TAILIEUCHUNG - Hiệu suất của hệ thống thông tin máy tính P17

THE SPNs we have addressed in the previous finite state space. In this chapter we focus on a special class of stochastic SPNs with unbounded state space, known as one-place unbounded SPNs or infinite-state (abbreviated as iSPNs). In particular, we focus on a class of SPNs of which the underlying CTMC has a QBD structure, for which efficient solution methods exist (see Chapter 8). The properties an SPN has to fulfill to belong to this class can be verified at the SPN level, without having to construct the reachability graph | 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 17 Infinite-state SPNs THE SPNs we have addressed in the previous chapters all have a possibly large but finite state space. In this chapter we focus on a special class of stochastic Petri nets with unbounded state space known as one-place unbounded SPNs or infinite-state SPNs abbreviated as iSPNs . In particular we focus on a class of SPNs of which the underlying CTMC has a QBD structure for which efficient solution methods exist see Chapter 8 . The properties an SPN has to fulfill to belong to this class can be verified at the SPN level without having to construct the reachability graph. The main advantage of iSPNs is that efficient matrix-geometric techniques for the solution are combined with the powerful description facilities of general SPNs. This not only allows non-specialists to use these methods it also avoids the state-space explosion problem that is so common in traditional SPN analysis based on the complete finite underlying Markov chain. We motivate the use of iSPNs in Section and characterise the class of iSPNs by defining a number of constraints that have to be fulfilled in Section . We then discuss in Section how matrix-geometric methods can also be applied in this case. In Section we comment on algorithms to detect the special iSPN structure and to compute reward-based measures efficiently. We finally discuss a number of application examples in Section . Introduction The general approach in solving SPNs is to translate them to an underlying finite CTMC which can be solved numerically. However a problem that often arises when following this approach is the rapid growth of the state space. Various solutions have been proposed for this problem . the use of state space truncation techniques 121 or lumping techniques 384 17 .

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