Myself and my friend are doing a research based on twitter. We need to
analyse each and every tweet real time. Can you guide how to approach
this.

There could be 2 ways of doing this (without Firehose):

1) Get Twitter Public timeline repeatedly.

Thankfully Twitter's caching has not been problem to me, they seem to
fetch me new data every request. But there are a lot of limitation for
this:

According to TweeSpeed.com:
 - Rate of New tweets in the Twitter Server is right now (Wed Jul 17
11:47:02 - GMT) at 9233 tweets/minute.
 - Ranges between 7K to 20K on an average Weekday.
 - On June 26 (MJ's death) - reached 25K tweets/minute.

Let us now consider the limitation of API requests per hour.
 - Currently @ 20K per hour.
 - 1 Req = 20 Tweets
 - Need 1K Req per minute = 60K req per hour.

To Use 1K Requests per minute, we should be using around 17 requests
per second. But my server is able to process only 28-33 requests/
minute.

Is this the right way to proceed, or am I fundamentally wrong on the
approach.

2) Get follower network - user profiles and get their statuses.
Frequency of request their new status updates could be set against
their general update frequency. But this is Google-like old way of
indexing things, which does not quite stand today in the REAL TIME
twitter.

I do know Firehose is an option, but that would again be something
like Approach 1. right?

Please guide me how to proceed.

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