The previous chapter it has become clear that the evaluation of large closed queueing networks can be quite unattractive from a computational point of view; this was also the reason for addressing approximation schemes and bounding methods. In this chapter we go a different way to attack large queueing network models: hierarchical modelling and evaluation. We address a modelling and evaluation approach where large submodels are solved in isolation and where the results of such an isolated evaluation are used in other models. To be able to do so, however, we need load-dependent queueing stations, that is, queueing nodes in. | 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 12 Hierarchical queueing networks IN the previous chapter it has become clear that the evaluation of large closed queueing networks can be quite unattractive from a computational point of view this was also the reason for addressing approximation schemes and bounding methods. In this chapter we go a different way to attack large queueing network models hierarchical modelling and evaluation. We address a modelling and evaluation approach where large submodels are solved in isolation and where the results of such an isolated evaluation are used in other models. To be able to do so however we need load-dependent queueing stations that is queueing nodes in which the service rate depends on the number of customers present. In Section we introduce load-dependent servers and show the corresponding productform results for closed queueing networks including such servers. We then continue with the extension of the convolution algorithm to include load-dependent service stations in Section and discuss two important special cases namely infinite-server systems and multi-server systems in Section . In Section we extend the mean-value analysis method to the load-dependent case. We then outline an exact hierarchical decomposition approach using load-dependent service centers in Section . The hierarchical decomposition method can also be used in an approximate fashion an example of that is discussed in Section where we study memory management issues in time-sharing computer systems. Load-dependent servers Up till now we have assumed that the service rate at the nodes in a queueing network is constant and independent of the state of the queue or the state of the queueing network. It is however also possible to deal with load-dependent service rates or .
