Stochastic Petri Nets Modelling, Stability, Simulation - Haas, Peter J. (Springer New York, 2002)
This book was motivated by a desire to bridge the gap between two important areas of research related to the design and operation of engineering and information systems. The first area concerns the development of mathematical tools for formal specification of complex probabilistic systems, with an eye toward subsequent simulation of the resulting stochastic model on a computer. The second area concerns the development of methods for analysis of simulation output. Research on modelling techniques has been driven by the ever-increasing size and complexity of computer, manufacturing, transportation, workflow, and communication systems. Many engineers and systems designers now recognize that the use of formal models has a number of advantages over simply writing complicated simulation programs from scratch. Not only is it much easier to generate software that is free of logical errors, but various qualitative system properties— absence of deadlock, impossibility of reaching catastrophic states, and so forth— can be verified far more easily for a formal model than for an ad-hoc computer program. Indeed, certain system properties can sometimes be verified automatically. Our focus is on systems that can be viewed as making state transitions when events associated with the occupied state occur. More specifically, we consider discrete-event systems in which the stochastic state transitions occur only at an increasing sequence of random times. The "Bedienungsprozess" (service process) framework, developed by König, Matthes, and Nawrotzki in the 1960s and early 1970s, provided the first set of building blocks for formal modelling of general discrete-event systems. The modern incarnation of the Bedienungsprozess is the "generalized semi-Markov process" (gsmp) viii Preface