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Queueing Petri Nets-A formalism for the combined qualitative and quantitative analysis of systems

System analysis is often needed with respect to both qualitative and quantitative aspects. In recent decades, several formalisms have been developed that attempt to combine these aspects in one description. Present emphasis is on stochastic Petri nets. One disadvantage of these formalisms is the difficulties when describing scheduling strategies with Petri net elements. A new version of queuing Petri nets (QPNs), which combines queuing networks and Petri nets, aiming at eliminating these disadvantages is described. The new version also exhibits the modeling of timed transitions and timeless queues for describing pure scheduling mechanisms. QPNs are a superset of queueing networks and (generalized stochastic) Petri nets. The analysis of QPNs is discussed, and it is shown that efficient analysis techniques from Petri net theory can be exploited for analysis of QPNs, thus supporting the general objective of combining Petri net and queueing network formalisms.<<ETX>>

Stochastic Petri Nets

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A Toolbox for Functional and Quantitative Analysis of DEDS

We present a toolbox for the combined functional and quantitative analysis of discrete event dynamic systems (DEDS) on the basis of a common model interchange format, the Abstract Petri Net Notation (APNN,[5]). This format covers a fair amount of Petri net like formalisms as well as certain Queueing network concepts. At a lower level the toolbox uses a format for communicating stochastic automata, a notation to describe DEDS at a state transition level. For a more detailed description of the toolbox we refer to [3].

QPN-Tool for the Specification ans Analysis of Hierarchically Combined Queueing Petri Nets

This article describes a new version of the QPN-Tool now supporting specification and analysis of hierarchically combined Queueing Petri nets (HQPNs). HQPNs are an extension of QPNs allowing the refinement of places by QPN subnets and/or queues. HQPNs can be analysed with respect to qualitative and quantitative aspects. Quantitative analysis is based on numerical Markov chain analysis. In contrast to conventional techniques the Markov chain underlying a HQPN is analysed by an approach exploiting the hierarchical structure of the model which results in a tensor representation of the generator matrix. This technique extends the size of solvable state spaces by one order of magnitude. Qualitative analysis of HQPNs relies on efficient analysis techniques based on Petri net theory. The new version of QPN-Tool implements the above analysis approaches supported by a graphical interface for a convenient specification of complex models.

Analysis of Petri Nets with a Dynamic Priority Method

In this paper we propose an efficient reachability set based Petri net analysis by introducing dynamic priorities which decreases the number of reachable markings in most cases. It is proved that for specific dynamic priority relations certain properties (especially liveness and the existence of home states) do hold if and only if these properties do also hold for the Petri net without priorities. We present an algorithm based on these priority relations additionally exploiting T-invariants thus being able to benefit from the structure of the net.

An Efficient Polynomial-Time Algorithm to Decide Liveness and Boundedness of Free-Choice Nets

In [3] J. Esparza presented an interesting characterization of structurally live and structurally bounded Free-Choice Nets (LBFC-Nets). Exploiting this characterization in combination with new results and refined algorithms the authors formulate an O(¦P∥T∥F¦) algorithm deciding whether a Free-Choice Net is a LBFC-Net or not. Furthermore the algorithm contains a simple and efficient test to ensure that the initial marking of a LBFC-Net is live. This test is based on a simplified characterization of liveness for LBFC-Nets.

On the analysis of Petri nets with static priorities

Priority specifications offer a convenient description technique to resolve conflicts in favour of particular actions. Apart from being employed for the specification of the functional behaviour of a system, priorities have also become important in the field of performance analysis using stochastic Petri nets. Here they are implicitly given due to the separation of transitions into immediate and timed. In the performance analysis of such stochastic Petri nets specific properties, like liveness and existence of home states, are of major interest, because they ensure the applicability of a Markovian based analysis. Since several efficient analysis techniques have been developed for Petri nets without priorities, our interest is in using these techniques also for the priority case. This paper shows that positive properties of a net such as liveness and the existence of home states do also hold for the net with static priorities, if a simple condition is imposed on the priority relation.

Queueing Petri nets with product form solution

The product form results recently published for stochastic Petri nets are combined with the well-known product form results for queueing networks in the model formalism of queueing Petri nets yielding the class of product form queueing Petri nets. This model class includes stochastic Petri nets with product form solution and BCMP queueing networks as special cases. We introduce an arrival theorem for the model class and present an exact aggregation approach extending known approaches from queueing networks.

ProFiDo - The Processes Fitting Toolkit Dortmund

This paper describes the Java-based toolkit ProFiDo which integrates several tools for fitting input models. Currently supported are command line tools for fitting probability distributions, ARIMA processes and Markovian arrival processes. The toolkit provides a graphical user interface which allows for the specification of workflows that describe the different steps of data preprocessing, parameter fitting and result visualization. The basis for the interoperability of the different tools is an XML based interchange format for the specification of various types of processes. An XML based configuration file supports the extension of the toolkit by integrating additional fitting methods or analysis approaches.

A Framework for Simulation Models of Service-Oriented Architectures

Service-Oriented Architectures (SOA) are one of the main paradigms for future software systems. Since these software systems are composed of a large number of different components it is non trivial to assure an adequate Quality of Service (QoS) of the overall system and performance analysis becomes an important issue. To consider performance issues early in the development process, a model based approach becomes necessary which has to be embedded into the development process of SOA to avoid overhead and assure consistency. In particular the specification of the software system should be used as a base for the resulting performance model. However, since common specification techniques for SOA are very high level, many details have to be added to come to an executable simulation model which is often needed for a detailed analysis of performance or dependability. This paper presents an approach which combines an extended version of process chains to describe the SOA components and some quantitative specifications at the higher levels. For the modelling of the detailed architecture and protocols the simulation tool OMNeT++ is used. Both modelling levels are combined resulting in an executable simulation model for the whole architecture.