SQL Server 2017

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CREATE TABLE dbo.[UserSession]
(
     [UserName] varchar(50) NOT NULL,
     [LoginDateTime] datetime NOT NULL,
     [LogoutDateTime] datetime NULL
);

INSERT dbo.[UserSession]
    (UserName, LoginDateTime, LogoutDateTime)
VALUES
    ('Jsmith' ,'2018-04-01T12:01:00.000','2018-04-01T12:23:00.000'),
    ('Adownon','2018-04-02T11:11:00.000','2018-04-02T15:31:00.000'),
    ('Jsmith' ,'2018-04-01T14:34:00.000','2018-04-01T18:12:01.000'),
    ('Adownon','2018-04-30T15:43:01.000','2018-04-30T21:32:50.000'),
    ('MHoles' ,'2018-04-30T16:20:01.000','2018-04-30T20:01:15.000'),
    ('MHoles' ,'2018-04-01T10:00:01.000','2018-04-01T11:10:00.000'),
    ('Jsmith' ,'2018-04-30T20:00:01.000','2018-04-30T20:22:20.000');
7 rows affected

CREATE FUNCTION dbo.MaxConcurrentUserSessions
(
    @WeekStart datetime
)
RETURNS table
WITH SCHEMABINDING AS
RETURN
    WITH
        WeekSessions AS
        (
            SELECT
                US.UserName,
                US.LoginDateTime,
                US.LogoutDateTime 
            FROM dbo.UserSession AS US
            WHERE
                US.LoginDateTime >= @WeekStart
                AND US.LogoutDateTime < DATEADD(DAY, 7, @WeekStart)
        ),
        C1 AS
        (
            SELECT
                ts = WS.LoginDateTime,
                event_type = +1,
                start_ordinal = ROW_NUMBER() OVER (
                    ORDER BY WS.LoginDateTime)
            FROM WeekSessions AS WS
            UNION ALL
            SELECT
                ts = WS.LogoutDateTime,
                event_type = -1,
                start_ordinal = CONVERT(bigint, NULL)
            FROM WeekSessions AS WS
        ),
        C2 AS
        (
            SELECT 
                C1.ts,
                C1.event_type,
                C1.start_ordinal,
                start_or_end_ordinal =
                    ROW_NUMBER() OVER (
                        ORDER BY C1.ts, C1.event_type)
          FROM C1
        )
    SELECT
        mx = MAX(2 * start_ordinal - start_or_end_ordinal)
    FROM C2
    WHERE 
        C2.event_type = 1;
-- The month to report on
DECLARE @MonthStart datetime = CONVERT(datetime, '20180401');

-- Holds the start of each week in the given month
DECLARE @Weeks AS table (WeekStart datetime PRIMARY KEY);

-- Find the week start dates
INSERT @Weeks (WeekStart)
SELECT CA.WeekStart
FROM master.dbo.spt_values AS SV
CROSS APPLY
(
    VALUES (DATEADD(DAY, 7 * SV.number, @MonthStart))
) AS CA (WeekStart)
WHERE SV.[type] = 'P'
AND SV.number BETWEEN 0 AND 5
AND CA.WeekStart < DATEADD(MONTH, 1, @MonthStart);

-- Find the concurrent sessions for all weeks
SELECT 
    W.WeekStart,
    mx = ISNULL(MCUS.mx, 0)
FROM @Weeks AS W
CROSS APPLY dbo.MaxConcurrentUserSessions(W.WeekStart) AS MCUS
ORDER BY W.WeekStart;


WeekStart
mx


01/04/2018 00:00:00
1

08/04/2018 00:00:00
0

15/04/2018 00:00:00
0

22/04/2018 00:00:00
0

29/04/2018 00:00:00
3
WeekStart	mx
01/04/2018 00:00:00	1
08/04/2018 00:00:00	0
15/04/2018 00:00:00	0
22/04/2018 00:00:00	0
29/04/2018 00:00:00	3