Chapter 10 we addressed queueing networks with, in principle, an unbounded number of customers. In this chapter we will focus on the class of queueing networks with a fixed number of customers. The simplest case of this class is represented by the so-called GordonNewell queueing networks; they are presented in Section . As we will see, although the state space of the underlying Markov chain is finite, the solution of the steady-state probabilities is not at all straightforward (in comparison to Jackson networks). A recursive scheme to calculate the steady-state probabilities in Gordon-Newell queueing networks is presented in Section. | 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 11 Closed queueing networks IN Chapter 10 we addressed queueing networks with in principle an unbounded number of customers. In this chapter we will focus on the class of queueing networks with a fixed number of customers. The simplest case of this class is represented by the so-called Gordon-Newell queueing networks they are presented in Section . As we will see although the state space of the underlying Markov chain is finite the solution of the steady-state probabilities is not at all straightforward in comparison to Jackson networks . A recursive scheme to calculate the steady-state probabilities in Gordon-Newell queueing networks is presented in Section . In order to ease the computation of average performance measures we discuss the mean value analysis MVA approach to evaluate GNQNs in Section . Since this approach still is computationally quite expensive for larger QNs or QNs with many customers we present MVA-based bounding techniques for such queueing networks in Section . We then discuss an approximate iterative technique to evaluate GNQNs in Section . We conclude the chapter with an application study in Section . Gordon-Newell queueing networks Gordon-Newell QNs GNQNs named after their inventors are representatives for a class of closed Markovian QNs all services have negative exponential service times . Again we deal with M M M 1 queues which are connected to each other according to the earlier encountered routing probabilities Tij. The average service time at queue i equals 1 ij. Let the total and fixed number of customers in such a QN be denoted K so that we deal with a CTMC on state space T M K n G JNm m nM K . 230 11 Closed queueing networks To stress the dependence of the performance measures on both the number of queues and the .
