IN this chapter the basic theory theory SPNs grew out of the general 1960s through of (non-timed) of stochastic nets developed in these models. the early the introduction for an overview. networks, papers in the field of stochastic to the end of the chapter SPNs are, like queueing easy specification the involved numerically, butions to an underlying In this chapter computed. performance CTMCs Note that modelling. Notation | Performance of Computer Communication Systems A Model-Based Approach. Boudewijn R. Haverkort Copyright 1998 John Wiley Sons Ltd ISBNs 0-471-97228-2 Hardback 0-470-84192-3 Electronic Part IV Stochastic Petri net models Performance of Computer Communication Systems A Model-Based Approach. Boudewijn R. Haverkort Copyright 1998 John Wiley Sons Ltd ISBNs 0-471-97228-2 Hardback 0-470-84192-3 Electronic Chapter 14 Stochastic Petri nets IN this chapter we present the basic theory concerning stochastic Petri nets SPNs . SPNs grew out of the general theory of non-timed Petri nets developed by Petri in the early 1960s through the introduction of stochastic timing in these models. The first papers in the field of stochastic Petri nets appeared in the late 1970s and early 1980s refer to the end of the chapter for an overview. SPNs are like queueing networks a graph-based modelling formalism allowing for the easy specification of finite-state machine models. Under suitable assumptions regarding the involved stochastic timing a large class of SPN models can be mapped automatically to an underlying CTMC with finite state space. Such a CTMC can then be analysed numerically thus yielding information about the SPN. In this chapter we present a fairly general class of SPNs in which the involved distributions are all of negative exponential type so that an underlying CTMC can be readily computed. Notation and terminology is introduced in Section . Structural properties of these Petri net models are discussed in Section . We present important SPN-related performance measures in Section . The actual mapping of SPNs to the underlying CTMCs is then discussed in Section . Note that the discussion of the numerical solution of the CTMCs generated from the SPNs is postponed until Chapter 15. Chapter 16 is devoted to various applications of SPN modelling. Definition In this section we introduce a class of SPN models. In Section we present the static structure of SPNs
