QUESTION 2

Consider the technique of trading-off completeness for latency to reduce the latency response in datacenter networks.

Part I: Assuming that the top ranked document lies in one of 1000 servers, calculate the utility loss of getting response from the fastest 990 servers.

Part II: Assuming that the top ranked document lies in type A servers (300 of them) with probability 0.6 and in type B servers with probability 0.4 (700 of them), calculate the utility loss of getting response from the fastest 295 type A servers and the fastest 690 type B servers.

Part III: Repeat Part II by assuming that the final response is returned when we get a response from the fastest 990 servers. Assume server response times are identically distributed for all the servers.