Technical Report CS0558

Title: Exact and Asymptotic Analysis of Large Multiple-Bus Multiprocessor Systems
Authors: M. Hofri and Y. Kogan
Abstract: A multiprocessor system with partially-available busses connecting several groups of memory modules, under non-uniform addressing patterns, is modeled as a closed queueing networlc. Exact expressions for the standard performance measure-processing power and memory bandwidth-are presented, using the system partition function. Recursion relations for their computation are developed.

For large systems we aetive simple approximations of the performance measures, in terms of asymptotic estimates of the partitions functions and the steady-state probability distribution functions. A radically new approach is used to estimate the key quantity in the approximation: the relative weights of the system macrostates, expressed in terms of an equivalent queueing network, where each memory group is replaced by a single-server node with variable service rate. The approach is based on an integral representation of these weights in terms of the Cauchy integrals of thefr generating functions, and the estimation of these integrals by the saddle-point method. Numerical examples exhibit the dependence of the quality of the estimates on the system parameters.

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