I have a pandas DataFrame that looks like this:

```
             start_time             end_time    user
0  2016-12-17 03:10:07   2016-12-17 03:18:10  andrew
1  2016-12-17 03:11:07   2016-12-17 03:15:07   eddie
2  2016-12-17 03:12:08   2016-12-17 03:19:08  andrew  
3  2016-12-17 03:13:08   2016-12-17 03:14:06   eddie
...

```

Each row represents a job that was submitted to a compute cluster. `start_time` is when to scheduled job started to run, and `end_time` is when it completed.

How can I create a new DataFrame indexed by time, which describes how many jobs each user had running at a given moment?