Count datetime intervals which contains timestamp with DAX - powerbi

Question

I have two tables:
A calendar table with both dates and hours.
And a table that contains incidents, with start time and end time in addition to set of attributes (only one, incident_code, in the example table).
For a specific date range, I want to show how many incidents occurred each hour.
The following measure works, but struggles when the incident table becomes large and there is several slicers
incidentCnt =
CALCULATE(
COUNTROWS(incidents);
FILTER(
incidents;
incidents[start_datetime] < MAX(date_hour[datetime]) &&
incidents[end_datetime] > MAX(date_hour[datetime])
)
)
What would be a more efficient way to calculate this with DAX in Power BI?
EDIT: This expression will work with the data presented above (minor edits to the accepted answer).
Expanded_Incidents =
GENERATE(
incidents;
SELECTCOLUMNS(
GENERATESERIES(
DATE(
YEAR(incidents[start_datetime]);
MONTH(incidents[start_datetime]);
DAY(incidents[start_datetime])
) + TIME(HOUR(incidents[start_datetime]);0;0);
incidents[end_datetime];
TIME(1;0;0)
);
"Expanded_incident_time"; [Value]
)
)

Answer 1

A more effectiv way would be to expand the incidents table so that each incident occurs for each time between the start and end datetime. This you can do with a calculated table like this:
Expanded_Incidents =
GENERATE(
incidents;
SELECTCOLUMNS(
GENERATESERIES(
incidents[start_date];
incidents[end_date];
TIME(h;m;s)
);
"Expanded_incident_time"; [Value]
)
)
Change the TIME(h;m;s) to the time resolution of your choosing.
Then make a relationship between your dateTime dim table and the [Expanded_incident_time] column (this should be a 1:*). Then you only have to make a measure which counts the number of rows in the new table. This will give you the number of active incidents during a specific time and I believe it will be faster than reitterating over the table each time.