[GENERAL] time series data

I have a data stream of a call center application coming in  to postgres in this format :

user_name, user_status, event_time

'user1', 'ready', '2017-01-01 10:00:00'

'user1', 'talking', '2017-01-01 10:02:00'

'user1', 'after_call', '2017-01-01 10:07:00'

'user1', 'paused', '2017-01-01 10:20:00'

...

...

so as you see each new insert of an "event" is in fact the start_time of that event and also the end_time of the previous one so should be used to calculate the duration of this previous one.

What is the best way to get user_status statistics like total duration, frequency, avg ...etc , does any body have an experience with this sort of data streams ?

Thanks in advance.