Technical Report CS0247

Title: Analysis of Interleaved Storage via a Constant Service Queueing System with "Markov-Chain Driven" Input
Authors: Micha Hofri
Abstract: A popular means of increasing the effective rate of main storage accesses in a large computer is a multiplicity of memory modules accessible in parallel. While such an organization usually achieves a net gain in access rate, it also creates new modes of congestion at the storage controller. This paper analyzes the variables that describe such a congestion queue lengths and delays. We consider a controller that malntains separate register sets to accommodate the request queue of each module. The various processors attached to the storage are assumed to generate, in each memory cycle, a random mumber of access requests. The addresses specified by these requests - reduced to the module index -are further assumed to follow the states of a first order markov chain. The analysis then becomes one of a single server queueing system with constant service time and indexed batch arrival process. We derive results for several descriptors of the congestion and thus of the quality of service offered by such an organization. The aim throughout is to embody the results in a form readily suitable for numerical evaluation.
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