Question

Caching can be used to reduce the access overhead. Hierarchical caching takes the advantage of the topology of the Internet and deploys the cache at different ISPs. Suppose the hierarchical topology of the Internet is composed of three-level ISPs, national, regional and local. The hit ratios of searching a webpage at different level of the cache of the ISP are as follows:

ISP Level | Hit Ratio
National      0.2
Regional     0.4
Local           0.6

The Internet delays for retrieving the web pages (a round trip time) from the remote trans-continental Internet website is 200msec, the Internet delay for retrieving the web pages from a National ISP’s cache is 10msec, and the Internet delay for other caches are all negligible.

1. What does hit-ratio mean? The bigger the number, the faster to retrieve from cache?
2. What is the probability that a requested website is not found in the hierarchical caching?
3. What is the average delay for retrieving a web page?

Here we assume the web page is very small and the transmission time is negligible.

Answer 1

1. hit ratio = (# requests satisfied from cache)/ (# requests)
   more hit from local cache would result in faster loading

2. probability not found in any of cache = (1-0.6) * (1-0.4) * (1-0.2)
   [not found in local cache * not found in regional cache * not found in national cache

3. average delay= 0.6×0 ms + (1-0.6)x0.4×0 ms + (1-0.6)x(1-0.4)x0.2×10 ms + (1-0.6)x(1-0.4)x(1-0.2)x100 ms