Modelling and Simulation of Queuing Models through the concept of Petri Nets

In recent years Petri Nets has been in demand due to its visual depiction. Petri Nets are used as an effective method for portraying synchronization, a concurrency between different system activities. In queuing models Petri networks are used to represent distributed modeling of the system and thus evaluate their performance. By specifying suitable stochastic Petri Nets models, the authors concentrate on representing multi-class queuing systems of various queuing disciplines. The key idea is to define SPN models that simulate a given queue discipline 's behavior with some acceptable random choice. Authors have find system queuing with both a single server and multiple servers with load-dependent service rate. Petri networks in the queuing model have enhanced scalability by combining queuing and modeling power expressiveness of 'petri networks.' Examples of application of SPN models to performance evaluation of multiprocessor systems demonstrate the utility and effectiveness of this modeling method. In this paper, authors have made use of Stochastic Petri nets in queuing models to evaluate the performance of the system

Mechatronic system reliability evaluation using petri networks and PHI2 method

In this paper, we propose an approach allowing us to study the performance of a mechatronic system using Petri Nets in which we use particularly the PH12 method for the evaluation of failure probability of a mechanical component. The Petri Nets are used to describe the process of sequential dynamics of a system. Deterministic stochastic Petri networks have been implemented to introduce random phenomena following the laws of distribution. After the functional and dysfunctional modeling of a mechatronic system using Petri Nets, it is necessary to associate times to different transitions of the network. It is necessary to take into account a physical modeling in order to determine functional times of different components which are associated with functional transitions. Regarding dysfunctional transitions, the laws of probability are assigned depending on the knowledge concerning the reliability of different types of components: the exponential law for electronic devices, the Jelinski-Moranda model for software, etc. For the mechanical components, we use the PH12 method for the evaluation of the time variant failure probability

Using the probabilistic evaluation tool for the analytical solution of large Markov models

Stochastic Petri net-based Markov modeling is a potentially very powerful and generic approach for evaluating the performance and dependability of many different systems, such as computer systems, communication networks, manufacturing systems, etc. As a consequence of their general applicability, SPN-based Markov models form the basic solution approach for several software packages that have been developed for the analytic solution of performance and dependability models. In these tools, stochastic Petri nets are used to conveniently specify complicated models, after which an automatic mapping can be carried out to an underlying Markov reward model. Subsequently, this Markov reward model is solved by specialized solution algorithms, appropriately selected for the measure of interest. One of the major aspects that hampers the use of SPN-based Markov models for the analytic solution of performance and dependability results is the size of the state space. Although typically models of up to a few hundred thousand states can conveniently be solved on modern-day work-stations, often even larger models are required to represent all the desired detail of the system. Our tool PET (probabilistic evaluation tool) circumvents problems of large state spaces when the desired performance and dependability measure are transient measures. It does so by an approach named probabilistic evaluatio

Validating the behavior of a supervised system using petri nets

A fundamental issue of production systems is the validating of their output. In order to obtain this output, mathematical models such as Petri nets are used to validate concurrent behaviors, presence/absence of blockings, and activity synchronization, among other aspects of this industrial process. Despite its advantages, the use of Petri nets does not allow for the evaluation of other important issues in manufacturing processes, or how to manage them. Therefore, stochastic system simulation and agent technology are used in the experiments to obtain other performance measures. A combination of Petri nets, multi-agent systems, and stochastic systems is used within a proposed method for validating the output of production systems. This paper shows how this method is used in an academic manufacture sample

Performance Bounds for Synchronized Queueing Networks

Las redes de Petri estocásticas constituyen un modelo unificado de las diferentes extensiones de redes de colas con sincronizaciones existentes en la literatura, válido para el diseño y análisis de prestaciones de sistemas informáticos distribuidos. En este trabajo se proponen técnicas de cálculo de cotas superiores e inferiores de las prestaciones de redes de Petri estocásticas en estado estacionario. Las cotas obtenidas son calculables en tiempo polinómico en el tamaño del modelo, por medio de la resolución de ciertos problemas de programación lineal definidos a partir de la matriz de incidencia de la red (en este sentido, las técnicas desarrolladas pueden considerarse estructurales). Las cotas calculadas dependen sólamente de los valores medios de las variables aleatorias que describen la temporización del sistema, y son independientes de los momentos de mayor orden. Esta independencia de la forma de las distribuciones de probabilidad asociadas puede considerarse como una útil generalización de otros resultados existentes para distribuciones particulares, puesto que los momentos de orden superior son, habitualmente, desconocidos en la realidad y difíciles de estimar. Finalmente, las técnicas desarrolladas se aplican al análisis de diferentes ejemplos tomados de la literatura sobre sistemas informáticos distribuidos y sistemas de fabricación. ******* Product form queueing networks have long been used for the performance evaluation of computer systems. Their success has been due to their capability of naturally expressing sharing of resources and queueing, that are typical situations of traditional computer systems, as well as to their efficient solution algorithms, of polynomial complexity on the size of the model. Unfortunately, the introduction of synchronization constraints usually destroys the product form solution, so that general concurrent and distributed systems are not easily studied with this class of models. Petri nets have been proved specially adequate to model parallel and distributed systems. Moreover, they have a well-founded theory of analysis that allows to investigate a great number of qualitative properties of the system. In the original definition, Petri nets did not include the notion of time, and tried to model only the logical behaviour of systems by describing the causal relations existing among events. This approach showed its power in the specification and analysis of concurrent systems in a way independent of the concept of time. Nevertheless the introduction of a timing specification is essential if we want to use this class of models for the performance evaluation of distributed systems. One of the main problems in the actual use of timed and stochastic Petri net models for the quantitative evaluation of large systems is the explosion of the computational complexity of the analysis algorithms. In general, exact performance results are obtained from the numerical solution of a continuous time Markov chain, whose dimension is given by the size of the state space of the model. Structural computation of exact performance measures has been possible for some subclasses of nets such as those with state machine topology. These nets, under certain assumptions on the stochastic interpretation are isomorphic to Gordon and Newell's networks, in queueing theory terminology. In the general case, efficient methods for the derivation of performance measures are still needed. Two complementary approaches to the derivation of exact measures for the analysis of distributed systems are the utilization of approximation techniques and the computation of bounds. Approximate values for the performance parameters are in general more efficiently derived than the exact ones. On the other hand, "exactness" only exists in theory! In other words, numerical algorithms must be applied in practice for the computation of exact values, therefore making errors is inevitable. Performance bounds are useful in the preliminary phases of the design of a system, in which many parameters are not known accurately. Several alternatives for those parameters should be quickly evaluated, and rejected those that are clearly bad. Exact (and even approximate) solutions would be computationally very expensive. Bounds become useful in these instances since they usually require much less computation effort. The computation of upper and lower bounds for the steady-state performance of timed and stochastic Petri nets is considered in this work. In particular, we study the throughput of transitions, defined as the average number of firings per time unit. For this measure we try to compute upper and lower bounds in polynomial time on the size of the net model, by means of proper linear programming problems defined from the incidence matrix of the net (in this sense, we develop structural techniques). These bounds depend only on the mean values and not on the higher moments of the probability distribution functions of the random variables that describe the timing of the system. The independence of the probability distributions can be viewed as a useful generalization of the performance results, since higher moments of the delays are usually unknown for real cases, and difficult to estimate and assess. From a different perspective, the obtained results can be applied to the analysis of queueing networks extended with some synchronization schemes. Monoclass queueing networks can be mapped on stochastic Petri nets. On the other hand, stochastic Petri nets can be interpreted as monoclass queueing networks augmented with synchronization primitives. Concerning the presentation of this manuscript, it should be mentioned that chapter 1 has been written with the object of giving the reader an outline of the stochastic Petri net model: its definition, terminology, basic properties, and related concepts, together with its deep relation with other classic stochastic network models. Chapter 2 is devoted to the presentation of the net subclasses considered in the rest of the work. The classification presented here is quite different from the one which is usual in the framework of Petri nets. The reason lies on the fact that our classification criterion, the computability of visit ratios for transitions, is introduced for the first time in the field of stochastic Petri nets in this work. The significance of that criterion is based on the important role that the visit ratios play in the computation of upper and lower bounds for the performance of the models. Nevertheless, classical important net subclasses are identified here in terms of the computability of their visit ratios from different parameters of the model. Chapter 3 is concerned with the computation of reachable upper and lower bounds for the most restrictive subclass of those presented in chapter 2: marked graphs. The explanation of this fact is easy to understand. The more simple is the model the more accessible will be the techniques an ideas for the development of good results. Chapter 4 provides a generalization for live and bounded free choice nets of the results presented in the previous chapter. Quality of obtained bounds is similar to that for strongly connected marked graphs: throughput lower bounds are reachable for bounded nets while upper bounds are reachable for 1-bounded nets. Chapter 5 considers the extension to other net subclasses, like mono-T-semiflow nets, FRT-nets, totally open deterministic systems of sequential processes, and persistent nets. The results are of diverse colours. For mono-T-semiflow nets and, therefore, for general FRT-nets, it is not possible (so far) to obtain reachable throughput bounds. On the other hand, for bounded ordinary persistent nets, tight throughput upper bounds are derived. Moreover, in the case of totally open deterministic systems of sequential processes the exact steady-state performance measures can be computed in polynomial time on the net size. In chapter 6 bounds for other interesting performance measures are derived from throughput bounds and from classical queueing theory laws. After that, we explore the introduction of more information from the probability distribution functions of service times in order to improve the bounds. In particular, for Coxian service delay of transitions it is possible to improve the throughput upper bounds of previous chapters which held for more general forms of distribution functions. This improvement shows to be specially fruitful for live and bounded free choice nets. Chapter 7 is devoted to case studies. Several examples taken from literature in the fields of distributed computing systems and manufacturing systems are modelled by means of stochastic Petri nets and evaluated using the techniques developed in previous chapters. Finally, some concluding remarks and considerations on possible extensions of the work are presented

The use of Petri nets for modeling pipelined processors

This paper discusses the use of Petri Nets for modeling and analyzing pipelined processors. Petri Nets are particularly well-suited to modeling the synchronization, buffering, resource contention and delicate timing so common in pipelined processors. Tools for simulating, animating and analyzing the behavior of the models are described. The usefulness of the tools and the analysis methods they support in evaluating the performance and analyzing the detailed timing of pipelined microprocessors is illustrated through an example

Evaluation of software architecture using fuzzy colored Petri nets

Software Architecture (SA) is one of the most important artifacts for life cycle of a software system because it incorporates some important decisions and principles for the system development. On the other hand, developing the systems based on uncertain and ambiguous requirement has been increased, significantly. Therefore, there have been significant attentions on SA requirements. In this paper, we present a new method for evaluation of performance characteristics based on a use case, response time, and queue length of SA. Since there are some ambiguities associated with considered systems, we use the idea of Fuzzy UML (F-UML) diagrams. In addition, these diagrams have been enriched with performance annotations using proposed Fuzzy-SPT sub profile, the extended version of SPT profile proposed by OMG. Then, these diagrams are mapped into an executable model based on Fuzzy Colored Petri Nets (FCPN) and finally the performance metrics are calculated using the proposed algorithms. We have implemented CPN-Tools for creating and evaluating the FCPN model