You are in charge of a datacenter that handles web requests. Each incoming request first goes to a processor that assigns it to one of N web servers operating in parallel. This process takes 100 μs (10^-6 seconds) and cannot be parallelized. Each web server takes 100 ms to handle a request assigned to it. With N=1, the total time per request is 100.1 ms, and the server can thus handle 1/(100.1 ms) ~ 35,964 requests per hour. Your task is to increase throughput to 7.2 million requests per hour.

Given that all server are working in parallel and each server takes 100 μs for each request to process and assign it to a server. Total time taken during assigning process will be

[tex]1 process=10^{-6}\\ 7.2 mil process=7,200,000 * 10^{-6}\\[/tex]

Time taken for 7.2 mil request to process =7.2 sec

Now for our server to handle request, time taken for server to handle a request is 100.1ms and server can handle 35964 request per hour approximately.

[tex]1 server= 35964 request/hour[/tex]

Number of server per request

1 server handles35964 request / hour.From this we can find time taken for 7.2mil request/hour

For 7.2mil request

[tex]X=7200000* number of server per request per hour[/tex][tex]X=200.2 ~ 200 servers[/tex]