The limits of incremental multiprocessors

The author explores the yields and limits of a large-scale multiprocessor architecture. He shows four results. First, that there is a single resource in every multiprocessor system that limits incremental expansion. Once this resource approaches full utilization, adding processors is useless and possibly detrimental. With uniform resource access by statistically identical processors, the maximum number of effective processors is 1/X, where X is the fraction of its own productive time that one processor uses this resource. Secondly, he finds that this limiting resource can be discovered by measuring the resource usage behavior of one processor. Reducing contention for this resource will extend the limits of an architecture. Third, the author shows that approaching the 1/X upper limit, the incremental yield curve is spectacularly near linear, implying that nearly one full effective processor from each additional processor should be expected. Last, he shows that previously published formulas for incremental yield are too pessimistic and should not be applied to a general purpose multiple-instruction-multiple-data-stream (MIMD) architecture. It is shown how pessimistic these views are and why the formulas do not apply. It is demonstrated that a multiprocessor system can be extended to its limit with minimal degradation, generally with 90% or better effective yield for small numbers of shared resources