We investigate delaying the update of summaries until the percentage of cached documents that are ``new'' (that is, not reflected in the summaries) reaches a threshold. The threshold criteria is chosen because the number of false misses (and hence the degradation in total hit ratio) tends to be proportional to the number of documents that are not reflected in the summary. An alternative is to update summaries upon regular time intervals. The false miss ratio under this approach can be derived through converting the intervals to thresholds. That is, based on request rate and typical cache miss ratio, one can calculate how many new documents enter the cache during each time interval and their percentage in the cached documents.
Using the traces, we simulate the total cache hit ratio when the threshold is 0.1%, 1%, 2%, 5% and 10% of the cached documents. For the moment we ignore the issue of summary representations and assume that the summary is a copy of the cache directory (i.e. the list of document URLs). The results are shown in Figure 2. The top line in the figure is the hit ratio when no update delay is introduced. The second line shows the hit ratio as the update delay increases. The difference between the two lines is the false miss ratio. The bottom two curves show the ratio of remote stale hits and the ratio of false hits (the delay does introduce some false hits because documents deleted from the cache may still be present in the summary).
The results show that, except for the NLANR trace data, the degradation in total cache hit ratio grows almost linearly with the update threshold. At the threshold of 1%, the relative reductions in hit ratio are 0.2% (UCB), 0.1% (UPisa), 0.3% (Questnet), and 1.7% (DEC). The remote stale hit ratio is hardly affected by the update delay. The false hit ratio is very small since the summary is an exact copy of the cache directory, though it does increase linearly with the threshold.
For the NLANR trace, it appears that some clients are simultaneously sending two requests for the exact same document to proxy ``bo'' and another proxy in the NLANR collection. If we only simulate the other three proxies in NLANR, the results are similar to those of other traces. With ``bo'' included, we also simulated the delay being 2 and 10 user requests, and the hit ratio drops from 30.7% to 26.1% and 20.2%, respectively. The hit ratio at the threshold of 0.1%, which roughly corresponds to 200 user requests, is 18.4%. Thus, we believe that the sharp drop in hit ratio is due to the anomaly in the NLANR trace. Unfortunately, we cannot determine the offending clients because client IDs are not consistent across NLANR traces .
The results demonstrate that in practice, a summary update delay threshold of 1% to 10% results in a tolerable degradation of the cache hit ratios. For the five traces, the threshold values translate into roughly 300 to 3000 user requests between updates, and on average, an update frequency of roughly every 5 minutes to an hour. Thus, the bandwidth consumption of these updates can be very low.