Special Issue on Stochastic Petri Nets Christoph Lindemann University of Dortmund Department of Computer Science August-Schmidt-Str. 12 44227 Dortmund, Germany E-math cl@cs.uni-dortmund.de http://ls4-www.informatik.uni-dortmund.de/home/lindemann/ The introduction of stochastic Petri nets (Molloy 1982) and generalized stochastic Petri nets (GSPNs, Ajmone Marsan, Balbo, Conte 1984) as high-level representations of Markov chains constituted a major result in methodological performance evaluation in the 1980s. Generalized stochastic Petri nets have matured over the years and a number of important extensions and analysis methods have been introduced. Deterministic and stochastic Petri nets (DSPNs, Ajmone and Chiola, 1987) constitute a class of nonMarkovian stochastic Petri nets because, due to the presence of not only exponential but also deterministic delays, their underlying stochastic process is either a Markov regenerative process (Choi, Kulkarni, Trivedi 1994) or a generalized semi-Markov process (Lindemann, Shedler 1996). In general, extensions to GSPNs increase their modeling power (i.e., allow additionally the representation of non-exponentially distributed delays) or provide means for a more compact graphical model representation. Further research in analysis techniques include the exploitation of hierarchical structures in GSPNs for reducing the CPU solution time and memory space required for model analysis. The popularity of stochastic Petri nets also significantly gained by the availability of software packages with user-friendly graphical interfaces. Such packages allow easy model construction, graphical model animation by playing the token game, and automated model solution. Thus, the mathematics necessary for analyzing a model can be completely hidden to the user. As a consequence, stochastic Petri nets are attractive for engineers who are evaluating design alternatives in early stages in the design process of computer systems and communication networks. This special issue contains four invited papers on stochastic Petri nets. Two papers review recent methodological results and provide illustrating examples. The two other papers present applications of stochastic Petri nets to performance modeling of communication systems. Three monographs dealing with stochastic Petri nets have been published in recent years. Thus, this issue concludes with short descriptions of these books taken from their covers. The first paper by Buchholz and Kemper presents a methodology for automatically partitioning a GSPN into a set of individual components (i.e., subnets) with asynchronuous communication. Subsequently, the resulting hierarchical model structure can be exploited for reducing the CPU solution time of very large GSPN models. The second methodological paper by Fricks~ Puliafito~ Telek~ and Trivedi deals with numerical analysis methods for a class of non-Markovian stochastic Petri nets called Markov regenerative stochastic Petri nets. They recall the features of Markov regenerative stochastic Petri nets and present a number of application examples taken from computer systems reliability analysis. The third paper authored by Ajmone Marsan and Gaeta reviews their work in performance analysis of ATM networks. They illustrate how to model and analyze ATM networks with GSPNs and a special class of high-level stochastic Petri nets, called stochastic well-formed nets. The fourth paper by Ost and Haverkort introduces a class of generalized stochastic Petri nets that may have an infinite number of states, though, can be efficiently analyzed numerically by exploiting a quasi-birth-death structure in the underlying Markov chain. The proposed class of stochastic Petri nets is employed for analyzing the performance of the TCP slow-start congestion avoidance mechanism considering a typical World Wide Web workload. I would like to thank the invited authors for their excellent contributions. I hope that you enjoy reading the papers as much as I did!

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