Kusto number of overlapping intervals in a time range - azure

Question

I'm trying to write a Kusto query that needs to count how many intervals overlap for a certain date range. This is how my table looks like:
userID | interval1 | interval2
24 | 21.1.2012 10:40 | 21.1.2012 11:00
25 | 21.1.2012 9:55 | 21.1.2012 10:50
I would like to to consider the time range given by [min(interval1), max(interval2)] with 1s step and for each instance of this interval I would like to know how many intervals from the previous table overlap. For example, for 21.1.2012 10:00 there is only one interval but for 10:45 there are two intervals overlapping.
Thank you

Answer 1

Every interval1 indicates additional user's session start (+1).
Every interval2 indicates additional user's session end (-1).
The accumulated sum indicates the number of active sessions.
Solution 1 (Rendering level)
with (accumulate=True)
let t = (datatable (userID:int,interval1:datetime,interval2:datetime)
[
24 ,datetime(2012-01-21 10:40) ,datetime(2012-01-21 11:00)
,25 ,datetime(2012-01-21 09:55) ,datetime(2012-01-21 10:50)
]);
let from_dttm = datetime(2012-01-21 09:30);
let to_dttm = datetime(2012-01-21 11:30);
let sessions_starts = (t | project delta = 1, dttm = interval1);
let sessions_ends = (t | project delta = -1, dttm = interval2);
union sessions_starts, sessions_ends
| make-series delta = sum(delta) on dttm from from_dttm to to_dttm step 1s
| render timechart with (accumulate=True)
Fiddle
Solution 2 (Data level)
mv-apply + row_cumsum
let t = (datatable (userID:int,interval1:datetime,interval2:datetime)
[
24 ,datetime(2012-01-21 10:40) ,datetime(2012-01-21 11:00)
,25 ,datetime(2012-01-21 09:55) ,datetime(2012-01-21 10:50)
]);
let from_dttm = datetime(2012-01-21 09:30);
let to_dttm = datetime(2012-01-21 11:30);
let sessions_starts = (t | project delta = 1, dttm = interval1);
let sessions_ends = (t | project delta = -1, dttm = interval2);
union sessions_starts, sessions_ends
| make-series delta = sum(delta) on dttm from from_dttm to to_dttm step 1s
| mv-apply delta to typeof(long), dttm to typeof(datetime) on (project active_users = row_cumsum(delta), dttm)
| render timechart with (xcolumn=dttm, ycolumns=active_users)
Fiddle

Answer 2

Take a look at this sample from the Kusto docs:
https://learn.microsoft.com/en-us/azure/data-explorer/kusto/query/samples?pivots=azuredataexplorer#chart-concurrent-sessions-over-time
X
| mv-expand samples = range(bin(interval1, 1m), interval2, 1m)
| summarize count_userID = count() by bin(todatetime(samples), 1m)