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Figure 6.12
Hellerman's model. In this model, B is the
average length of conflict-free sequences of
addresses. |
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there are m memory modules. Further, we assume that there is no bus contention. The Strecker model assumes that the memory request pattern for the processors is uniform and the probability of any one request to a particular memory module is simply 1/m. The key modeling assumption is that the state of the memory system at the beginning of the cycle is not dependent upon any previous action on the part of the memoryhence, not dependent upon contention in the past (i.e., Markovian). Unserved requests are discarded at the end of the memory cycle. |
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1. A processor issues a request as soon as its previous request has been satisfied. |
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2. The memory request pattern from each processor is assumed to be uniformly distributed; i.e., the probability of any one request being made to a particular memory module is 1/m. |
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Analytical approximation: |
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The state of the memory system at the beginning of each memory cycle (i.e., which processors are awaiting service at which modules) is ignored by assuming that all unserviced requests are discarded at the end of each memory cycle and that the corresponding processors randomly issue new requests. |
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Let the average number of memory requests serviced per memory cycle be represented by B(m,n). This is also equal to the average number of memory modules busy during each memory cycle. Looking at events from any given module's point of view during each memory cycle, we have: |
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Prob [a given processor does not reference the module] = (1 - 1/m) |
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