SYMPOSIUM MINISYMPOSIA

ABSTRACT

Multiple bus systems represent a very attractive alternative in multiprocessor interconnection network implementation. In a full connection multiple bus system all the processors and memory modules are connected to all the busses. In such systems the cast complexity is clearly O(P+M)B), where P is the number of processors, M is the number of memory modules and B is the number of busses. This implies that cost could be prohibitively large even for modest size systems. Considerable research effort has focused on reducing connectivity cost a multiple bus systems. Some proposals omitted some connections to memory modules or to processors (partial connection systems) while others focused on using certain connection patterns that are suitable for certain application domains. There has been no effort to formalize the process of connection reduction or to base it on some theoretical foundation.

In the paper we propose the first systematic and formal methodology for connectivity reduction in MIMD multiple bus systems. Our work is based on the important observation that some connectivity is only required for some highly improbable request patterns. The hypothesis here is that significant reduction in connectivity is achievable by eliminating such connectivity with almost no degradation in performance. We assume a very general request model that encompasses most widely assumed models including unifor, hot spot and locality-based model sand combinations thereof. We consider a generalized base model for an MIMD multiple bus system and apply a probabilistic technique to reduce connectivity such that only some highly improbable request patterns will be allocated fewer buses than in a base model system. We also propose an architecture which encompasses this base model system and can be used to directly model conventional multiple bus systems including full connections and partial connection systems. The proposed probabilistic technique is applied to the based model to arrive at anew architecture which we call the probabilistically reduced connection multiple bus system (PRMB). We show through analysis that a properly designed PRMB can offer performance that is very close to that of a corresponding base model system while significantly reducing connectivity cost. Our numerical results fully support the hypothesis.

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