The GreatSPN tool: recent enhancements

GreatSPN is a tool that supports the design and the qualitative and quantitative analysis of Generalized Stochastic Petri Nets (GSPN) and of Stochastic Well-Formed Nets (SWN). The very first version of GreatSPN saw the light in the late eighties of last century: since then two main releases where developed and widely distributed to the research community: GreatSPN1.7 [13], and GreatSPN2.0 [8]. This paper reviews the main functionalities of GreatSPN2.0 and presents some recently added features that significantly enhance the efficacy of the tool

Stepwise reduction and approximation method for performance analysis of generalized stochastic petri nets

This thesis delves into the performance analysis of generalized stochastic Petri net (GSPN) model by using an approximation method: the Stepwise Reduction and Approximation (SRA) Method. The key point is that we are able to analyze a subnet in isolation by keeping its token flow direction and its sub-throughput equivalent with all the possible tokens entering into the subnet. The thesis first defines various kinds of potentially reducible subnets, subnet selection rules, approximation subnet construction rules, and reduction evaluation rules. Then corresponding to the possible subnets, the approximation method is used stepwisely until the interested measures are found with the global state space reduced. Two GSPN model examples from the literature are analyzed by using the proposed method. The approximation errors are given and discussed. Finally, the conclusions are drawn and future research is discussed

Approximation methods for stochastic petri nets

Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay equivalence often fails to converge, while flow equivalent aggregation can lead to potentially bad results if a strong dependence of the mean completion time on the interarrival process exists

Deadlock prevention and deadlock avoidance in flexible manufacturing systems using petri net models

Deadlocks constitute an important issue to be addressed in the design and operation of FMSs. It is shown that prevention and avoidance of FMS deadlocks can be implemented using Petri net models. For deadlock prevention, the reachability graph of a Petri net model of the given FMS is used, whereas for deadlock avoidance, a Petri-net-based online controller is proposed. The modeling of the General Electric FMS at Erie, PA, is discussed. For such real-world systems, deadlock prevention using the reachability graph is not feasible. A generic, Petri-net-based online controller for implementing deadlock avoidance in such real-world FMSs is developed

Getting the Priorities Right: Saturation for Prioritised Petri Nets

Prioritised Petri net is a powerful modelling language that often constitutes the core of even more expressive modelling languages such as GSPNs (Generalized Stochastic Petri nets). The saturation state space traversal algorithm has proved to be efficient for non-prioritised concurrent models. Previous works showed that priorities may be encoded into the transition relation, but doing so defeats the main idea of saturation by spoiling the locality of transitions. This paper presents an extension of saturation to natively handle priorities by considering the priority-related enabledness of transitions separately, adopting the idea of constrained saturation. To encode the highest priority of enabled transitions in every state we introduce edge-valued interval decision diagrams. We show that in case of Petri nets, this data structure can be constructed offline. According to preliminary measurements, the proposed solution scales better than previously known matrix decision diagram-based approaches, paving the way towards efficient stochastic analysis of GSPNs and the model checking of prioritised models

A Markov Chain Model Checker

Markov chains are widely used in the context of performance and reliability evaluation of systems of various nature. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both the discrete [17,6] and the continuous time setting [4,8]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen Twente Markov Chain Checker $(E \vdash MC^2$), where properties are expressed in appropriate extensions of CTL. We illustrate the general bene ts of this approach and discuss the structure of the tool. Furthermore we report on first successful applications of the tool to non-trivial examples, highlighting lessons learned during development and application of $(E \vdash MC^2$)

Simulation and numerical solution of stochastic Petri nets with discrete and continuous timing

We introduce a novel stochastic Petri net formalism where discrete and continuous phase-type firing delays can appear in the same model. By capturing deterministic and generally random behavior in discrete or continuous time, as appropriate, the formalism affords higher modeling fidelity and efficiencies to use in practice. We formally specify the underlying stochastic process as a general state space Markov chain and show that it is regenerative, thus amenable to renewal theory techniques to obtain steady-state solutions. We present two steady-state analysis methods depending on the class of problem: one using exact numerical techniques, the other using simulation. Although regenerative structures that ease steady-state analysis exist in general, a noteworthy problem class arises when discrete-time transitions are synchronized. In this case, the underlying process is semi-regenerative and we can employ Markov renewal theory to formulate exact and efficient numerical solutions for the stationary distribution. We propose a solution method that shows promise in terms of time and space efficiency. Also noteworthy are the computational tradeoffs when analyzing the embedded versus the subordinate Markov chains that are hidden within the original process. In the absence of simplifying assumptions, we propose an efficient regenerative simulation method that identifies hidden regenerative structures within continuous state spaces. The new formalism and solution methods are demonstrated with two applications