Assume that Hoodle.com is a leading search engine in the World. At Hoodle.com, time counts. Specifically, Hoodle.com aims to respond to search queries on average within 0.4 seconds. Facing about 7.5 billion queries per month (i.e., 30 days), Hoodle uses 450,000 servers to respond to search queries, spread across 5 data centers. In theory, Hoodle can return one page of 10 results to any search query in 0.1 seconds by simultaneously using a cluster of 500 different servers. But the total response time is in general larger due to queuing and telecommunication delays; in particular, it takes on average 0.05 seconds to send a request from a computer located anywhere in the world to Hoodle, as well as to send the search results from Hoodle to the computer. For simplicity, assume that search queries get randomly assigned to any cluster of servers and that each cluster operates as an independent M/M/1 queuing system.

a) With their current infrastructure, is Hoodle able to respond to search queries within 0.4 seconds on average? Justify your answer numerically.

Hoodle is now considering displaying 30 search results per page instead of 10. (More is better.) Assume that returning the results to search queries would now take 0.2 seconds due to the larger number of results.

b ) What would be the total response time if they display 30 search results per page?

c) How many additional servers would Hoodle need to buy in order to sustain response times shorter than 0.4 seconds when they display 30 search results per page?