Pick some point in the day that is your "yardstick" time, when you want to make your measurements. Good choices are 00:00 (midnight), 23:59 (end of the day), and 12:00 (noon), but you can use whatever time is the most meaningful to you. Populate a working table with datetime values for all of the days you want to measure and the yardstick time.
For each row in the yardstick table, count the number of rows in the service table that straddle the yardstick row... Where the service start datetime is before the yardstick datetime, and the service end datetime is after the yardstick datetime. Use the yardstick table to determine the bounds of your query... In other words, when the query starts and when it ends.
I could write some SQL to do this, but it would take too long to build an Access MDB unless I'm really unclear.