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Queueing mạng lưới và chuỗi Markov P10

Algorithms for Non-Product-Form Networks Although many algorithms are available for solving product-form queueing networks (see Chapters 8 and 9), most practical queueing problems lead to non-product-form networks. If the network is Markovian (or can be Markovized), automated generation and solution of the underlying CTMC via stochastic Petri nets (SPNs) is an option provided the number of states is fewer than a million. Instead of the costly alternative of a discrete-event simulation, approximate solution may be considered. Many approximation methods for non-product-form networks are discussed in this chapter. . | Queueing Networks and Markov Chains Gunter Botch Stefan Greiner Hermann de Meer Kishor S. Trivedi Copyright 1998 John Wiley Sons Inc. Print ISBN 0-471-19366-6 Online ISBN 0-471-20058-1 Ni ra ill ill 6 Algorithms for Non-Produ ct-Fo rm Networks Although many algorithms are available for solving product-form queueing networks see Chapters 8 and 9 most practical queueing problems lead to non-product-form networks. If the network is Markovian or can be Markovi-zed automated generation and solution of the underlying CTMC via stochastic Petri nets SPNs is an option provided the number of states is fewer than a million. Instead of the costly alternative of a discrete-event simulation approximate solution may be considered. Many approximation methods for non-pro duct-form networks are discussed in this chapter. These algorithms and corresponding sections of this chapter are laid out as shown in the flowchart of Fig. 10.1. Networks with non-exponentially distributed service times are treated in the next section while networks with FCFS nodes having different service times for different classes are treated in Section 10.2. Priority queueing networks and networks with simultaneous resource possession are treated in Sections 10.3 and 10.4 respectively. Network models of programs with internal concurrency are treated in Section 10.5. Fork-join systems and parallel processing are treated in Section 10.6. Networks with asymmetric server nodes and blocking networks are discussed in Section 10.7 and Section 10.8 respectively. 421 422 ALGORITHMS FOR NON-PRODUCT-FORM NETWORKS NPFQN Nonexponent iaily distributed Service Times Diffusion 10.1.1 MEM 10.1.2 Pujolle Whitt Chylla Gelenbe Kühn y Nonexponeut iaily distributed Service Time Closing method 10.1.5 Priorities PRIOMVA 10.3.1 Nonexponentially distributed Service Times Diffusion 10.1.1 MEM 10.1.2 Marie SUM 10.1.1 BOTT Different Service Times at FCFS Nodes Priorities PRIOMVA 10.3.1 Asymmetric Nodes Asymmetric _ . Jackson 10. .2 EMVA .