39
On the other hand, the latencies of the remote cache read requests of the three
server models are more distinguishable. The adaptive model has the shortest latency
over the entire workload. The throughput results in Figure 3.7 (b) indicate that the
contribution of the local cache read is almost the same in all the three models.
3.5.2
Replication Percentage
To maximize the local cache hits, the most frequently requested files are replicated
in each Web server [23]. Several studies support that Web requests from a fixed user
community have a skewed distribution according to the Zipf's law [18, 5, 40], which is
given by
p(i) =
C
N
i
- 
)
-1
,
i 
,
where C = (
i=1
where N is the total number of Web content. Although   is close to unity, it
can capture the popularity skewness for each Web content. The bigger   is, the more
popularity skewness Web content has. Thus, the temporal locality of the cache becomes
high. By the Zipf distribution, we can roughly calculate the cache hit ratio. Let the
average file size serviced by the cluster, replication percentage and the cache size of each
node be  a, R and S
cache
, respectively. N
rep
, the number of the replicated files, can be
calculated by R   S
cache
   a, and N
nrep
, the number of the non replicated files in the
cluster, is calculated by S
cache
  a (1-R) N
node
[23]. Let H
remote
, H
local
and H
disk
be the probability that the requests are served as the remote cache read, local cache read,
and the disk access, respectively. Then H
remote
, H
local
and H
disk
are calculated by,
N
N
H
rep+Nnrep C
rep C
remote
= (
i=1
i 
-
i=1 i 
)  
n-1
n












  

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