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Ring Behavior

A pipeline can be closed by connecting the inputs to the outputs, as shown in Figure 12.1 to form a pipeline ring. The behavior of a ring is determined by the closed nature of its structure. There have been previous characterizations of ring behavior [17,61]. This characterization does not differ from the literature in substance but differs in point of view which allows ring behavior to be much more intuitively and easily understood.


The throughput performance of the ring is the number of wavefronts flowing through any cycle per unit time. A ring pipeline can exhibit four distinct throughput behaviors distinguished by how long it takes a wavefront or a bubble to flow around the ring and by how long it takes all the wavefronts or bubbles in the ring to flow through the cycle in the ring with the slowest period, which will be called the reference cycle. If all cycles in the ring have the same period, then any cycle can be taken as the reference cycle. The throughput of a ring can be wavefront limited, bubble limited, delay limited, or perfectly balanced.


Figure 12.1 Four cycle rings.

Figure 12.2 Cycle path.

A ring has a population of ...

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