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].

A Toolbox for Functional and Quantitative Analysis of DEDS

The analysis of stochastic marked graphs is considered. The underlying idea is to decompose the marked graph into subnets, to generate state spaces and transition matrices for these isolated parts and then to represent the generator matrix underlying the complete net by means of much smaller subnet matrices combined via tensor operations. Based on this matrix representation, efficient numerical analysis techniques can be used to compute the stationary solution. Furthermore we propose on approximation technique which is similar to known approximate solution techniques for this kind of nets, but our approach is completely integrated in the structured description of the generator matrix. This allows an estimation of the approximation error and the usage of the approximate results as an initial guess for a subsequent iterative analysis, such that the number of required iterations is often significantly reduced.

/pdf/numerical-analysis-of-stochastic-marked-graph-nets-4rarnbqng1.pdf

Numerical analysis of stochastic marked graph nets

We present a new approximate solution technique for the numerical analysis of stochastic Petri nets and related models. The approach combines numerical iterative solution techniques and fixed point computations using the complete knowledge of state space and generator matrix. In contrast to other approximation methods, the proposed method is adaptive by considering states with a high probability in detail and aggregating states with small probabilities. Probabilities are approximated by the results derived during the iterative solution. Thus, a maximum number of states can be predefined and the presented method automatically aggregates states such that the solution is computed using a vector of a size smaller or equal to the maximum. By means of non-trivial examples it is shown that the approach computers good approximations with a low effort for many models.

Adaptive decomposition and approximation for the analysis of stochastic petri nets

Stochastic timed Petri nets are a useful tool in the performance analysis of concurrent systems such as parallel computers, communication networks and flexible manufacturing systems In general, performance measures of stochastic timed Petri nets are difficult to obtain for practical problems due to their sizes In this paper, we provide a method to efficiently compute upper and lower bounds for the throughputs and mean token numbers for a large class of stochastic timed Petri nets Our approach is based on uniformization technique and linear programming

Performance analysis of stochastic timed Petri nets using linear programming approach

An adaptive aggregation/disaggregation algorithm for hierarchical Markovian models

Complete decomposition is a new strategy for evaluating the performance of a network of generalized service centers, represented in the notation of Generalized Stochastic Petri Nets (GSPNs). Each service center can have arbitrary internal structure (including internal parallelism), but it must conserve tokens at the boundaries, and its inputs must be i/o-connected to its outputs. Routing between centers can depend on the state of the departure center. The new method adapts a delay equivalence decomposition technique used previously. Within this framework, it reduces the solution complexity of the auxiliary models which must be solved in the iteration. This new method is applied to a scalable model for computer system performance. >

Complete decomposition of stochastic Petri nets representing generalized service networks

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Complete decomposition of stochastic Petri nets representing generalized service networks