Best SQL Challenege: TSQL Query Maximum Concurrent Connections (Participants)

Question

Hi All,
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

Answer 1

Thanks George.
That was fantastic.
But 
But I don't want  the participants to be concurrent in the same call. And should consider the different call.
Lets say Phone Call P1 having 2 participants , obviously they are concurrent according to that call.
Only the Phone calls with more than one participant should match with other phone call with more than one participant.
A Phone call with any number of participants not matching with the time slot of other phone call should be ignored.
There might be a different call say P2, having some 3 participants at the same time or atleast fall in P1's time slot.
So
P1 --> 2 participants ---> start hour 10:00am  ; End Hour 12:00pm
P2 --> 3 participants ---> start hour 10:30am ; End hour 12:30 pm
P3 --> 4 participants ----> start hour 11:00am ; End hour 11:10am
So the concurrency should ignore for P1 and should consider for P2 and P3. From above P2 having 3 participants, P3 having 4 participants. So the common time for all P1,P2,P3 is 11:00am - 11:10am.
Concurrency should be
Starthour    EndHour  ConConnections
10:00am    11:00am   (2+3+4) ---> 2 for P1, 3 for P2, 4 for P3, because at exactly 11:00am there are 4 participants. So the time bucket or the slab for 1 hour will give us that concurrency at that particular slab. Except that independent
participants to that call.
So Result should be
Start Hour     End Hour            Concurrent Connections
10:00am       11:00am                      9
11:00am       12:00pm                      9
12:00pm       01:00pm                      5