Samir M. Koriem

A Fuzzy Petri Net Tool For Modeling and Verification of Knowledge-Based Systems

A new method for automated modeling and verification of the knowledge-based systems (KBSs) is presented. It is based on a formal technique called modified fuzzy Petri nets (MFPNs). MFPNs combine the basic aspects of Petri net theory and the basic features of fuzzy set theory. The MFPN modeling technique proposed in this paper is concerned with the fuzzy decision making problems of the fuzzy rule tree structures. The proposed method is illustrated by its application to the airport control system as a practical KBS. Modeling methodology for conversion of the KBS into a MFPN model permits us to develop an effective MFPN verification technique. This technique has the capability of detecting and recovering the possible errors that can occur within the fuzzy rules of KBSs. The modeling and verification techniques we develop are quite general and can be applied to most practical fuzzy systems.

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

An interesting modeling problem is the need to model one or more of the system modules without exposition to the other system modules. This modeling problem arises due to our interest in these modules or incomplete knowledge, or inherent complexity, of the rest of the system modules. Whenever the performance measures (one or more) of the desired modules are available through previous performance studies, data sheets, or previous experimental works, the required performance measures for the whole system can be predicted from our proposed modeling technique. The incomplete knowledge problem of the dynamic behavior of some system modules has been studied by control theory. In the control area, such systems are known as partially observed discrete event dynamic systems, or POS systems. To the best of our knowledge, the performance evaluation of the POS system has not been addressed by the Petri net theory yet. Therefore, in this paper, we propose a new modeling technique for solving this kind of problem based on using the Petri net theory (i.e. Stochastic Reward Nets (SRNs)) in conjunction with the optimal control theory. In this technique, we develop an SRN Equivalent Model (EM) for the modeled system. The SRN EM-model consists of two main nets and their interface nets. One of the main nets represents the part(s) of interest or the known part(s) of the overall POS system that allows us to model its dynamic behavior and evaluate its performance measures. The other main net represents the remaining part(s) of the overall POS system that feeds the part(s) of interest. The well-known maximum principles have been used to develop an algorithm for determining the unknown transition rates of the proposed model. Numerical simulations are given to show that the proposed approach is more effective than the conventional modeling techniques, especially when dealing with systems having a large number of states.

A New Petri Net Modeling Technique for the Performance Analysis of Discrete Event Dynamic Systems

An interesting modeling problem is the need to model one or more of the system modules without exposition to the other system modules. This modeling problem arises due to our interest in these modules or incomplete knowledge, or inherent complexity, of the rest of the system modules. Whenever the performance measures (one or more) of the desired modules are available through previous performance studies, data sheets, or previous experimental works, the required performance measures for the whole system can be predicted from our proposed modeling technique. The incomplete knowledge problem of the dynamic behavior of some system modules has been studied by control theory. In the control area, such systems are known as partially observed discrete event dynamic systems, or POS systems. To the best of our knowledge, the performance evaluation of the POS system has not been addressed by the Petri net theory yet. Therefore, in this paper, we propose a new modeling technique for solving this kind of problem based on using the Petri net theory (i.e. Stochastic Reward Nets (SRNs)) in conjunction with the optimal control theory. In this technique, we develop an SRN Equivalent Model (EM) for the modeled system. The SRN EM-model consists of two main nets and their interface nets. One of the main nets represents the part(s) of interest or the known part(s) of the overall POS system that allows us to model its dynamic behavior and evaluate its performance measures. The other main net represents the remaining part(s) of the overall POS system that feeds the part(s) of interest. The well-known maximum principles have been used to develop an algorithm for determining the unknown transition rates of the proposed model. Numerical simulations are given to show that the proposed approach is more effective than the conventional modeling techniques, especially when dealing with systems having a large number of states. Keywords: Discrete event dynamic systems; stochastic reward nets; largeness problem; parameter identification; partially observed systems.

Development, Analysis and Evaluation of Performance Models for Mobile Multi-Agent Networks

Mobile agents have a number of interesting features such as creation, disposal of agents, execution of services at various network nodes, migration to other network nodes and communication with other agents. Such features are related to the performance area. Based on some examples, scenarios, or case studies, Petri net models (ordinary Petri net, colored Petri net or predicate/transition net), mathematical models, simulation models and queuing models have been developed in the literature. Such research works concentrate on studying the performance of mobile agent networks with much attention on deadlock problems, dynamic behavior problems and the calculation of response time problems. In order to better understand how to design distributed systems using the mobile agent paradigm and how to build a model with the capability of studying all such performance problems in an easy and a realistic way, we propose a new mobile agent performance model using the capability of the generalized stochastic Petri net (GSPN) modeling technique. We amended this model with new mobile agent behaviors to fully describe the dynamic behavior of the mobile agent network when it manipulates parallel/multiple agents, and uses some of the most important agent communications (e.g. remote, local, direct, indirect and parallel). Furthermore, the proposed model describes the creation process of new agents during the migration process, the execution of tasks among the network nodes, the way of handling the agent and its service task at each node and the interaction of a group of agents (as a collective result of the behaviors of each individual agent). To the best of our knowledge, such aspects are not included into one model because it is difficult to describe all these aspects into one model. Therefore, the developed GSPN mobile model gives the facility to study the performance of mobile agent networks with more details. In the performance analysis, we develop four studies to investigate the effect of different parameters such as agent communication time, size of mobile agent, number of mobile agents and number of hops on the performance of mobile agent networks. By performance of mobile agent networks, we mean the response time of the users request. To the best of our knowledge, such four performance studies are not investigated previously by the GSPN modeling technique. Finally, we propose a reduction-modeling methodology to facilitate the modeling process of the practical mobile agent network that incorporates a large number of network nodes, a large number of users, and subsequently a large number of parallel/multiple agents. Such methodology reduces the original model to a simpler one while preserving the basic features and properties of the original model.

R-nets for the performance evaluation of hard real-time systems

Time Petri net (TPN) is a powerful technique for studying the specification, verification, and temporal behavior of real-time distributed systems. For evaluating the performance of these systems, in this paper, we extend the TPNs by distributing probability density functions (pdfs) with uniform distributions over the time intervals associated with the transitions of the net. These pdfs are used to determine the state transition probabilities of branching from the current state to the possible next states. Thus, the reachability graph obtained from the extended TPN can be interpreted as a Markov process. We call this extended TPN a Real-net or R-net. To improve the modeling capability of R-net, we allow its structure to contain multiple tokens, multiple arcs, inhibitor arcs, and two types of transitions: real-time transitions and zero-time transitions. The R-net methodology is illustrated through a simple example. In view of the important applications for which R-net is used, a performance model for a fault-tolerant real-time multiprocessor (FRMP) system is developed and analyzed. The FRMP system is used as the central computer in air traffic control applications.

A new disk-based technique for solving the largeness problem of stochastic modeling formalisms

Stochastic modeling formalisms such as stochastic Petri nets, generalized stochastic Petri nets, and stochastic reward nets can be used to model and evaluate the dynamic behavior of realistic computer systems. Once we translate the stochastic system model to the underlying corresponding Markov Chain (MC), the developed MC grows wildly to several hundred thousands states. This problem is known as the largeness problem. To tolerate the largeness problem of Markov models, several iterative and direct methods have been proposed in the literature. Although the iterative methods provide a feasible solution for most realistic systems, a major problem appears when these methods fail to reach a solution. Unfortunately, the direct method represents an undesirable numerical technique for tolerating large matrices due to the fill-in problem. In order to solve such problem, in this paper, we develop a disk-based segmentation (DBS) technique based on modifying the Gauss Elimination (GE) technique. The proposed technique has the capability of solving the consequences of the fill-in problem without making, assumptions about the underlying structure of the Markov processes of the developed model. The DBS technique splits the matrix into a number of vertical segments and uses the hard disk to store these segments. Using the DBS technique, we can greatly reduce the memory required as compared to that of the GE technique. To minimize the increase in the solution time due to the disk accessing processes, the DBS utilizes a clever management technique for such processes. The effectiveness of the DBS technique has been demonstrated by applying it to a realistic model for the Kanban manufacturing system.

A generalized stochastic high-level Petri net model for performance analysis

Abstract: We present a generalized stochastic high-level Petri net (GSHLPN) model for evaluating the performance of parallel/distributed systems. In our model, we have classified the transitions of the predicate/transition nets (PrT-nets) into two types: timed predicate transitions with exponentially distributed firing times and immediate predicate transitions with zero firing times. Also, the PrT-nets are extended by including inhibitor predicate arcs. The motivation for introducing these new constructs in the GSHLPN model is discussed. The model is developed to be a hybrid of the PrT-net and generalized stochastic Petri net models. We define the GSHLPN model and show how performance estimates are obtained from the GSHLPN model. To manage the complexity of large systems, we have reduced the size of the reachable state space by combining the GSHLPN model with the compound marking technique (CMT). We show how the GSHLPN model with the CMT can be useful for the performance analysis of complex systems, such as hypercube multicomputer systems. Finally, we investigate another approach to further reduce the size of the state space of this model by applying two different types of aggregation techniques on the GSHLPN model: time scale decomposition technique and CMT. This aggregation concept is illustrated through the example of a degradable Star multicomputer system.

Modeling Concurrent, Sequential, Storage, Retrieval, and Scheduling Activities of Multimedia Systems

As real-time systems continue to grow, performance evaluation plays a critical role in the design of these systems since the computation time, the service time, and the responsive actions must satisfy the time constraints. One of these systems is the real-time distributed multimedia-on-demand (MOD) service system. The MOD system usually fails when it misses a task deadline. The main units of the MOD system usually communicate with each other and work concurrently under timing constraints. The MOD system is designed to store, retrieve, schedule, synchronize, and communicate objects comprised of mixed data types including images, text, video, and audio, in real-time. In the MOD system, such data types represent the main concept of movie files. Modeling of such concurrency, communication, timing, and multimedia service (e.g. store, retrieve) is essential for evaluating the real-time MOD system. To illustrate how to model and analyze the important multimedia aspects of the MOD system, we use the Real-net (R-net) modeling technique. We choose R-net as an extension of Time Petri Net due to its ability to specify hard real-time process interaction, represent the synchronization of multimedia entities, describe concurrent multimedia activities, and illustrate the inter-process timing relationships as required for multimedia presentation. Based on modular techniques, we build three R-net performance models for describing the dynamic behavior of the MOD service system. The first model adopts the Earliest Deadline First (EDF) disk scheduling algorithm. The other models adopt the Scan-EDF algorithm. These algorithms help us to illustrate how the real-time user requests can be satisfied within the specified deadline times. Since R-nets are amenable to analysis including Markov process modeling, the interesting performance measures of the MOD service system such as the quality of service, the request response time, the disk scheduling algorithm time, and the actual retrieval time can be easily computed. In the performance analysis of the MOD models, we use our R-NET package.

A New Disk-based Technique for Solving the Largeness Problem of Stochastic Modeling Formalisms

Stochastic modeling formalisms such as stochastic Petri nets, generalized stochastic Petri nets, and stochastic reward nets can be used to model and evaluate the dynamic behavior of realistic computer systems. Once we translate the stochastic system model to the underlying corresponding Markov Chain (MC), the developed MC grows wildly to several hundred thousands states. This problem is known as the largeness problem. To tolerate the largeness problem of Markov models, several iterative and direct methods have been proposed in the literature. Although the iterative methods provide a feasible solution for most realistic systems, a major problem appears when these methods fail to reach a solution. Unfortunately, the direct method represents an undesirable numerical technique for tolerating large matrices due to the fill-in problem. In order to solve such problem, in this paper, we develop a Disk-Based Segmentation (DBS) technique based on modifying the Gauss Elimination (GE) technique. The proposed technique has the capability of solving the consequences of the fill-in problem without making assumptions about the underlying structure of the Markov processes of the developed model. The DBS technique splits the matrix into a number of vertical segments and uses the hard disk to store these segments. Using the DBS technique, we can greatly reduce the memory required as compared to that of the GE technique. To minimize the increase in the solution time due to the disk accessing processes, the DBS utilizes a clever management technique for such processes. The effectiveness of the DBS technique has been demonstrated by applying it to a realistic model for the Kanban manufacturing system.