Algorithms for Non‐Product‐Form Networks

Abstract

Solution algorithms for different types of NPFQN (such as networks with priorities, non-exponential service times, blocking, or parallel processing) are presented in this chapter. Although many algorithms are available for solving product-form queueing networks (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. These algorithms and corresponding sections of this chapter are laid out. Networks with non-exponentially distributed service times are treated, while networks with FCFS nodes having different service times for different classes are also treated. Priority queueing networks and networks with simultaneous resource possession are discussed. Network models of programs with internal concurrency, and fork-join systems and parallel processing are detailed. Networks with asymmetric server nodes and blocking networks are discussed.