T-SQL (SS2K8) :: Query Maximum Concurrent Connections (Participants)

I have a table called dbo.PhoneCalls with below columns

PhoneID |PhoneNumber| Callstarttime| CallEndtime|
1 |111-111-1111|2013-04-01 05:13:03.000|2013-04-01 05:13:03.000
1 |222-222-2222|2013-04-01 05:15:12.000|2013-04-01 05:16:52.000
2 |333-333-3333|2013-04-01 05:17:29.000|2013-04-01 05:24:08.000
2 |444-444-4444|2013-04-01 05:21:50.000|2013-04-01 05:22:31.000
2 |555-555-5555|2013-04-01 05:22:41.000|2013-04-01 05:23:11.000
2 |666-666-6666|2013-04-01 05:23:20.000|2013-04-01 05:23:46.000
..........

1. PhoneID is nothing but the participant in the call. PhoneID = 1 is twice from above. Which means 2 particpants (Same call )with 2 numbers with their callstarttime and callendtime. Similarly for PhoneID =2, there are 4 participants. And the list goes on for a day and then for a month.

2. For example a phone call P1 with 2 participants is going on for a particular day. We should not consider the same phone call having 2 participants involved. So that the concurrency would be 2. We have to ignore that here.

3. Only to be considered is other Phone calls for that day. Lets say P1 having call with 2 participants, P2 having some 4 participants which fall in the time period of P1. Then we should consider P1 and P2 the common period

4. In order to find number of concurrent calls happened for a day basing on callstarttime and callendtime. What would be the query?

5. Should consider the Timeperiod or the bucket with 1 hour as the period.

6. A Phone Call P1, Phone Call P2, should have matching (common) time ( keeping all the scenarios) is required for this query.

Result for Concurrent calls for a day should be like below. Should get all the concurrent connections happened for a particular day.

Date|TimePeriod/Bucket(hr part)|Concurrentconnections|
Jan-01-2015|01 to 02|3
Jan-01-2015|11 to 12|2
Jan-02-2015|04 to 05|5
Jan-02-2015|12 to 13|13
........

ii) So once the above is achieved.

Have to find the Maximum concurrent connections for day from the above.

For below Maximum Concurrent connections are '3'
Date|TimePeriod/Bucket(hr part)|Concurrentconnections|
Jan-01-2015|01 to 02|3
Jan-01-2015|11 to 12|2

Hence the Result for Maximum Concurrent Connections would be

Date|TimePeriod/Bucket(hr part)|MaxConcurrentconnections|
Jan-01-2015|01 to 02|3
Jan-02-2015|12 to 13|13
.............