In this paper we describe two types of complex server aggregations which can be used to model collections of components in certain types of parallel computer systems and give a case study showing how the aggregations may be applied in practice. Analytical models of such systems are becoming increasingly important as a means of guiding the often complex design processes, particularly since recent developments in VLSI technology now make it possible to fabricate many paper-designs hitherto impractical for reasons of cost. We argue that aggregations of the type described are essential in the modelling of parallel systems; using the proposed techniques, large numbers of components can be modelled as queue-length-dependent servers within a queueing network in which the number of servers is the same as the number of distinct types of processing element in the system being modelled. Because the number of severs in the model is fixed i.e. is independent of the number of processors, very large multiprocessor systems can be modelled efficiently with no explosion in the size of the state space.
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