Python time series: count simultaneous occurrences during 30 min time windows

My dataframe df stores data of times during which machines were working, for example

start_time                  end_time                  machine
2019-01-01 00:00:03         2019-01-01 17:10:03       A
2019-01-01 00:31:03         2019-01-01 18:11:03       B
2019-01-01 12:00:00         2019-01-01 13:08:03       C

I want to see how many machines are working simultaneously at any 30 min time window, that is

time_window_start       machine_count
2019-01-01 00:00:00     1
2019-01-01 00:30:00     2
        ...             ...
2019-01-01 12:00:00     3
        ...             ...
2019-01-01 13:30:00     2           

I started by creating a data frame with time references:

ref_date_range = pd.date_range(start='31/1/2018 00:00:00', end='1/1/2020 23:30:00', freq='30Min')
ref_df = pd.DataFrame(np.random.randint(1, 20, (ref_date_range.shape[0], 1)))
ref_df.index = ref_date_range  

But how do I match both data frames including a distinct count of the machines?