We have carried out simulations for ten consecutive days. The curves provided in Figures 1, 2 as well as in Figures 3, 4 are a snapshot of one day. The variation in time of the efficiency of the caching (removal) policies is illustrated in Figure 5. One can see that the qualitative comparison among the policies holds for all the days, except for day 7, which corresponds to a Monday, on the INRIA Web server. The ``bad'' performance of static caching can be explained by the fact that the estimates of the request rates used for the cache on Monday were computed based on the few requests of the previous Sunday where the server was very lightly loaded.
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Since the request rates used in the implementation of the static policy are estimated from the statistics of previous requests, one expects that the performance of the static policy will vary over time, as we have already seen in Figure 5. We thus conducted more simulation to see how it varies over time for different sizes of the cache. The results are reported in Figures 6 and 7, which seem to indicate that the forms of the curves are insensitive to the sizes of the cache.
One can see, without surprise, that static policy is very stable for the W3C server. For the INRIA server, however, it varies slightly. One reason for this is the small amount of data (i.e. number of request) used in the estimation. Indeed, in this case, the total number of requested documents is larger whereas the total number of requests is much smaller.
The observation that hit rate varies from day to day
motivates our investigation to the behavior
of the static policy on the INRIA server when we increase the
number of days taken into account for the estimation
of the request rates of the documents.
The results are illustrated in Figure 8.
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Last, we investigate the impact of the stationarity assumption we made on the data accesses while presenting theoretical justification of the static caching policy. Indeed, the hypothesis of stationarity is not always true, in which case the approximate solution, which is based on past access frequency, may significantly loose its efficiency in comparison with the ideal optimal solution. To examine this effect, we compare the approximate solution with the upper bound Sr which is implemented such that it uses the access frequency computed a posteriori.
With the W3C server traces, the approximate policy is still very close to the upper bound, so to the optimal solution, see Figure 9. For the INRIA server's traces, it is no longer the case, especially with large caches, as illustrated in Figure 10.
