rep C
i=1 i 
+ H
= 1 - (H
+ H
Therefore, as the replication ratio increases, H
increases, but H
creases because the total number of the cached files in the cluster decreases causing many
disk accesses. If the replication ratio becomes small, many requests should be served as
remote cache read, and thus it reduces the number of disk accesses.
Figure 3.8 shows the average latency as a function of the replication percentage
(R), when the cluster is loaded differently. Figure 3.8 (a), (b), (c) and (d) are the
latency results when k is set to 10, 8, 6 and 4 respectively, where k is the parameter
of the Pareto distribution for the incoming request interval. In Figure 3.8, the Y axis
represents the average latency and the X axis represents the replication ratio in the
cluster. Figure 3.8 (a) and (b) show the latency results when the servers are lightly 
loaded. These figures show that as the replication percentage increases, the latency of the
three models decreases slightly, and then increases. As shown above, as the percentage of
replication increases, the local cache hit ratio increases, but the accumulated cache size
decreases resulting in additional disk accesses. The press via model benefits more than
the adaptive and dcs models do because in the press via model, the remote cache read
latency is much longer than the local cache read latency. Thus, the increase of local
cache hits helps to reduce the average latency time in the press model. However, the
latency of the three models increases slightly as the replication ratio increases due to
the additional disk accesses. But when the cluster is lightly loaded, the performance
degradation due to the disk access is not very significant.



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