion of the action, which have not been planned by the developer model, have a tendency to be initiated by the conditions defined for this particular action. Terms of the beginning or the end of an action are generally checked after the next advancement of simulation time. If the specified conditions are met, a corresponding action has to take place. To make every action performed throughout the model, detectability for the discrete event system is usually performed for all conditions which have been set for each action advancing simulation time (Shu and Lin, 2011).
The approach provides a simple scanning, the active circuit simulation to solve a number of problems. It is most effective for situations in which the duration of action is determined depending on whether the system state satisfies predetermined conditions. However, since it is necessary to scan the environment for each action, the approach of scanning activities is less effective compared to event-driven approach, and therefore is of limited use in discrete simulation.
To analyze the processes occurring in the world, in both local and global meanings, it is sometimes convenient to consider them as a sequence of individual important moments that are generally referred to as events (Shu and Lin, 2011). The approach to the construction of simulation models are invited to provide real action. Such events is called 'discrete event' simulation.
In addition to this, Shu and Lin (2011) claim that before using this approach, it is highly necessary to ensure that the system is modeled in terms of the project objectives described as a sequence of operations. In these cases, it is always important to keep in mind alternative approaches; for example, if it is easier to describe behavior of each object individually or separately than to try through a common process, the solution may be agent-based modeling. Similarly, if there is interest in the overall quantitative assessment processes only, but not in the dynamics of individual objects, it may be convenient to describe the system in terms of system dynamics. Such systems have a tendency to support all three approaches, so that it becomes possible to freely experiment with the level of abstraction in a wide range staying within one tool.
Modeling and Control of Fuzzy Discrete System
The process of modeling and control of fuzzy discrete system is known to be applied in the middle or lower level of abstraction: each object is modeled individually as a separate entity, where various details compose a 'physical layer' (geometry acceleration/deceleration) are, as a rule, omitted. This approach is widely used in modeling business processes, production, logistics, health care, etc.
The investigation conducted by Lin and Ying (2002) can be characterized as the basis for the development of detectability of the discrete events system. The methodology used for discrete event simulation consisted in the nature of an object and its required behavior (and its specifications) in the design of automation systems, which are presupposed to be operating in real time. The methodology is based on the analysis of functionality and consistency model: structured discrete event system.
According to some investigations conducted in the area of the fuzzy discrete events system, it is possible to model and control by identifying changes in their essential stages of accomplishment of a necessary amount of events (Lin and Ying, 2002). In this particular case, the investigator's task has to be focused on depicting the events that are actually meant to change the state of the system(s) and the definition of logical relationships between them. Simulation of the system is usually implemented by performing a time-ordered sequence of logically related events (Lin and Ying, 2002).
To understand the fuzzy discrete event system, it is necessary to illustrate and analyze its activity. Hence, it is important to consider the example of a bank with a cashier. Clients go to the bank, after a possible expectations served as a cashier, and then they leave. System status in this example is totally dependable on the state of the cashier and the number of outstanding customer services, which had been once elaborated. They are known to remain unchanged for a certain period of time except when a client comes in or leaves. Therefore, the event system model in this case consists of a description of the actions that have a tendency to occur at the time of arrival and closure of the next customer service. Since the change in the system state is, in practice, able to occur only at these times, the use of the event from its so-called 'arrival' or 'start' and the 'end of service' is supposed to provide full reproduction of the system dynamics.
The first step presupposes the arrival of the next customer. This simulation with repeated reference to a certain procedure allows organizing a continuous stream of arrivals. Behavior sample of a customer is totally dependable on the state of the system at the current time, i.e. at this very moment. If the cashier is busy, the customer arrives in the queue. Consequently, the state of the system has a tendency to undergo a change, which is caused by the increasing number of customers waiting in the unit. If the cashier is free, the client who came is mostly immediately served. Thus, the status of the system is again changed: it is performed by passing the cashier in a state of 'busy.' In addition, the event is scheduled to be the 'end of service' for the client at the time to the current time plus the time it takes a cashier service.
The investigation which had been conducted by Lin and Ying (2002) discusses the aspects of modeling network systems. It demonstrates that the network features are most important for the adequate preparation of mathematical models. These features significantly distinguished the proposed approach further by modeling techniques generally accepted, for example, in the theory of systems and control theory. The basic tools are integral-differential equations, methods of probability theory, mathematical statistics, and stochastic processes.
The authors highlights that the theory of systems and control theory in the usual description of the system are mainly regulated by the process of 'input-output.' Besides, they have a tendency to change the output relative to the input. In other words, the space of states of a fixed transfer function in the matrix form. Most systems that are subject to simulation are non-linear, and, in this case, substantial efforts are aimed at simulation of linearization systems performed by solving a system of differential equations in the matrix form. The simulation results are reduced phase space of the simulated systems and characteristics of control and regulation units.
In this case, the modeling methods are generators of some types of random processes (imitating the times of receipt of applications for service), and the simulation results are (often average) residence times in the application queue, system, service times, the probability of staying in the queue, the likelihood of service (for some period), and other.
The problem analysis represented in the literature review on the discrete event system is determined by the plurality of discrete states and the event flow. These results are expected to bring new possibilities in the design of logic-based management of the discrete event systems. Raising the question of the existence of a problem of synthesis, it is important to provide an analytical answer to the basic logic control question, ‘How the specified object and required specification are solvable?’ Moreover, if the answer is found to be negative, then the question of any changes in specifications has to be studied more precisely. This fact presupposes that the constraints of the behavior of the object control are solvable. Potentially new opportunities make a breakthrough in the management of the logic in terms of increasing its reliability. This is the main manifestation of detectability of the fizzy discrete event system.